Part Number: MDNA*R3*Z*Z*Z*SM-NAS120-WBK Copyright 2008 MSC.Software Corporation August 2008 Linear Static, Normal Modes, and Buckling Analysis Using MD Nastran R3 and Patran 2008r1 NAS120 Course Notes MSC.Software Corporation Europe MSC.Software GmbH Am Moosfeld 13 81829 Munich, Germany Telephone: (49) (89) 43 19 87 0 Fax: (49) (89) 43 61 71 6 Corporate MSC.Software Corporation 2 MacArthur Place Santa Ana, CA 92707 USA Telephone: (800) 345-2078 Fax: (714) 784-4056 Asia Pacific MSC.Software Japan Ltd. Shinjuku First West 8F 23-7 Nishi Shinjuku 1-Chome, Shinjuku-Ku Tokyo 160-0023, JAPAN Telephone: (81) (3)-6911-1200 Fax: (81) (3)-6911-1201
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Part Number: MDNA*R3*Z*Z*Z*SM-NAS120-WBK Copyright 2008 MSC.Software CorporationAugust 2008Linear Static, Normal Modes, and BucklingAnalysis Using MD Nastran R3 and Patran2008r1NAS120 Course NotesMSC.Software CorporationEuropeMSC.Software GmbHAm Moosfeld 1381829 Munich, GermanyTelephone: (49) (89) 43 19 87 0Fax: (49) (89) 43 61 71 6CorporateMSC.Software Corporation2 MacArthur PlaceSanta Ana, CA 92707 USATelephone: (800) 345-2078Fax: (714) 784-4056Asia PacificMSC.Software Japan Ltd.Shinjuku First West 8F23-7 Nishi Shinjuku1-Chome, Shinjuku-KuTokyo 160-0023, JAPANTelephone: (81) (3)-6911-1200Fax: (81) (3)-6911-12012Copyright 2008 MSC.Software CorporationLegal InformationMSC.Software Corporation reserves the right to make changes in specifications and other information contained in thisdocument without prior notice. The concepts, methods, and examples presented in this text are for illustrative andeducational purposes only, and are not intended to be exhaustive or to apply to any particular engineering problem ordesign. MSC.Software Corporation assumes no liability or responsibility to any person or company for direct or indirectdamages resulting from the use of any information contained herein.Copyright 2008 MSC.Software Corporation. All Rights Reserved. This notice shall be marked on any reproduction ofthis documentation, in whole or in part. Any reproduction or distribution of this document, in whole or in part, without theprior written consent of MSC.Software Corporation is prohibited.The MSC.Software corporate logo, Adams, Dytran, Easy5, Fatigue, Laminate Modeler, Marc, Mentat, MD Nastran, Patran,MSC, MSC Nastran, Mvision, Patran, SimDesigner, SimEnterprise, SimManager, SimXpert and Sofy are trademarks orregistered trademarks of the MSC.Software Corporation in the United States and/or other countries. NASTRAN is aregistered trademark of NASA. All other trademarks belong to their respective owners.3Copyright 2008 MSC.Software CorporationCONTENTS4-57 Workshop 4 Stadium Truss3-40 Workshop 3 Editing a Nastran Input File2-50 Workshop 2 Simply Supported Beam1-37 Workshop 1 Landing Gear Strut Analysis4-48 Post Processing CROD Results4-19 The CROD Element4-5 MD Nastran Element Library3-22 The Nastran Input File3-19 Patran-Nastran Workflow and Files3-3 Patran GUI2-48 FEM References2-22 Key Concepts in FEM2-7 What is the Finite Element Method?2-3 Engineering Methods1-32 Company Information1-12 Case Study: Landing Gear Strut1-9 What is Patran?1-4 What is MD Nastran?1-3 Course ObjectivesCase Study: Stadium Arched Roof Truss 4.0Basics of MD Nastran and Patran 3.0Introduction to the Finite Element Method 2.0Overview 1.0Page Section4Copyright 2008 MSC.Software CorporationCONTENTS5-109 Workshop 8 A-C Tension Coupon7-105 Element Distortion6-82 Workshop 7 Tapered Plate5-153 Workshop 6 Bridge Truss5-59 Workshop 5 Coordinate Systems7-52 Loads7-45 Single Point Constraints7-29 2-D Elements7-19 Meshing6-76 Post Processing CBEAM Results6-50 Fields6-31 The CBEAM Element6-19 Material Properties5-149 Post Processing CBAR Results5-142 Multiple Subcases5-68 The CBAR Element5-48 Grid Points5-34 Coordinate Systems5-3 Introduction to GeometryCase Study: Aircraft Wing Rib 7.0Case Study: Traffic Signal Pole 6.0Space Station Truss 5.0Page Section5Copyright 2008 MSC.Software CorporationCONTENTS10-134 Workshop 12 RBE2 vs. RBE310-40 Workshop 11 Spacecraft Fairing9-104 Workshop 10 Support Bracket8-71 Workshop 9 A-B 2 D Clamp7-127 Workshop 8 D Composite Tension CouponCase Study: Aircraft Wing Rib cont. 7.07-110 Analysis of Composite MaterialsCase Study: Intercooler Structure 8.08-9 Solid Geometry8-14 The CHEXA Element8-34 Post Processing Solid Element Results8-68 Solid Elements10-82 Rigid Body Elements10-41 0-D Elements10-6 Groups and Lists9-87 Axisymmetric Elements9-64 Mesh Density Control9-51 Viewports9-11 Importing Geometry9-6 Model Simplification MethodsCase Study: Car Design 10.0Case Study: Scuba Tank 9.0Page Section6Copyright 2008 MSC.Software CorporationCONTENTS15-33 Workshop 17 Glued Contact15-33 Workshop 16 3D Contact14-92 Workshop 15 Parasolid Modeling13-36 Workshop 14 Buckling of a Submarine Pressure Hull12-43 Workshop 13 Normal Modes of a Rectangular PlateUnits 11.011-3 Units in MD NastranCase Study: Communications Tower 12.012-3 Normal Modes AnalysisCase Study: Submarine Pressure Hull - 3D 13.013-3 Linear Buckling AnalysisParasolid Modeling 14.014-3 Parasolid Modeling ToolsLinear Contact 15.015-3 Linear vs. Nonlinear Analysis15-9 Contact Bodies15-14 Contact Detection15-25 Plate Contact Case StudyPage Section7Copyright 2008 MSC.Software CorporationCONTENTS17-18 Good Modeling Practice17-10 AutoSPC17-3 Minimum Recommended Model Checks16-75 Create Tool16-69 Report Tool16-66 Animations16-62 Graph Tool16-54 Cursor Tool16-49 Marker Tool16-32 Fringe Tool16-18 Deformation Tool16-6 Quick Plot ToolModel Checkout 17.0Results Postprocessing 16.0Page Section8Copyright 2008 MSC.Software CorporationS1-1NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSECTION 1OVERVIEWS1-2NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationS1-3NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationCOURSE OBJECTIVES Learn the basic features in MD Nastran Data structure Element library Linear static, normal modes, and buckling analyses Learn the basic functionalities in Patran Build finite element models (pre-processing) Evaluate analysis results (post-processing) Become familiar with solving engineering problems in an integratedPatran/Nastran environment through hands-on training Students will work through a number of workshop problems in classwith assistance from the instructor Simple workshop problems designed to introduce basic concepts Real-world workshop problems designed to lead the students throughengineering problems from beginning to endS1-4NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationWHAT IS MD NASTRAN?MD Nastran offers multidiscipline simulation capabilitiesbased on proven technologies and industry leadership ofover four decades.In addition to the analysis capabilities of MSC Nastran, MDNastran offers key capabilities that drive efficiency andstreamline processes: Broad Analysis Capabilities - Supports key engineering disciplines thatprovide the basis for a superior multidiscipline simulation system Integration - Unparalleled support for interaction between multiple disciplinesin simulations that facilitates true multidisciplinary analysis Optimization - Multidisciplinary optimization capabilities with combined sizing,shape, and topology optimization, special constraints and response functionsacross disciplines High Performance Computing - Optimized for parallel and 64-bitsupercomputing environmentsS1-5NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationWHAT IS MD NASTRAN?This course primarily covers basic features that are commonto both MD Nastran and MSC Nastran.Some course material uses the enhanced functionality of MDNastran, while the majority of the course may be completedusing either MSC Nastran or MD Nastran.S1-6NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationWHAT IS MD NASTRAN?MD Nastran is a general-purpose finite element analysisprogram capable of solving a wide variety of engineeringproblems, including: Linear static analysis Static analysis with geometric and material nonlinearity Transient analysis with geometric and material nonlinearity Normal modes analysis Buckling analysis Direct and modal complex eigenvalue analysis Direct and modal frequency analysis (including random analysis) Direct and modal transient analysis (including responsespectrum analysis)S1-7NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationWHAT IS MD NASTRAN? (Cont.)MD Nastran Capabilities (Cont.) Linear cyclic symmetry analysis (including static, normalmodes, buckling, and direct frequency response) Linear and nonlinear steady-state heat transfer Linear and nonlinear transient heat transfer Aeroelasticity Substructure analysis (superelements) Design sensitivity and optimization Acoustics Composite material analysis P-element analysis Rotor DynamicsS1-8NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationWHAT IS MD NASTRAN? (Cont.)MD Nastran is Extensively documented (including online encyclopedia) Extensively tested Continually enhanced with new capabilities Highly efficient in using modern numerical analysis techniques Used extensively by aerospace, automotive, energy,biomedical, civil, and other industriesS1-9NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationWHAT IS PATRAN?Patran is a CAE pre- and post-processing softwarepackage. It consists of the following majorcomponents:User-Friendly Graphical User InterfacePowerful Geometry Import, Export, and CreationRobust Meshing AlgorithmsFast Results Visualization and ReportingExtensive Analysis Code PreferencesS1-10NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationWORKFLOW IN PATRANThe Main Menu2 - Import Geometry1 - Select Analysis Code2 - or Build Geometry3 - CreateAnalysis Model5 - Evaluate and PublishAnalysis Results4 - Perform theAnalysisS1-11NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSOLVING A TYPICAL ENGINEERINGPROBLEMThe following case study demonstrates how to usePatran and MD Nastran in a typical engineeringapplicationS1-12NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: LANDING GEAR STRUTThe design team has created a nose landing gear strutdesign for the new fighter jet. Determine if the landinggear strut has been designed properly to withstand thelanding load.S1-13NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: LANDING GEAR STRUT (Cont.)Design Specifications Material: SteelE = 30 x 106psi = 0.3 Landing load = 7,080 lb7,080 LBS1-14NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 1 - CREATE DB AND SET ANALYSISPREFERENCEOpen a new database inPatran.Select MD Nastran andStructural Analysis for this casestudy.S1-15NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 2 - IMPORT OR BUILD GEOMETRYThe user can import or build geometry in Patran: Import geometry models from CAD systems:CATIAPro/ENGINEERUnigraphicsEUCLID 3I-DEAS Import geometry models in standard formats:STEPParasolid xmtACISIGESSTLVDA Build the geometry directly in