Fundamentals of Strength of Materials and FEM
METHODS TO SOLVE ANY ENGINEERING PROBLEMS ANALYTICAL
METHODNUMERICAL METHODEXPERIMENTAL METHOD
-CLASSICAL APPROACH -100% ACCURATE RESULTS-CLOSED FORM SOLUTION-
PL/3EI- APPLICABLE ONLY FOR SIMPLE PROBLEMS LIKE CANTILEVER &
SIMPLY SUPPORTED BEAMS ETC-MATHEMATICALREPRESENTATION -APPROXIMATE
, ASSUMPTIONS MADE-APPLICABLE EVEN IF PHYSICAL PROTOTYPE NOT
AVAILABLE - REAL LIFE COMPLICATED PROBLEMS -RESULTS CANNOT BE
BLINDLY BELIEVED
-ACTUAL MEASUREMENTS -TIME CONSUMING AND NEEDS EXPENSIVE SET UP
- APPLICABLE ONLY IF PHYSICAL PROTOTYPES ARE AVAILABLE
THOUGH ANALYTICAL METHODS COULD ALSO GIVE APPROXIMATE RESULTS IF
THE SOLUTION IS NOT IN CLOSED FORM , BUT IN GENERAL AND BROAD SENSE
ANALYTICAL METHODS ARE CONSIDERED AS CLOSED FORM SOLUTIONS I.E.
100% ACCURATE FINITE ELEMENT METHOD - LINEAR , BUCKLING , THERMAL ,
DYNAMIC AND FATIGUE ANALYSIS BOUNDARY ELEMENT METHOD ACOUSTICS /
NVH FINITE VOLUME METHOD CFD AND ELECTROMAGNETICS FINITE DIFFERENCE
METHOD THERMAL AND FLUID FLOW ANALYSIS -STRAIN GUAGE -PHOTO
ELASTICITY-VIBRATION MEASUREMENTS -SENSORS FOR TEMP. & PRESSURE
-FATIGUE TEST
How does numerical methods solve the problem?This is achieved by
discretization of problems . All real life objects are continuous .
Means there is no physical gap between two consecutive particles .
As per material science any object is made of small particles ,
particles of molecules , molecules of atoms and so on and are
bonded together by attraction . Solving a real life problems with
continuous material approach is difficult and basic of all
numerical methods is to simplify the problem by discretizing(
discountinuation ) it . In simple words nodes work like atoms and
gap in between them is filled by entity called as element .
Calculations are made at nodes and results are interpolated for
entire elements. FEMFinite Any continuous object has infinite
degrees of freedom & its just not possible to solve the problem
in this format . Finite Element Method reduces degrees of freedom
from Infinite to Finite with the help of discretization i.e.
meshing (nodes & elements ).Element All the calculations are
made at limited number of points known as nodes . Entity joining
nodes and forming a specific shape such as quadrilaterals or
triangular is known as element .Method There are three methods to
solve any engineering problem . FEM belongs to one of them.
ADVANTAGES OF FEM1> Improved visualization2> Lesser design
cycle time3> Lesser number of prototypes4> Lesser no. of
testing required 5> Decrease in cost of production
VISUALIZATION OF RESULTS : For simple geometries such as simply
supported beams or cantilever beams it is easy to visualize point
of maximum stress and displacement . But in real life for parts or
assemblies with complex geometrical shapes , made up of different
materials with many discontinuities subjected to flexible
constraints , complex loading conditions it is not easy to predict
failure location . Here CAE softwares gives you stresss contours
for any complex loading case which helps you to easily determine
failure location .
STAGES OF ANALYSIS
STAGE 1: PRE-PROCESSINGCAD&MESHING There are specialized
softwares for CAD , Meshing & Analysis . CAD and meshing
consumes most of the time .BOUNDARY CONDITIONS Consumes least time
but the most important step
STAGE 2: SOLUTION Software carries out matrix formulations ,
inversions , multiplications and solutions for unknown for eg:
displacements and then stress and strain for static analysis .
STAGE 3 : POST-PROCESSING Post processing is viewing results ,
verifications , conclusions and thinking about what steps be taken
to improve the design .
BASICS OF STATICS AND STRENGTH OF MATERIALS STRESS Internal
resistance to external force . In simple words it is defined as
force per unit area .