PatranS1-16NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 2 - IMPORT OR BUILD GEOMETRY (Cont.)For this case study, the landing gear strut geometrymodel is available as a parasolid xmt file.Import this model directly into Patran.S1-17NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 2 - IMPORT OR BUILD GEOMETRY (Cont.)Import the landing gear strut geometry.S1-18NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 2 - IMPORT OR BUILD GEOMETRY (Cont.)The landing gear strut geometry is imported.S1-19NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 3 - CREATE ANALYSIS MODELNext, create the analysis model:Create a finite element meshApply boundary conditionApply loadingCreate material propertiesCreate element propertiesS1-20NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 3 - CREATE ANALYSIS MODEL (Cont.)Create the finiteelement mesh.S1-21NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 3 - CREATE ANALYSIS MODEL (Cont.)Constrain the hubcylinder at thebottom of thestrut.S1-22NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 3 - CREATE ANALYSIS MODEL (Cont.)Apply 7,080 lb tothe upper face ofthe strut.S1-23NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 3 - CREATE ANALYSIS MODEL (Cont.)Define a materialproperty for thelanding gear strut.S1-24NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 3 - CREATE ANALYSIS MODEL (Cont.)Create anelement propertyfor the landinggear strut.S1-25NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 4 - PERFORM THE ANALYSISSubmit the model toMD Nastran toperform a linearstatic analysis.S1-26NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 5 - EVALUATE ANALYSIS RESULTSReview .f06 filea. Verify that theanalysis hascompletedsuccessfully.b. Review warningmessages.c. Review analysisresults.S1-27NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 5 - EVALUATE ANALYSIS RESULTSRead the analysisresults intoPatran.S1-28NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 5 - EVALUATE ANALYSIS RESULTS (Cont.)Plot displacementsand stresses.S1-29NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 6 - PUBLISH ANALYSIS RESULTSPublish a stresssummary report.S1-30NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSTEP 6 - PUBLISH ANALYSIS RESULTS (Cont.)Under File/Imagesor Results/Create/Quick Plot:Create static,animated, and vrmlimages for reportsand presentations.S1-31NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationSUMMARY OF PATRAN-NASTRAN WORKFLOWPatranMD NastranMD NastranPre-Processing Import/create geometry Create finite element mesh Apply boundary condition Apply loads Create material properties Create element properties Submit model to solverSolver Solve for displacements Compute strains Compute stressesPost-Processing Deformation plots Stress fringe plots ReportsS1-32NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationCOMPANY OVERVIEWThe MSC.Software Corporation has been supplyingsophisticated computer-aided engineering (CAE) toolssince 1963.MSC.Software is the developer, distributor, andsupporter of the most complete and widely-usedstructural analysis program in the world, MD Nastran.MSC.Software is also the developer, distributor, andsupporter of the state of the art CAE analysis program,Patran.Patran is an open architecture, pre and post processorfor all major finite element analysis (FEA) software,including MD Nastran and Marc.S1-33NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationWHERE TO GO FOR HELPThe MSC Technical Support Hotline1-800-732-7284is staffed Monday through Friday, 8:00 a.m. to 5:00 p.m.Email support:[email protected]@mscsoftware.comWebsite support at www.mscsoftware.com/supportS1-34NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationWHERE TO GET TRAININGMD Nastran and Patran seminars are held worldwideLocations, dates, and descriptions of all scheduledclasses can be found atwww.mscsoftware.com/support/msc_instituteMSC also conducts cost-effective in-house seminarsat clients facilities. These seminars can be tailoredto meet clients specific needs.Contact the MSC Institute at 1-800-732-7211S1-35NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationPATRAN SEMINARS Following Patran seminars are offered PAT301 - Introduction to Patran PAT302 Patran for Advanced Users PAT304 - Introduction to Patran Command Language (PCL) PAT312 - Thermal Analysis Using Patran Thermal PAT318 - Durability and Fatigue Life Analysis Using MSC Fatigue PAT325 - Introduction to Laminate Modeler PAT328 - New Features in PatranS1-36NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationMD NASTRAN SEMINARS Following MD Nastran seminars are offeredNAS101 Basic MD Nastran Linear Static and Normal Modes AnalysisNAS102 MD Nastran Dynamic AnalysisNAS103 MD Nastran Nonlinear AnalysisNAS104 MD Nastran Thermal AnalysisNAS105 Practical Finite Element Modeling Techniques Using MD NastranNAS106 MD Nastran Superelement AnalysisNAS107 Design Sensitivity and Optimization in MD NastranNAS108 New Capabilities in MD NastranNAS110 DMAP and Database Applications in MD NastranNAS111 MD Nastran Aeroelastic AnalysisNAS113 Analysis of Composite Materials with MD NastranNAS115 Fluid-Structure Analysis in MD NastranNAS116 Practical Dynamic Analysis with MD NastranNAS120 Linear Static and Normal Modes Analysis Using MD Nastran and PatranNAS122 Dynamic Analysis Using Patran and MD NastranNAS123 MD Nastran Implicit Nonlinear (SOL600) AnalysisNAS125 Stochastic Simulation Using MSC Robust DesignS1-37NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationEXERCISEPerform Workshop 1 Landing Gear StrutAnalysis in your exercise workbook.S1-38NAS120, Section 1, August 2008Copyright 2008 MSC.Software CorporationS2-1NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationSECTION 2INTRODUCTION TO THEFINITE ELEMENT METHODS2-2NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationS2-3NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationEngineering AnalysisClassical MethodsNumerical MethodsClosed-formApproximateFinite ElementFinite DifferenceBoundary ElementMETHODS FOR SOLVING ENGINEERINGPROBLEMSAs shown below, the finite element method is one ofseveral methods for solving engineering problemsS2-4NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationMETHODS FOR SOLVING ENGINEERINGPROBLEMS (Cont.)Classical Methods: Closed-form solutions are available for simple problems such asbending of beams and torsion of prismatic bars Approximate methods using series solutions to governingdifferential equations are used to analyze more complexstructures such as plates and shells The classical methods can only be used for structural problemswith relatively simple geometry, loading, and boundaryconditionsS2-5NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationMETHODS FOR SOLVING ENGINEERINGPROBLEMS (Cont.)Numerical Methods: Boundary Element MethodSolves the governing differential equation for the problem withintegral equations over the boundary of the domain. Only theboundary surface is meshed with elements. Finite Difference MethodReplaces governing differential equations and boundary conditionswith corresponding algebraic finite difference equations.S2-6NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationMETHODS FOR SOLVING ENGINEERINGPROBLEMS (Cont.)Numerical Methods (Cont.) Finite Element Method (FEM)Capable of solving large, complex problems with general geometry,loading, and boundary conditionsIncreasingly becoming the primary analysis tool for designers andanalystsThe Finite Element Method is also known as the Matrix Method ofStructural Analysis in the literature because it uses matrix algebrato solve the system of simultaneous equations.S2-7NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationWHAT IS THE FINITE ELEMENT METHOD?The Finite Element Method (FEM) is a numericalapproximation method. It is a method of investigatingthe behavior of complex structures by breaking themdown into smaller, simpler pieces.These smaller pieces of structure are calledelements. The elements are connected to each otherat the nodes.The assembly of elements and nodes is called a finiteelement model. The piston head shown in the nextslide is an example of a finite element model.S2-8NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationSAMPLE FINITE ELEMENT MODELElementSample Finite Element ModelNodeS2-9NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationFINITE ELEMENTSFinite elements have shapes which are relatively easy toformulate and analyze. The three basic types of finiteelements are beams, plates, and solids.Beam(1D)Plate(2D)Solid(3D)S2-10NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationONE DIMENSIONAL ELEMENTS1D beam elements are used to model long, slenderstructural members, as demonstrated in thiscommunications tower finite element model.S2-11NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationTWO DIMENSIONAL ELEMENTS2D plate elements are used to model thin structuralmembers such as aircraft fuselage skin or car bodyS2-12NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationTHREE DIMENSIONAL ELEMENTS3D solid elements are used to model thickcomponents such as the piston head shown below:S2-13NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationBUILDING A FINITE ELEMENT MODELThe Finite Element Method approximates thebehavior of a continuous structure with a finitenumber of elements.As one increases the number of elements (andhence, decrease the size of the elements), the resultsbecome increasingly accurate, but the computingtime also increases.Patran provides numerous modeling tools to help theuser build finite element models with the rightbalance between accuracy and model size.S2-14NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationHOW DOES FEM WORK ?Basic Approach A given problem is discretized by dividing the originaldomain into simply shaped elements. Elements are connected to each other by nodes.XYZS2-15NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationHOW DOES FEM WORK ? (Cont.)uxuyuzuzuyuxThree translations (ux, uy, uz)Three rotations (qx, qy, qz){u} = displacement vector= { ux uy uz qx qy qz}Each node is capable of moving in six independentdirections: three translations and three rotations. Theseare called the degrees of freedom (DOF) at a node.S2-16NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationHOW DOES FEM WORK ? (Cont.) The relationship between an element and its surrounding nodescan be described by the following equation:[ k ]e{ u }e={ f }e The elemental stiffness matrix [ k ]e is derived from geometry,material properties, and element properties. The elemental load vector { f }e describes the forces acting on theelement. The displacement vector { u }e is the unknown in this equation. Itdescribes how the nodes are moving as a result of the appliedforces.[ k ]e{ u }e={ f }eElemental EquationS2-17NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationHOW DOES FEM WORK ? (Cont.) Next, the elemental stiffness matrices are assembled into aglobal stiffness matrix. The loads are also assembled into aglobal load vector. This results in the following matrix equationfor the overall structure:[ K ] { u } ={ F }[ K ] { u } ={ F }[ k ]e{ u }e={ f }eElemental EquationGlobal EquationS2-18NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationHOW DOES FEM WORK ? (Cont.) Next, apply the boundary condition to the model (constrain themodel). Mathematically, this is achieved by removing rows andcolumns corresponding to the constrained degrees of freedomfrom the global matrix equation.Boundary Condition[ K ] { u } ={ F }Global Matrix Equationwith boundary conditionappliedS2-19NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationHOW DOES FEM WORK ? (Cont.) Finally, the global matrix equation is solved to determine theunknown nodal displacements. Element strains and stresses are then computed from the nodaldisplacements.Deformation Plot Stress Fringe PlotS2-20NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationSummary of the finite element method:HOW DOES FEM WORK ? (Cont.)Assemble loads into a global load vector {F}Represent continuous structure as a collection ofdiscrete elements connected by nodesDerive element stiffness matrices frommaterial properties, element properties, and geometryAssemble all element stiffness matrices into aglobal stiffness matrix [K]Apply boundary conditions to constrain themodelSolve the matrix equation [K] {u} = {F} fornodal displacementsCompute strains and stresses fromdisplacement resultsS2-21NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationTYPES OF FINITE ELEMENT METHODS There are two different types of finite element methods - thedisplacement method and the force method. In both methods,equilibrium, compatibility, and stress-strain relations are used togenerate a system of equations that represent the behavior of thestructure. In the displacement method, the grid point displacements are thebasic unknowns in the system of equations. In the force method, the member forces are the basic unknowns inthe system of equations. Both methods can be used to solve structural problems. Thedisplacement method is used by most modern finite element codes,including MD Nastran.S2-22NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationKEY CONCEPTS IN FEMThe Displacement MethodFormulation of the Element Stiffness MatrixMatrix Assembly and DecompositionS2-23NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationTHE DISPLACEMENT METHOD All structural engineering analyses must satisfy thefollowing three general conditions:1. Equilibrium of forces and moments:EF = 0, EM = 02. Strain-Displacement relations (also called compatibility ofdeformations): ensures that the displacement field in adeformed continuous structure is free of voids or discontinuitiesS2-24NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationTHE DISPLACEMENT METHOD (Cont.)3. Stress-Strain relations (also called constitutive relations): For a linear material, the generalized Hookes law states{o} = [E] {c}where {o} = { ox oy oz txy tyz tzx}{c} = { cx cy cz xy yz zx}[E] = 6 x 6 matrix of elastic constantsS2-25NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationTHE DISPLACEMENT METHOD (Cont.) These three conditions can be used to generate a system ofequations in which the displacements are unknown. The stiffness matrix [K] is used to relate the forces acting on thestructure and the displacements resulting from these forces in thefollowing manner:{F} = [K] {u}where {F} =forces acting on the structure[K] =stiffness matrix [kij], where each kij term is theforce of a constraint at coordinate i due to a unitdisplacement at j with all other displacementsset equal to zero{u} =displacements resulting from {F} Boundary conditions are applied to prevent rigid body motions,and the system of linear equations is solved for the unknown {u}.S2-26NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationFORMULATION OF THE ELEMENTSTIFFNESS MATRIX A key step in the displacement method is theformulation of the element stiffness matrix Each element in a finite element model is representedby an element stiffness matrix [K]e A single-rod case study is used to demonstrate theelement stiffness matrix formulation for a rod elementS2-27NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: ROD ELEMENT STIFFNESSMATRIX Consider an elastic rod of uniform cross section A andlength L under axial load. Axial translations u1 and u2 are the only displacementsat grid points 1 and 2. Thus, this element has twodegrees of freedom.F1F2X 1 2u1u2LX = 0AS2-28NAS120, Section 2, August 2008Copyright 2008 MSC.Software Corporation Step 2: Relate strain to displacements Assume that the rod changes length by an amount AL due tothe axial load. The strain in the rod is Step 1: Satisfy static equilibriumCASE STUDY: ROD ELEMENT STIFFNESSMATRIX (Cont.)F2F1 =cxALL-------u2u1L----------------- = =(1)(2)FxF1F2+ 0 = =ES2-29NAS120, Section 2, August 2008Copyright 2008 MSC.Software Corporation Step 3: Relate stress to strain Step 4: Relate force to stressCASE STUDY: ROD ELEMENT STIFFNESSMATRIX (Cont.)(3)(4)oxEcx=PA----ox1F1A------ =ox2F2A------ =o =andS2-30NAS120, Section 2, August 2008Copyright 2008 MSC.Software Corporation Step 5: Relate force to displacement Substitution of Equations 2 and 3 into Equation 4 yieldsCASE STUDY: ROD ELEMENT STIFFNESSMATRIX (Cont.)F1 oxA EcxAEAL--------u2u1 ( ) = = =F1AEL--------u2AEL--------u1 =F2EAL--------u2EAL--------u1 =orsimilarly,EA EA(5)(6)S2-31NAS120, Section 2, August 2008Copyright 2008 MSC.Software Corporation{F}=[K]e {u} Equations 5 and 6 represent two linear equations withtwo unknowns. Rewrite them in matrix form:CASE STUDY: ROD ELEMENT STIFFNESSMATRIX (Cont.)F1F2 ) ` EAL--------1 1 1 1u1u2 ) ` =(6)or[K]ewhere [K]e = [kij], the known 2x2 rod element stiffness matrix{F} = vector of known applied forces{u} = vector of unknown displacementsS2-32NAS120, Section 2, August 2008Copyright 2008 MSC.Software Corporation The method used in the previous case study to derivethe rod element stiffness matrix is called the directmethod or the stiffness method. This method workswell for simple elements such as rods and beams. For more complex 2D and 3D elements, thevariational method is used The variational method is also known as the Rayleigh-Ritzmethod. Assumed element shape functions and energy principles areused to derive the element stiffness matrices. The variational method is covered in detail in text books onthe finite element method. A list of reference books on thefinite element method is included at the end of this section.FORMULATION OF THE ELEMENTSTIFFNESS MATRIXS2-33NAS120, Section 2, August 2008Copyright 2008 MSC.Software Corporation The stiffness matrix for a rod element under torsion isshown below:ADDITIONAL EXAMPLES OF ELEMENTSTIFFNESS MATRIXT1T2 ) ` GJL-------1 1 1 1ux1ux2 ) ` =[K]eT1T2X 1 2ux1LX = 0Jux2S2-34NAS120, Section 2, August 2008Copyright 2008 MSC.Software Corporation The stiffness matrix for a beam element under in-planeshear and bending is shown below:ADDITIONAL EXAMPLES OF ELEMENTSTIFFNESS MATRIX (Cont.)Py1Mz1Py2Mz2 ) ` 2EIL3---------6 3L 6 3L3L2L23L L26 3L 6 3L 3L L23L 2L2y1uz1y2uz2 ) ` ={P} [K] {u}eFS2-35NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: TWO-ROD ASSEMBLY The following case study demonstrates the assemblyof the the individual element stiffness matrices and thesolution to the entire problem.X = 0Xu1, F1 u2, F212 3u3, F3L2L1PS2-36NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: TWO-ROD ASSEMBLY (Cont.) Write the following element stiffness equations basedon the previous derivation of stiffness matrix for a rodelement:)`(((((
=)`2111 111 111 111 121uuLA ELA ELA ELA EFF)`(((((
=)`3222 222 222222 232uuLA ELA ELA ELA EFF[K]1[K]2S2-37NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: TWO-ROD ASSEMBLY (Cont.) Rewrite the stiffness matrices in simpler terms:||((
=1 11 1k kk kK1| |((
=2 22 22k kk kK11 11LA Ek =22 22LA Ek =where andS2-38NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: TWO-ROD ASSEMBLY (Cont.) Assemble the two stiffness matrices by superposition.The resulting matrix is called the global stiffness matrix.||((
=1 11 11k kk kK||((
=2 22 22k kk kK( )Global Stiffness Matrix [K]S2-39NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: TWO-ROD ASSEMBLY (Cont.) Apply external loads to the structureF1 = -P F2 = 0 F3 = 0)`((((
+ =)`3212 22 2 1 11 1uuuk k 0k k k k0 k k00PS2-40NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: TWO-ROD ASSEMBLY (Cont.) Next, impose the boundary condition The right end is fixed, so u3 = 0. This is achieved by discardingrow 3 and column 3 from the global stiffness matrix.)`((((
+ =)`3212 22 2 1 11 1uuuk k 0k k k k0 k k00P)`((
+ =)`212 1 11 1uuk k kk k0PS2-41NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: TWO-ROD ASSEMBLY (Cont.) Now, solve the matrix equation One way to solve this equation is to multiply both sides by theinverse of [K])`((
+ =)`212 1 11 1uuk k kk k0Por {F}=[K] {u}[K]-1{F} = {u} In actual practice, inverting the stiffness matrix to solve the systemof equations is highly inefficient. MD Nastran uses a more efficientmatrix decomposition procedure rather than the matrix inversionmethod.S2-42NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: TWO-ROD ASSEMBLY (Cont.) Inversion of the [K] matrix requires that [K] be squareand that det[K] = 0 (i.e. nonsingular). If rigid body motion or mechanisms are not prevented(constrained), the structure is unstable and the stiffnessmatrix will be singular. Always remember that MD Nastran is working in a 3-Dspace when considering rigid body motion. Therefore,the set of constraints you apply must be able to preventany possible rigid body motion in 3-D space.S2-43NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationCASE STUDY: TWO-ROD ASSEMBLY (Cont.)Example of InadequateConstraintsExample of AdequateConstraintsS2-44NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationThe same procedure used for the two-rod model can beextended to a general structure such as the aircraftstructure shown below:The two highlighted stringer elements are representedby the two element stiffness matrices developed in theprevious case study.Element 100Element 200PROCEDURE FOR GENERAL STRUCTURESS2-45NAS120, Section 2, August 2008Copyright 2008 MSC.Software Corporation The stiffness characteristics of the rest of the aircraft are obtained byassembling the individual element stiffness matrices to the globalstiffness matrix using the same procedure as used in the two-rodmodel.k1-k10-k1(k1+ k2) -k20 -k2k2Stiffness contributions fromthe rest of the aircraftN x NPROCEDURE FOR GENERAL STRUCTURES(Cont.)S2-46NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationRule of thumb for computer resources (CPU time) usedby MD Nastran for a problem with N DOF Overhead (~ constant) Stiffness