S.I. unit of stress is N/m2 . But the results are in very small
numerical figure & hence N/mm2 (or MPa , Mega Pascal ) is more
popular among CAE engineersTypes of StressHow many types of
stresses are there in engineering world?Only two- Normal and Shear
i.e. normal and shear . Bending , torsion , tension , compression ,
max. principal , von-mises etc. are forms of Normal and Shear
stresses. Normal Stress: Acts perpendicular to cross section and
causes elongation / compressionShear Stress: Acts parallel to cross
section , causes distortion (changes original shape)
Types of Forces in engineering world1> Based on direction of
force:There are 3 types of forces Fx,Fy,Fz and 3 types of moments
Mx,My,Mz in the world . All the loading conditions like
concentrated load , distributed loads , pressure , traction ,
gravity , torsion etc are forms of Fx,Fy,Fz, Mx,My & Mz
FORCEFX FY FZ
2> Based on region of force application FORCES Point Area
Line Volume
If perpendicular If inclined or parallel Gravitational force
Centrifugalcalled pressure called traction force
Types of moments in engineering worldMx Torsion , Shear
stress
My Bending Normal Stress
Mz Bending Normal Stress
What is torque ? Is it force or moment.Torque is moment acting
along the axis of shaft/object eg. In above fig. is Mx . Torque
causes shear stress while other 2 moments causes normal stress.
Basic assumptions for nature of stress
Uni-axial Bi-axial Triaxial 1-D 2-D
By default all the post processors gives von-mises stress plot ?
What is von mises stress & max. principal stress ?
The stress-strain diagram is plotted from standard uniaxial
tensile test . This curve is helpful in designing dimensions of
component if tensile force is known , based on yield stress one can
easily determine safe area of c/s (Area=Force/yield stress). But
when component is subjected to multi-axial loading (i.e. normal and
shear stress together) nature of stress-strain curve will not be
same . It indicates for different combinations for loading
(FX,FY,FZ,MX,MY,MZ) different graphs should be referred to .
Therefore it is just not practical to conduct so many tests. Here
we use different theories of failure which gives us equivalent max.
normal or max. shear stress or energy of component subjected to
multiaxial loading . It is then equated with respective value at
yield point(uniaxial tensile test)
vonMises Stress: Based on distortion energy or shear strain
energy theory
FAILURE CRITERIA Shear strain energy (multiaxial loading) =
shear strain energy at yield point (uniaxial tensile
test)RECOMMENDED for ductile materials i.e. steel , aluminium
components
Why vonmises stress is recommended for ductile and Principal
stresses for brittle materials?
BRITTLE Failure of cast iron rod subjected to uniaxial test is
along a plane perpendicular to axis of loading . Clearly the
failure is due to normal stress . Out of different theories of
failure max. principal stress theory is the one which is based on
normal stress . Hence for brittle material component Max. Principal
stress is used Mild steel fails at a plane inclined at 450 to axis
of loading . Normal stress cant act on this plane and the only
other possibility is shear stress . Out of different theories of
failure its max. shear stress and vonMises stress which are based
on shear stress. Von mises gives better correlation with
experimental results and hence preferable for ductile materials
.
Types of analysis 1> Linear static analysis
Equation of motion is given by f=kx where F is forceK is
stiffness constant X is displacement Linear means straight line
.Static:There are 2 conditions for static analysis 1> Force is
static i.e. no variation with respect to time ( dead weight)
Df/dt=0
2> Equilibrium condition - forces (Fx,Fy,Fz) and Moments
(Mx,My,Mz) =0 . Finite Element model fulfils this condition at each
and every node .
Practical Application : Most commonly used analysis in aerospace
, automobile , offshore and civil engineering industries perform
linear static analysis 2> NONLinear static analysis Non-
Linearity
Geometrical Material Contact Force(stress) vs
Displacement(strain) curve is non linear Stiffness K varies and is
not constant as in the case of linear analysis Deals with true
stress & true strain (unlike engineering stress &
engineering strain in linear static analysis)
A> Geometric Non LinearityThough component is within the
elastic limit but due to very large length even small force causes
large deformation . Regular formulas of strength of materials like
deflection PL3 /3EI not applicable as these are based on small
displacement assumption . Example : Fishing Rod
B> Material Non LinearityStress strain diagram along with
hardening rule for material is required as Input data . Metallic
non linearity applications: Automobiles , aerospace , ship
industries . To know exact value of stress/strain when it crosses
yield point . For low cycle fatigue analysis this data is
considered as input for strain life approach.Nonmetallic non
linearity applications : Automobile , aerospace industry , analysis
of rubber , plastic , asbestos , fibre components .Creep At
elevated temperatures even small magnitude of foce if kept alive
over long time period say for months and years would cause failure
. Application Nuclear / Thermal power plants , Civil engineering
etc.
C> Contact Non Linearity To simulate physical gap between two
parts eg. Bearing and shafts or press fit between two cylinders
3> Dynamic analysis DYNAMIC ANALYSIS
FREE VIBRATION FORCED VIBRATION
Practical Applications: Natural frequency is characteristic and
basic design property of any component while forced vibrations are
applicable for components subjected to
force/displacement/velocity/acceleration varying with respect to
time/frequency.