matrix assembly (~ N) Solution cost ( ~ N2) Data recovery ( ~ N)PROCEDURE FOR GENERAL STRUCTURES(Cont.)S2-47NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationOTHER APPLICATIONS OF FINITE ELEMENTMETHOD In general, the finite element method can be applied toany continuum described by partial differentialequations. Example: Steady-state heat conduction Replace the structural stiffness matrix with the matrix of thermalconductivities Single DOF at each node (temperature) Other fields Fluid flow/wave propagation Electromagnetics DynamicsS2-48NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationREFERENCESV. AdamsBuilding Better Products with Finite Element AnalysisOnWord Press, 1999K. J. BatheFinite Element Procedures in Engineering AnalysisPrentice-Hall, 1982R. D. CookConcepts and Applications of Finite Element AnalysisJohn Wiley & Sons, 1989R. H. MacNealFinite Elements: Their Design and PerformanceMarcel Dekker, 1994S2-49NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationREFERENCES (Cont.)NAFEMSA Finite Element PrimerDepartment of Trade and Industry, UK, 1986J. S. PrzemienieckiTheory of Matrix Structural AnalysisMcGraw-Hill, 1968B. A. Szabo and I. BabuskaFinite Element AnalysisJohn Wiley & Sons, 1991O. C. ZienkiewiczThe Finite Element MethodMcGraw-Hill, 1994S2-50NAS120, Section 2, August 2008Copyright 2008 MSC.Software CorporationEXERCISEPerform Workshop 2 Simply Supported Beam in yourexercise workbook.S3-1NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationSECTION 3BASICS OFMD NASTRAN AND PATRANS3-2NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationS3-3NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationPATRAN GRAPHICAL USER INTERFACEThe Patran GUI for the Windows and Unixplatforms are shown in the following slides.Except for the color scheme and iconarrangements, the two GUIs are basicallyidentical.The course material will be presented using theWindows GUI.S3-4NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationWINDOWS GUIS3-5NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationUNIX GUIS3-6NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationTHE MAIN MENUMenu BarTool BarHistory WindowCommand LineStatus IconStatic Green indicates Patran iswaitingfor user inputRotating Blue indicates Patran isperforming a process which canbe stopped immediately with theabort iconRotating Red indicates thatPatran is performing a processwhich cannot be interruptedApplication ButtonsS3-7NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationTHE MAIN MENU (Cont.)File SavePrintCopy to ClipboardUndo - will undo last commandAbort - Stops operation in progressReset GraphicsRefresh GraphicsDisplay and Viewing IconsS3-8NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationTHE VIEWPORTDisplay ModeCurrent GroupCurrent ViewportDatabase NameS3-9NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationAPPLICATION FORMSActionObjectMethodSelect Menu(Filter Buttons)S3-10NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationAPPLICATION FORMS (Cont.)Toggle button is an on/offswitchSelect databox is used toenter dataData can be inserted byplacing the mouse at thedesired location, clickingthe left mouse button,and typing in the desireddataExisting text can beedited... suffix denotes that asubordinate form will open upupon clicking the buttonApply causes action to executeHyphens indicate action can beundone only immediately afterits executionSlide bar assigns a value to associated variableControl icon allows the switching between different actions.In this example, the icon can be set to highlight or split.Causes the content of a form to reset back to default values;the default values may be constant or can changeS3-11NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationENTITY PICKING Picking is performed in two ways: Keyboard entry into a databox Graphical picking with the mouseS3-12NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationENTITY ID SYNTAXAll points Point 1:#Signifies an axis with first point representing thebase and the second determining the direction{[ ][ ]}< > signifies a vector definition Mathematical operations like division are possible todetermine the individual components[1, 2, -64.0/20.0]y = the z coordinate of point 5When a point is referenced the letter p can bedropped[1, zp5, 3][1, z5, 3]Individual coordinates can reference existingentities, such as x = the x coordinate of node 28[xn28, 1, 2]Square brackets signifies coordinate specification [x y z]Combinations of entity ID syntax is possible (face 2of solids 1 through 10)Solid 1:10.2References an entity associated with a higher orderone (i.e. edge 1 of surface 3, that is similar to acurve)Surface 3.1Different forms for delimiters: space, , and / Curve 1 2, 3/ 4Points 1 through 9 by 2 Point 1:9:2Refers to points 1, 2, and 3 Point 1 2 3Description SyntaxS3-13NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationENTITY GRAPHICAL PICKING Individual and collective entity picking iscontrolled by the Picking option underPreferences. For Single Entity Picking, a portion of theselected entity must be within the physicallimits of the cursor. For Centroid Single Picking, the closest entityto the location of the cursor will be picked. Additional tools are available to aid theprocess of picking, such as Cycle picking. The Preselection Settings highlight the Entityand Label (ID #) of the entity before youselect it.S3-14NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationCURSOR PICKING Single EntityMove the cursor to the entity label/centroid and pressthe left mouse button Multiple PickingHold down the shift key and select the entitieswith the left mouse buttonShiftS3-15NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationCURSOR PICKING (Cont.)Ctrl Rectangle Picking(Click & Drag) Polygon PickingClickClickYou can alsoselect this iconfrom the selectmenuNote: To complete your selection, double-click the left mouse buttonS3-16NAS120, Section 3, August 2008Copyright 2008 MSC.Software Corporation Deselect Cycle PickingMove the cursor to the entitys label/centroid andclick on the right mouse buttonPicking an entity underneath another, or that isclose to other entities. Once the cycle pickingwindow appears, make the selection from thewindow.CURSOR PICKING (Cont.)S3-17NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationMANIPULATING THE MODEL FORVIEWINGClick on one of these icons, then dragwith the middle mouse buttonXY RotateZ Rotate XY TranslateZoomS3-18NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationPATRAN ONLINE HELPTwo ways to use on-line help Use the drop-down help menu to get topical help or helpvia the world wide web Press the F1 key to get context sensitive help on aform in questionS3-19NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationPATRAN-NASTRAN WORKFLOW AND FILESPatranPatranMD NastranMD NastranSolverK u = F Solve for u Compute strain Compute stress.bdf.xdb.op2.db.ses.db.jou.f04.f06.logPre-Processing Import/create geometry Create finite element mesh Apply boundary condition Apply loads Create material properties Create element properties Submit model to solverPost-Processing Deformation plots Stress fringe plots ReportsS3-20NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationBASIC PATRAN FILESOne per model. Record of all PCL commandsfrom database creation to present.Concatenated session files. EXTREMELY usefulfor rebuilding a database.Journal File .db.jouA Session File is opened at Patran start-upand it is closed when you quit Patran.Session File .sesOne per model Database .dbComments File Type File ExtensionS3-21NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationBASIC MD NASTRAN FILESUsed by Patran for post processing. Results File .xdbUsed by Patran for post processing. Results File .op2Contains a time history of job execution. Execution Summary File .f04Operating System Log File .logThis is the main Nastran output file. It containsthe results of your analysis such as displacementsand stresses. It is in ASCII format so it can beviewed in any text editor. It also containswarning messages, error messages, and diagnosticmessages to help the user evaluate the quality ofthe analysis results.Results File .f06Contains model definition. Popular extensions are.bdf and .datInput File .bdfComments File Type File ExtensionS3-22NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationTHE MD NASTRAN INPUT FILEThe two files which contain the finite element modeldefinition are The Patran database file The Nastran input fileThe Nastran input file is useful in a number of ways: Can be viewed and edited in any text editor Can include comments to document modeling assumptionsand changes Allows the user to add entries which are not supported inPatran Useful in debugging a modelS3-23NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationORGANIZATION OF THE NASTRAN INPUTFILEThe Nastran input file is arranged in five sections:Nastran StatementNastran StatementFile Management SectionFile Management SectionExecutive Control SectionExecutive Control SectionCase Control SectionCase Control SectionBulk Data SectionBulk Data SectionCENDBEGIN BULKENDDATAOptional SectionsRequired SectionsRequiredDelimitersID A,BOptionalDelimiterS3-24NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationNASTRAN INPUT FILE SECTIONSNastran Statement Used to modify systemdefaults. Not needed in most runs.File Management Section Allocates files, controlsrestarts and database operationsExecutive Control Section Solution type, timeallowed, program modifications, and systemdiagnosticsCase Control Section Requests Output andselects Bulk Data items such as loadings andconstraints to be usedBulk Data Section Model definition, loadings, andboundary conditionsS3-25NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationNASTRAN INPUT FILE DELIMITERSThe delimiters are ID A,B First statement in Executive ControlSection (optional) CEND End of Executive Control Section,beginning of Case Control Section BEGIN BULK End of Case Control Section, beginning ofBulk Data Section ENDDATA Last entry in the input fileSAMPLE MODELS3-26E = 30x106psi = 0.3 A = 4.0 in2J = 1.27 in4NAS120, Section 3, January 2007Copyright 2007 MSC.Software CorporationS3-27NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationNASTRAN INPUT FILE OF SAMPLE MODELID TRUSS,SAMPLESOL 101TIME 5CENDTITLE = SAMPLE INPUT FILESUBTITLE = TRUSS STRUCTURELOAD = 10SPC = 11DISP = ALLELFORCE = ALLSPCFORCE = ALLBEGIN BULK$$ GRID POINTS DESCRIBE THE GEOMETRY$GRID 1 0. 0. 0.GRID 2 0. 120. 0.GRID 3 600. 120. 0.GRID 4 600. 0. 0.$$ TRUSS MEMBERS MODELED WITH ROD ELEMENTS$CROD 1 21 2 3CROD 2 21 2 4CROD 3 21 1 3CROD 4 21 1 4CROD 5 21 3 4$PROD 21 22 4. 1.27MAT1 22 30.E6 .3FORCE 10 4 1000. 0. -1. 0.SPC1 11 12 1 2SPC1 11 3456 1 2 3 4ENDDATAExecutiveControlCase ControlBulk DataComments startwith a dollar signS3-28NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationTHE BULK DATA SECTIONThe Bulk Data Section contains all datanecessary for describing a structural modelEach item described in the Bulk Data section iscalled an EntryThe Bulk Data entries are not required to be inputin any orderFORMAT OF BULK DATA ENTRIES Each Bulk Data entry has a specific pre-defined format andpurpose (described in the MD Nastran Quick Reference Guide,Section 5) Shown below is the CROD entry description from the QuickReference Guide:S3-29NAS120, Section 3, January 2007Copyright 2007 MSC.Software CorporationS3-30NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationFORMAT OF BULK DATA ENTRIES (Cont.)Each line contains 80 columnsA Bulk Data entry may span multiple linesThere are three data formats Integer Real Character StringEach field in a particular entry has a required dataformat. See the Quick Reference Guide for thecorrect format.S3-31NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationFORMAT OF BULK DATA ENTRIES (Cont.)Following representations of the real number 123.4are numerically equivalent and acceptable to MDNastran:Real numbers must be entered with a decimal point.Integers must be entered without a decimal point.123.4 1.234+2 1.234E2 12.34E+10.1234E3 .1234E3S3-32NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationFIELD FORMATEach Nastran input file line contains 80 columns.There are three field formats for entering data in these80 columns: Small Field Format Large Field Format Free Field FormatS3-33NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationFIELD FORMAT (Cont.)Small Field Format Each line is divided into 10 fields Each field is 8 columns wide456 9.0 8.6 7.5 10 GRID 8 8 8 8 8 8 8 8 8 8 10 9 8 7 6 5 4 3 2 1FIELD FORMAT (Cont.)Large Field Format A high degree of accuracy is required in some MD Nastranapplications. The large field format is used when the small fieldformat does not provide enough significant digits. An asterisk after the keyword signifies large field format.GRID* 10 7.5 8.6 *GRID10*GRID10 9.0 456S3-34NAS120, Section 3, January 2007Copyright 2007 MSC.Software CorporationS3-35NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationFIELD FORMAT (Cont.)Free Field Format Fields are separated by commas or blanks (commas arestrongly recommended) To skip a field, use two commas in succession Integer numbers or character strings with more than eightcharacters cause a fatal error Real numbers with more than eight characters are rounded offand will lose some precisionExample:GRID,10,,7.5,8.6,9.0,,456S3-36NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationCONTINUATION ENTRIESMany input entries require more than one line of inputIf this is the case, then continuation entries must beused.Continuation entries may be generated automaticallywhen the entries are in sorted order. The parent entrymay be blank in columns 74-80 (field 10), and thecontinuation entry may be blank in columns 2-8 (field 1).For small field entries, the first column of the continuationentry may be blank or contain a + symbol. For large fieldentries, the first column of the continuation entry mustcontain a * symbol.S3-37NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationCONTINUATION ENTRIES (Cont.)Input rules Unless you use automatic generation, a (+) or (*) is required incolumn 1, field 1 of a continuation entry. The remaining contents infield 1 of a continuation entry must be identical to the entry in field10 (columns 2 through 8) of the parent entry (or the precedingcontinuation entry). Any entry in the first column of field 10 on the parent entry isignored by the continuation entry Small field and large field continuation entries may be usedtogether in defining a single data item entryAn example of the use of continuation is shown in the nextslideS3-38NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationCONTINUATION ENTRIES (Cont.)Two methods of entering a MAT8 entry with continuationare shown below: Method 1 Method 2+M101+M101+M102+M102S3-39NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationGENERAL INPUT FORMAT RULESInput data items in fields 1 and 10 must be leftjustified. Input data in fields 2 through 9 do not haveto be left or right justified.Error results if data extends beyond its field intoanother field.Input data items must not have any embeddedblanks.All real numbers, including zero, must contain adecimal point.Many fields have default values. If these fields areleft blank, the default values will be used (See theQuick Reference Guide).S3-40NAS120, Section 3, August 2008Copyright 2008 MSC.Software CorporationEXERCISEPerform Workshop 3 Editing a Nastran Input File inyour exercise workbook.S4-1NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationSECTION 4STADIUM ARCHED-ROOF TRUSSS4-2NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationSECTION 4STADIUM ARCHED-ROOF TRUSSS4-3NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationTopics covered in this section: MD Nastran Element Library Creating nodes and 1D Elements The MD Nastran CROD element Post-processing 1D element resultsSECTION 4STADIUM ARCHED-ROOF TRUSSS4-4NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationProblem Description The final design of a new support structure for the center fieldscoreboard of a baseball stadium is almost complete. Thearchitect has an exposed, overhanging, arched-roof truss inher design. An electric billboard will be hung from this truss.You are asked to analyze the design of the arched-roof trussto ensure that it can support the weight of the scoreboard.Analysis Objectives Determine stress levels in the truss members under loading.The maximum stress must be below the yield point of thetruss material. Determine the maximum vertical displacement of thestructure. The architect has specified that the maximumvertical movement of the scoreboard should not exceed 0.25inch.CASE STUDY:STADIUM ARCHED-ROOF TRUSSS4-5NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationThe MD Nastran element library contains over 50finite elements Zero-dimensional One-dimensional Two-dimensional Three-dimensional Scalar Axisymmetric Rigid Heat transfer Fluid-structure P-version Contact GENEL user-supplied elementMD NASTRAN ELEMENTSS4-6NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCOMMONLY USED MD NASTRAN ELEMENTSScalarElements1-DElements2-DElements3-DElementsRigidElementsCONM20-DElementsCBUSHCELASi(i=1,2,3,4)CRODCONRODCTUBECBARCBEAMCBENDCQUAD4CQUAD8CTRIA3CTRIA6CQUADRCTRIARCSHEARCHEXACPENTACTETRARBARRBE2RBE3RSSCONAxisymmetricElementsCTRIAX6CTRIAXCQUADXS4-7NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCREATING ELEMENTS IN PATRAN Two methods for creating elements in Patran:1. Mesh geometry to generate elements2. Create elements by connecting nodesMethod 1 Method 2S4-8NAS120, Section 4, August 2008Copyright 2008 MSC.Software Corporation For this case study, Method 2 will be used to directly createnodes and connect the nodes to create elements There are five identical planar truss assemblies supporting theroof. Only one truss assembly will be created. The table below shows the location of truss joints. Use this tableto create the nodes.CREATING TRUSS NODES AND ELEMENTSS4-9NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationInput location for node 1CREATING NODESS4-10NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCREATING NODES (Cont.)Repeat the processuntil all 13 nodeshave been createdS4-11NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCREATING ELEMENTSInput element connectivityfor element 1S4-12NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationRepeat the process until all 24elements have been createdCREATING ELEMENTS (Cont.)S4-13NAS120, Section 4, August 2008Copyright 2008 MSC.Software Corporation The Patran BAR2 element corresponds to a family of two-nodedNastran elements: The specific element type will be specified later when creating theelement properties.CREATING ELEMENTS (Cont.)ScalarElements1-DElements2-DElements3-DElementsRigidElementsCONM20-DElementsCBUSHCELASi(i=1,2,3,4)CRODCONRODCTUBECBARCBEAMCBENDCQUAD4CQUAD8CTRIA3CTRIA6CQUADRCTRIARCSHEARCHEXACPENTACTETRARBARRBE2RBE3RSSCONAxisymmetricElementsCTRIAX6CTRIAXCQUADXS4-14NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCreating Material Properties The architect has selected steel tubing as theconstruction material. The material properties are as follows:E = 30 x 106psi v = 0.3Tensile yield strength = 36 ksiCREATING MATERIAL PROPERTIESS4-15NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCreate a material named steelCREATING MATERIAL PROPERTIES (Cont.)S4-16NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationInput material propertiesCREATING MATERIAL PROPERTIES (Cont.)S4-17NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationFollowing are the most commonly used one-dimensionalelements in MD Nastran: CROD, CONROD, CTUBE: Pin-ended rod (4 DOFs) CBAR: Prismatic beam (12 DOFs) CBEAM: Straight beam with warping (14 DOFs) CBEND: Curved beam or pipe (12 DOFs)SELECT THE 1-D ELEMENT TYPES4-18NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationFor this case study, the primary load path in the trussmembers is axial. Assume the bending moments arenegligible.Select the MD Nastran CROD element to model thetruss members.The truss members have the following physicalproperties: 6.0 inch diameter tubing 0.25 inch wall thickness A = t/4 *(6.02-5.52) = 4.516 in2 J = t/32 *(6.04-5.54) = 37.398 in4SELECT THE 1-D ELEMENT TYPE (Cont.)S4-19NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationGeneral features of the CROD element are: Connected by two nodes Two force components:Axial force PTorque T Displacements components: ui and ui Straight, prismatic member The element stiffness matrix contains only terms for axial andtorsional degrees of freedomP TAT PB XeTHE CROD ELEMENTS4-20NAS120, Section 4, August 2008Copyright 2008 MSC.Software Corporation Element connectivity is defined on the Nastran CROD entryField ContentsEID Element identification numberPID Identification number of PROD property entryG1,G2 Grid point identification numbers of connectionpoints, where G1 = grid point at End A andG2 = grid point at End B7 1 1 23 CRODG2 G1 PID EID CROD10 9 8 7 6 5 4 3 2 1THE CROD ELEMENT (Cont.)S4-21NAS120, Section 4, August 2008Copyright 2008 MSC.Software Corporation Element property is defined on the Nastran PROD entryField ContentsPID Property identification numberMID Material identification numberA Cross-sectional areaJ Torsional constant (equals to polar moment ofinertia for circular cross sections)C Coefficient to determine torsional stressNSM Nonstructural mass per unit length (Real)37.398 4.516 1 1 PRODNSM C J A MID PID PROD10 9 8 7 6 5 4 3 2 1THE CROD ELEMENT (Cont.)S4-22NAS120, Section 4, August 2008Copyright 2008 MSC.Software Corporation Solid Circular Section Hollow Circular Section Solid Square Section Solid Rectangular Section Calculation of torsional constant J for sometypical cross sectionsJ12---tr4=2rJ12---tro4ri4 ( ) =roriJ 2.25a4=2aJ ab3163------ 3.36ba--- 1b412a4------------ \ . || | =2b2aTHE CROD ELEMENT (Cont.)S4-23NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCreate a 1D Rod propertynamed circular_rodCREATING ELEMENT PROPERTY FOR THETRUSSS4-24NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationInput element propertiesCREATING ELEMENT PROPERTY FOR THETRUSS (Cont.)S4-25NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCREATING ELEMENT PROPERTY FOR THETRUSS (Cont.)Select application regionS4-26NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationClick Add to sendselection to thecollector boxbelow and clickApply to create theelement property.CREATING ELEMENT PROPERTY FOR THETRUSS (Cont.)S4-27NAS120, Section 4, August 2008Copyright 2008 MSC.Software Corporation$ Material Record : steel$ Description of Material : Date: 06-May-02 Time: 09:25:28MAT1 1 3.+7 .3$ Elements and Element Properties for region : circular_rodPROD 1 1 4.516 37.398CROD 23 1 1 7A snap shot of the MD Nastran input file for this problem,showing how the connectivity entry, the property entry,and the material entry are linked together:ELEMENT-PROPERTY-MATERIAL CHAINREFERENCES4-28NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCreating Loads and Boundary Conditions The truss assembly is bolted down at the base. The billboard weighs 2,500 pounds, which is supportedby five truss assemblies. Each truss assembly,therefore, supports 500 pounds of weight.CREATING LOADS AND BOUNDARYCONDITIONSS4-29NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCreate a boundarycondition namedfixedCREATING BOUNDARY CONDITIONSS4-30NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationConstrain all six degreesof freedomCREATING BOUNDARY CONDITIONS (Cont.)S4-31NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCREATING BOUNDARY CONDITIONS (Cont.)Select the base of the trussS4-32NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationFinish creating theboundary conditionCREATING BOUNDARY CONDITIONS (Cont.)S4-33NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCreate a secondboundarycondition toconstrain DOFsnot connected toany elementCREATING BOUNDARY CONDITIONS (Cont.)S4-34NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationConstrain theT3 and R3degrees offreedomCREATING BOUNDARY CONDITIONS (Cont.)S4-35NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCREATING BOUNDARY CONDITIONS (Cont.)Select the restof the trussS4-36NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationFinish creatingthe boundaryconditionCREATING BOUNDARY CONDITIONS (Cont.)S4-37NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationClick here first, then drag themiddle mouse button to rotate themodelRotate the modelto get a better viewCREATING BOUNDARY CONDITIONS (Cont.)S4-38NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCreate a load named forceCREATING LOADSS4-39NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationCREATING LOADS (Cont.)Input -500 lbs in the y directionS4-40NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationSelect the application regionCREATING LOADS (Cont.)S4-41NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationFinish creating the loadCREATING LOADS (Cont.)S4-42NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationThe pre-processing phase of the analysis process isnow complete. The next step is to send the model toMD Nastran to perform the numerical analysis.CASE STUDY WORKFLOWSolverMD NASTRANPATRANPre-ProcessingPATRANPost-ProcessingS4-43NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationANALYSIS SETUP AND SUBMITTALSelect linear static analysis andsubmit the analysis job to MDNastranS4-44NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationANALYSIS SETUP AND SUBMITTAL (Cont.)Status window reports job progressS4-45NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationAfter MD Nastran completes the analysis, theanalysis results are ready to be post-processed.CASE STUDY WORKFLOWSolverMD NASTRANPATRANPre-ProcessingPATRANPost-ProcessingS4-46NAS120, Section 4, August 2008Copyright 2008 MSC.Software Corporation There are two types of Nastran results files: the .op2 file and the.xdb file When the .op2 file is read into Patran, it becomes a permanent part ofthe database. When the .xdb file is read into Patran, it is attached to the databasetemporarily and becomes detached when the Patran database isclosed.truss.op2truss.dbtruss.db +truss.op2truss.xdbtruss.dbtruss.xdbtruss.dbTWO TYPES OF RESULT FILESS4-47NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationATTACH THE XDB FILEBy default, Patranrequested for a.xdb file when thejob was submittedto Nastran.Attach the .xdb fileto Patran.S4-48NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationEvaluate the analysis results Examine the maximum vertical deflection. Theallowable deflection is 0.25 inch. Examine the truss member stresses. Therequirement is 36 ksi (material yield strength)POST PROCESS THE RESULTSS4-49NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationPLOT DEFORMATIONPlot the deformationMax y disp = 0.018 in < 0.25 inS4-50NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationBy default, Patran averages the stresses at anode from neighboring elements and plots thisaverage stress value.By switching off the averaging option, the truemaximum axial stresses in the truss membersare displayed.PLOT STRESSESS4-51NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationPlot the averaged axial stressesPLOT STRESSES (Cont.)S4-52NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationPLOT STRESSES (Cont.)Plot the un-averaged axialstressesS4-53NAS120, Section 4, August 2008Copyright 2008 MSC.Software Corporation Open the .f06 file with a text editor Check the total applied load against the total reaction loadTotal applied loadTotal reaction loadREVIEW THE .f06 FILES4-54NAS120, Section 4, August 2008Copyright 2008 MSC.Software Corporation Examine the constraint forces to verify that the boundary conditionhas been applied correctly:REVIEW THE .F06 FILE (Cont.)S4-55NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationReview the displacements and rod element stressesREVIEW THE .f06 FILE (Cont.)S4-56NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationAnalysis Summary: Maximum deflection of 0.018 inch is below the 0.25inch requirement Maximum axial stresses:Tensile Stress = 226 psiCompressive Stress = -268 psiThe strength margin of safety is high Effects such as dynamic loading and buckling will bediscussed at a later part of the course.CASE STUDY ANALYSIS SUMMARYS4-57NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationEXERCISEPerform Workshop 4 Stadium Truss in your exerciseworkbook.S4-58NAS120, Section 4, August 2008Copyright 2008 MSC.Software CorporationS5-1NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationSECTION 5SPACE STATION TRUSSS5-2NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationS5-3NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationSECTION 5SPACE STATION TRUSSTopics covered in this case study:Part 1: Modeling Introduction to Geometry Transform Geometry Organize the model using Groups Mesh control Coordinate systemsPart 2: 1D Finite Element entities NASTRAN CBAR element Definition of 1D element propertiesPart 3: Analysis and Results Multiple Subcases Postprocessing 1D dataS5-4NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationProblem Description The preliminary design of a Space Station truss segment iscomplete. The truss assembly carries a number of criticalcomponents used for navigation, communication, and heatrejection. This truss segment will be launched on the SpaceShuttle and assembled in space to other truss segments. Youare asked to analyze the design of the truss segment toensure that it can survive the launch and on-orbit loadingevents.Analysis Objectives Determine stress levels in the truss members under loading.The maximum stress must be below the yield point of thetruss material.CASE STUDY:SPACE STATION TRUSSS5-5NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationPART 1: MODELINGIn this section of the workshop, we will learn about: Modeling Geometry in Patran Types of Geometry Meshing Options for each type of geometry Organizing models using Groups Coordinate Systems in Patran and Nastran Nastran Grid Point entries Equivalent Terminology in Patran and NastranS5-6NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationGetting started on the Space Station truss analysis:For the previous case study, no geometry wasused. Nodes were directly created by entering xyz coordinates Rod elements were created by connecting the nodes This method works well for simple modelsIn general modeling situations, the structure is toocomplex to be modeled using the previousmethod. The more common method is to createor import the geometry first, then mesh thegeometry to generate the finite element model.CASE STUDY:SPACE STATION TRUSSS5-7NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationXYZ9YZXGEOMETRY BUILDING BLOCKS IN PATRANPoint (cyan)A point is a zero-dimensional CAD entity. Itrepresents a location in space.Patran creates points automatically whenconstructing curves, surfaces, and solids Points are created at vertices, e.g. surfacevertices (corners) It is not always necessary to construct entitiesstarting with their points, e.g. surface from pointsS5-8NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationGEOMETRY BUILDING BLOCKS IN PATRANCurve (yellow) A curve is a general vector function of thesingle parametric variable 1. It can havemany types of mathematical forms:(X,Y,Z) = function ( 1) A curve has: Two points, with one at each end A parametric coordinate (1) whose domain isfrom 0.0 at P1 (its origin) to 1.0 at P2 Meshing a curve produces bar elements1P21P1P(1)ZYXZXY5Bar ElementS5-9NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationGEOMETRY BUILDING BLOCKS IN PATRANSimple Surface (green) There are two types of surface: Simple - Green Complex (general trimmed) - Magenta A simple surface is a general vectorfunction of the two parametric variables1,2:(X,Y,Z) = function (1,2) A simple surface has: 3 or 4 bounding edges A parametric origin and parametriccoordinates whose domains are from 0 to 1 A simple surface with 3 visible edges has afourth edge that is degenerate12P2P1P4P32121ZYXZXYP(1,2)S5-10NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationMESHING A SIMPLE SURFACEMeshing a simple surface produces 2-D elementsTria meshQuad meshS5-11NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationGEOMETRY BUILDING BLOCKS IN PATRANComplex Surface (magenta)A complex or general trimmed surface (magenta) has morethan 4 edges and can have interior cutouts Not defined parametrically (1, 2 not used) It is a trimmed parametric surfaceOuter boundaryInner boundariesS5-12NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationMESHING A COMPLEX SURFACEMeshing a complex surface produces 2-D elementsQuad meshTria meshS5-13NAS120, Section 5, August 2008Copyright 2008 MSC.Software Corporation123P8P7P6P4P3P2P1P5P (1, 2, 3)GEOMETRY BUILDING BLOCKS IN PATRANSimple Solid (blue)There are two types of solid: Simple - Blue Complex - WhiteSimple solid Vector function of three parametric variables1, 2, 3A simple solid has: 4 to 6 bounding faces Parametric origin and coordinates whosedomains are from 0 to 1A simple solid with 4 to 5 visible faceshas some degenerate facesS5-14NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationMESHING A SIMPLE SOLIDMeshing a simple solid produces solid elementsHex meshWedge meshTet meshS5-15NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationGEOMETRY BUILDING BLOCKS IN PATRANComplex Solid (white)Complex Solid Can have an arbitrary number of faces which define the solidboundary. It is called a boundary representation (B-rep)solid. Complex solids can be either Patran native B-Rep orparasolid B-RepS5-16NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationMESHING A B-REP SOLIDMeshing a B-rep solid produces solid elementsTet meshS5-17NAS120, Section 5, August 2008Copyright 2008 MSC.Software Corporation Topological entities are subcomponents of the basic geometry entitiesTOPOLOGICAL ENTITIESVertexEdgeFaceSolid All topological entities can be cursor selected to perform PATRANfunctions. For example Solid 1.4 specifies face number 4 of solid 1 which is a surface Surface 2.3 specifies edge number 3 of surface 2 which is a curveS5-18NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCREATING THE SPACE STATION GEOMETRYS5-19NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCreate a group called bulkheadsCREATING A GROUPS5-20NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationInput 7 point locations-64.740 -30.675 0 60 0 0 7-64.740 30.675 0 564.740 -30.675 0 464.740 30.675 0 30 -81.200 0 20 81.200 0 1Z Y XCREATING POINTSS5-21NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCreate 12 curves for one bulkheadCREATING CURVESS5-22NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationMake 5 copies of the bulkheadgeometryX=100X=100X=100X=100X=120TRANSFORMING THE CURVESS5-23NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationDeleteunnecessarycurves and pointsfrom front andrear bulkheads.FINISH CREATING THE BULKHEADGEOMETRYS5-24NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCreate a newgroup calledlongerons.Groups are aneffective tool toorganize your modeland are covered ingreater detail inSection 10.CREATING A NEW GROUPS5-25NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCreate geometry for thelongeronsCREATING THE LONGERON GEOMETRYS5-26NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCreate a new groupcalled diagonalsCREATING A NEW GROUPS5-27NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCreate geometry for alldiagonal membersCREATING THE DIAGONAL GEOMETRYS5-28NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationThe truss geometry will next be meshed to generatenodes and elements.There are two ways to control the element sizeMesh seeds or Global edge lengthMESHING THE GEOMETRYS5-29NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCREATING A NEW GROUPCreate a new group called FEMS5-30NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationSet up a meshseed of 12elements percurve to controlthe mesh densityon the 4 diagonalmembers in thelongest baySETTING UP MESH SEEDSS5-31NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationNext mesh all thecurves with a globaledge length of 20 inMESH THE TRUSS GEOMETRYS5-32NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationRESULTING MESHCoarser globalmesh controlled byglobal edge lengthFiner local meshcontrolled by meshseedsS5-33NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationEquivalence the modelto merge coincidentnodesEQUIVALENCE THE MODELS5-34NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCOORDINATE SYSTEMS IN PATRANCoordinate systems are used in theconstruction and transformation of geometryS5-35NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCOORDINATE SYSTEMS IN PATRAN (CONT.)Coordinate systems are also used to define thedirection of loads and boundary conditionsS5-36NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCOORDINATE SYSTEMS IN PATRAN (CONT.)Coordinate systems can also be used to definethe analysis coordinate system of a nodeS5-37NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCREATING COORDINATE SYSTEMSThere are three types of coordinate systems:Rectangular, Cylindrical, and SphericalThere are many ways to create coordinate systems:S5-38NAS120, Section 5, August 2008Copyright 2008 MSC.Software Corporation MD Nastran Coordinate systems are used to Define locations of grid points in space Orient each grid points displacement vector Coordinate systems in MD Nastran: Basic Coordinate System - Implicitly defined referencerectangular coordinate system (Coordinate System 0).Orientation of this system is defined by the user throughspecifying the components of grid point locations. Local Coordinate Systems - User-defined coordinatesystems. Each local coordinate system must be relateddirectly or indirectly to the basic coordinate system. The sixpossible local coordinate systems are:Rectangular CORD1RRectangular CORD2RCylindrical CORD1CCylindrical CORD2CSpherical CORD1SSpherical CORD2SMD NASTRAN COORDINATE SYSTEMSS5-39NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationMD Nastran Local Coordinate Systems: The CORD1R, CORD1C, and CORD1S entries define a localcoordinate system by referencing the IDs of three existing gridpoints. The CORD2R, CORD2C, and CORD2S entries define a localcoordinate system by specifying the vector components of threepoints. This is the format used by Patran. All angular coordinates are input in DEGREES. All rotationaldisplacements associated with these coordinates are output inRADIANS.MD NASTRAN COORDINATE SYSTEMS (Cont.)S5-40NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationRectangular Local Coordinate System (X, Y, Z)Point A=local coordinate system originPoint B=reference point for z axis directionPoint C=reference point in the x-z planePoint P=grid point defined in local rectangular system(ux, uy, uz) =displacement components of P in local systemMD NASTRAN RECTANGULAR COORDINATESYSTEMS5-41NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCylindrical Local Coordinate System (R, u, Z)Point A=local coordinate system originPoint B=reference point for z axis directionPoint C=reference point in the x-z planePoint P=grid point defined in local cylindrical system(Ur, Uu, Uz) =displacement components of P in local systemMD NASTRAN CYLINDRICAL COORDINATESYSTEMS5-42NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationSpherical Local Coordinate System (R, u, |)Point A=local coordinate system originPoint B=reference point for z axis directionPoint C=reference point in the x-z planePoint P=grid point defined in local spherical system(Ur, Uu, U|) =displacement components of P in local systemMD NASTRAN SPHERICAL COORDINATESYSTEMS5-43NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationMD NASTRAN COORDINATE SYSTEM ENTRIESS5-44NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationDISPLAY OF COORDINATE SYSTEM 0Coordinate system 0is always displayed atthe lower left-handcorner of the viewportThe tick markrepresents the originof the coordinatesystem 0S5-45NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCORD1X VS. CORD2X ENTRIESBy default, coordinate systems aretranslated into MD Nastran CORD2XentriesIf Coordinate Frame Coordinates in theTranslation Parameters form is set toreference nodes, then CORD1X istranslated where applicableS5-46NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationNESTED COORDINATE SYSTEMSCreating nested coordinate systems By default, the nested relationship is lost duringtranslation to MD Nastran If nested coordinate system is desired, theCoordinate Frame Coordinates in theTranslation Parameters form needs to be set toreference frame.S5-47NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCreate a rectangularcoordinate system whichwill be used later todefine the direction ofthe applied loadCREATE A RECTANGULAR COORDINATESYSTEMPoint 16Point 23Point 17S5-48NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationGrid points are used to specify: Structural geometry Degrees of freedom of the structure Locations of points at which displacements areconstrained or loads are applied Locations where output quantities are to be calculatedGRID POINTSS5-49NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationEach grid point is capable of moving in sixdirections. These are called degrees of freedom(DOF).DOF1=T1 =u1=translation in direction 1DOF2=T2 =u2=translation in direction 2DOF3=T3 =u3=translation in direction 3DOF4=R1=u1=rotation in direction 1DOF5=R2=u2=rotation in direction 2DOF6=R3=u3=rotation in direction 3123456DEGREES OF FREEDOMS5-50NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationFor each grid point, all six degrees of freedom mustbe accounted for: Think in terms of 3D even if the problem is only 1D or 2D. Any un-used DOF must be constrained123456DEGREES OF FREEDOM (Cont.)The NASTRAN GRID entry is show below:Field ContentsID Grid point identification numberCP Identification number of coordinate system in whichthe location of the grid point is defined (integer > 0 orblank; default = basic coordinate system)X1, X2, X3 Location of grid point in coordinate system CP (real)CD Identification number of coordinate system in which displacements, degrees of freedom, constraints, andsolution vectors are defined at the grid point (integer > 0 or blank; default = basic coordinate system).PS Permanent single-point constraints associated with grid point (any of the digits 1-6 with no embedded blanks)This method of constraining a structure is not recommended.SEID Superelement IDTHE NASTRAN GRID ENTRYS5-51NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationEach GRID entry refers to two coordinate systems The coordinate system in field 3 is used to locate the grid point.This is called the positional coordinate system. The coordinate system in field 7 establishes the grid pointdisplacement coordinate system which defines for the given gridpoint the directions of displacements, degrees of freedom,constraints, and solution vectors.THE NASTRAN GRID ENTRY (Cont.)S5-52NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationS5-53NAS120, Section 5, August 2008Copyright 2008 MSC.Software Corporation The grid point displacement coordinate system is also known as theoutput coordinate system because all grid point results(displacements, grid point forces, etc.) are generated and output inthis coordinate system. The union of all displacement coordinate systems is called the globalcoordinate system.The grid point displacement coordinate system:THE GRID POINT DISPLACEMENTCOORDINATE SYSTEMCoordinate System 5(cylindrical)GRID POINT EXAMPLEGrid points 10 and 20 are located on the aircraft fuselage as show below.The GRID entry uses coordinate system 5 to define the location of the twopoints and uses coordinate system 0 to define the grid point displacements.Basic coordinate system 0GRID POINT EXAMPLES5-54NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationCoordinate System 5(cylindrical)Suppose we are interested in displacements and forces in the fuselage radialand tangential directions. We can accomplish this by changing field 7 of theGRID entries from coordinate system 0 to coordinate system 5.Basic coordinate system 0GRID POINT EXAMPLE (Cont.)S5-55NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationS5-56NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationExamples of how the grid point displacementcoordinate system is usedCONSTRAINTSSPRINGSRIGIDELEMENTS CLEARANCEUSING THE GRID POINT DISPLACEMENTCOORDINATE SYSTEMS5-57NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationThere are two ways to create grid points in PATRAN: Directly create the grid point Mesh the geometryEquivalent to grid pointin MD NastranEquivalent to thedisplacement coordinatesystem in MD NastranEquivalent to thepositional coordinatesystem in MD NastranCREATING A GRID POINT IN PATRANS5-58NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationEquivalent Terminology in NASTRAN andPATRAN:NASTRAN PATRANGrid Points NodesBasic Coordinate System Global Coordinate SystemGlobal Coordinate System NoneDisplacement CoordinateSystemAnalysis Coordinate SystemPositional Coordinate System Reference Coordinate SystemNASTRAN AND PATRAN TERMINOLOGYS5-59NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationEXERCISEPerform Workshop 5 Coordinate Systems in yourexercise workbook.S5-60NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationPART 2: 1D FINITE ELEMENT ENTITIESIn this section of the workshop, we will learn about: Types of 1D elements available in Nastran Selection of appropriate elements for modeling tasks The Nastran CBAR element Bar Offsets Element coordinate systems Definition of 1D element properties Orientation for Bar and Beam elements Display of element cross section Manual input of sectional propertiesS5-61NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationNow back to the case study. Lets create materialproperties. Aluminum 7075-T7351 plate and bar stock has been selectedfor the truss. The material properties are as follows:E = 10 x 106psiv = 0.3Tensile yield strength = 45 ksiCREATING MATERIAL PROPERTIESS5-62NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCreate a material namedal_7075CREATING MATERIAL PROPERTIES (Cont.)S5-63NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationInput materialpropertiesCREATING MATERIAL PROPERTIES (Cont.)S5-64NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationConsidering load paths in the truss assembly The truss members must carry axial and lateral loadsdue to the way they are loaded. Shear and bendingmoment will develop in the members as they areloaded laterally at locations between the truss joints asshown below. We must select an element type that iscapable of resisting the shear forces and moments.LOAD PATH IN TRUSSPMS5-65NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationFollowing are the most commonly used one-dimensional elements in NASTRAN: ROD Pin-ended rod (4 DOFs) BAR Prismatic beam (12 DOFs) BEAM Straight beam with warping (14DOFs)COMMONLY USED 1-D ELEMENTSS5-66NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationGuidelines on 1-D element selection: In general, select the simplest element which gives you thecorrect load path. More complex elements will still do the job,but may give you a lot of unwanted output. If only an axial load or torsional load is to be transmitted in anelement, then the CROD or CONROD element is the bestchoice. If shear and moment are to be transmitted in an element, thenthe CBAR is the easiest element to use. Use the CBEAM element instead of the CBAR element for thefollowing reasons: Variable cross-section The neutral axis and shear center are not coincident The effect of cross-sectional warping on the torsional stiffness issignificant The mass center of gravity and shear center are not coincident The effect of taper on the transverse shear stiffness (shear relief) issignificantELEMENT SELECTIONS5-67NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationFor this problem we will use the CBAR elementdue to its ability to transmit shear force andbending moment.The CBEAM element has additional capabilitieswhich we dont need for this problem. The useof CBEAM will be demonstrated in the nextsection.ELEMENT SELECTION (Cont.)S5-68NAS120, Section 5, August 2008Copyright 2008 MSC.Software Corporation Connected to two grid points Formulation derived from classical beam theory(plane sections remain plane under deformations) Includes optional transverse shear flexibility Neutral axis may be offset from the grid points(internally a rigid link is created) Principal moment of inertia axis need not coincidewith element axis. Pin flag capability used to represent slotted joints,hinges, ball joints, etc. General Features of the CBAR ElementTHE CBAR ELEMENTS5-69NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationGeneral limitations on CBAR: Straight, prismatic member (i.e., properties do not vary along thelength). Shear center and neutral axis must coincide (therefore, notrecommended for modeling channel or angle sections). The effect of cross-sectional warping is neglected.Displacement Components: Six degrees of freedom at each end.Force components: Axial force P Torque T Bending moments about two perpendicular directions M1 and M2 Shears in two perpendicular directions V1 and V2THE CBAR ELEMENT (Cont.)S5-70NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCBAR element entry:THE CBAR ELEMENT (Cont.)S5-71NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCBAR element entry:THE CBAR ELEMENT (Cont.)S5-72NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCBAR element entry:THE CBAR ELEMENT (Cont.)CBAR element coordinate system Defined by the orientation vector V Orients input cross-sectional properties Orients output forces and stresses Orients pin flagsxxzzTHE CBAR ELEMENT (Cont.)S5-73NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationS5-74NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCBAR Element Coordinate SystemTHE CBAR ELEMENT (Cont.)CBAR Element Coordinate System with OffsetsTHE CBAR ELEMENT (Cont.)S5-75NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationS5-76NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationFollowing are two examples of when you might define the CBAR elementcoordinate system orientation vector V with each of the two available options(G0 or X1, X2, X3).If you are representing stringers on a fuselage with CBAR elements, your input willbe minimized by using the G0 option to define the element coordinate systemorientation vector V.Example 1THE CBAR ELEMENT (Cont.)S5-77NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationExample 2To specify the orientation of the legs of a tripod modeled with CBARelements as shown, it would be most efficient to use the components ofa vector (X1, X2, X3) to define the orientation vector V since theorientation of each of the legs is unique.THE CBAR ELEMENT (Cont.)S5-78NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCBAR OffsetsThe ends of the CBAR element can be offset from the Grid Points(GA, GB) by specifying the components of offset vectors WA and WB onthe CBAR entry.The offset vector is treated as a rigid link between the grid point andthe end of the element.The element coordinate system is defined with respect to the offsetends of the bar element.THE CBAR ELEMENT (Cont.)S5-79NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationThin sheetStiffenersGrid PointsBar Offset ExampleTHE CBAR ELEMENT (Cont.)Centroid ofStiffenerOffsetS5-80NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationTHE CBAR ELEMENT (Cont.)The OFFT field OFFT is a character string code that describes how theoffset and orientation vector components are to beinterpreted. By default (string input is GGG or blank), the offset vectorsare measured in the displacement coordinate systems atgrid points A and B and the orientation vector is measured inthe displacement coordinate system of grid point A. At user option, the offset vectors can be measured in anoffset coordinate system relative to grid points A and B, andthe orientation vector can be measured in the basic systemas indicated in the following table:S5-81NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationTHE CBAR ELEMENT (Cont.)The OFFT field (Cont.)S5-82NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationThe user specifies DOFs at either end of the bar element thatare to transmit zero force or moment. The pin flags PA and PBare specified in the element coordinate system and defined infields 2 and 3 of the optional CBAR continuation.CBAR Pin FlagsExample: Pin flagapplied to rotationalDOF at this end ofCBAR creates ahinged joint.THE CBAR ELEMENT (Cont.)S5-83NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCBAR Element Properties entry:THE CBAR ELEMENT (Cont.)S5-84NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCBAR Element Properties entry (cont.)THE CBAR ELEMENT (Cont.)S5-85NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationCBAR Element Properties entry (Cont.)THE CBAR ELEMENT (Cont.)THE CBAR ELEMENT (Cont.)S5-86NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationTHE CBAR ELEMENT (Cont.)S5-87NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationShear Factor KTHE CBAR ELEMENT (Cont.)S5-88NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationTHE CBAR ELEMENT (Cont.)S5-89NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationS5-90NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationAlternative CBAR Element Properties entry:THE CBAR ELEMENT (Cont.)S5-91NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationTHE CBAR ELEMENT (Cont.)PBARL cross-section typesS5-92NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationTHE CBAR ELEMENT (Cont.)PBARL cross-section typesS5-93NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationTHE CBAR ELEMENT (Cont.)PBARL cross-section typesS5-94NAS120, Section 5, August 2008Copyright 2008 MSC.Software CorporationTHE CBAR ELEMENT (Cont.)PBARL cross-section typesBAR element internal forces and momentsTHE CBAR ELEMENT (Cont.)S5-95NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationBAR element internal forces and momentsTHE CBAR ELEMENT (Cont.)S5-96NAS120, Section 5, March 2007Copyright 2007 MSC.Software CorporationS5-97NAS120, Section 5, August 2008Copyrig