4> LINEAR BUCKLING ANALYSIS
Applicable for only compressive loads Slender beams & sheet
metal parts Bending stiffness fatigue ANALYSIS Calculations for
life of structure when subjected to repetitive loads S-N
curve(alternating stress vs cycles) or (alternating strain vs
reversals) is the base for fatigue calculations
Damage=n/N Endurance Factor of Safety(EFS)= =No. of cycles /
life Endurance strength/FE stress Damage < 1 safe Damage >1
fail EFS1 safeHigh cycle fatigue
Static and dynamic analysis can not tell how long component will
survive for given load . Also there is no consideration for factors
like surface finish, heat treatment , decarburizing , alloying
elements .
7> optimization Optimization
Geometrical Parameters Shape optimization Optimization for
geometry - Usually restricted to only linear static Parameters ,
work well at individual and normal mode dynamicsComponent level
rather than Complicated assemblies - Good tool for innovative kind
of Products
Software cant add or remove geometries - Software can give hint
for addition On its own but can play with only or removal of
geometriesPredefined parameters within specified limits.
Practical Applications: Applicable to any component which is
over or under designed
8> Cfd-computational fluid dynamicsCFD is the branch of fluid
mechanics which uses numerical methods to analyse fluid dynamics
problems . It is based on Navier-Stokes equation(mass, moment and
energy conservation equilibrium equations)
Practical Applications: Drag prediction and streamlining of a
car, combustion chamber design to check an optimum fuel-air mixing
, airplane design etc.
9> Crash analysis
STRUCTUTAL CRASHWORTHINESS/IMPACT SIMULATIONSDROP TEST
SIMULATIONS OCCUPANT SAFETY
To find deformation, stress and energy absorbing capacity of
various structural components of vehicle hitting a stationary or
moving object . The component is said to be crashworthy(safe) if it
meets the plastic strain and energy targets .
Applications: Frontal, side , Rear , Roof crush , car hitting
pole.etc.
Drop test is a free fall test carried out to check the
structural integrity of component.
Application: Blackbox of an aircraft, mobile phone , consumer
goods , TV Fridge etc.To find the effects of crash on human body
and making the ride safe for driver as well as passengers .
Several regulations have come across different countries to
ensure proper certifications e.g.FMVSS(Federal Motor vehicle safety
standards) in USA
In india ARAI has set up standard procedures for automotive
industry and called as AIS(Automotive Industry Standard)
10> Noise vibration and harshness (nvh) analysisSOUND
RADIATION OR SCATTERING COUPLED OR VIBROACOUSTICS PROBLEMS
Predicts how much sound pressure level is felt by a vibrating
source at a certain distance as a function of solid angle . Ex.
Sound felt due to horn or silencer vibrating at a certain
distance
These are solved by Boundary Element MethodThere is a clear
interaction of a structure and fluid cavity . A typical example is
noise level felt at drivers right ear due to engine vibration in
idle condition .
These are solved by Finite Element Method
Ansys Ansys is a complete FEA package used by engineers
worldwide in virtually all fields of engineering.
ANSYS workbench complete environment for geometry modeling ,
mesh manipulation , structural / thermal analysis , and
optimization , which is tightly integrated with CAD packages
CFX- state of the art CFD solvers , including the coupled ,
parallel CFX-5 solver
ICEM CFD Powerful meshing tools with general pre and post
processing features
ANSYS MULTIPHYSICS provides the analysis capabilities for
industrys most comprehensive coupled physics tool combining
structural, thermal , CFD , acoustics and electro-magnetic
simulation capabilities into a single software prouct . It is the
flagship product of ANSYS which includes analysis capabilities in
all engineering disciplines . It has two GUI ANSYS classic
environment for exposure of all functionality ANSYS workbench
environment for tight integration with CAD ANSYS Mechanical
Structural and Thermal analysis tool which includes a full
compliment of nonlinear and liner elements , material laws ranging
from metal to rubber and the most comprehensive sets of solvers
available
ANSYS Structural Provides the power of ANSYS non linear
structural capabilities as well as linear capabilities to deliver
highest quality, most reliable structural simulation results
possible
ANSYS Professional Inexpensive, easy to use program for
structural/thermal analysis projects
ANSYS Design Space An easy to use package that gives designers
the tool to conceptualize, design and validate ideas right on
desktop.
ANSYS LS-DYNA This tool helps engineers to understand elaborate
combinations of non-linear phenomena found in crash tests , metal
forging , stamping and catastrophic failures .
List of industries using ansys Aerospace Automotive Biomedical
Bridges and buildings Electronics and appliances Heavy equipment
and machinery MEMS- Micro Electromechanical systems Sporting
goods
Description of ANSYS Menus and WindowsWhen using the ANSYS
program in Interactive Mode, the Graphical UserInterface (GUT) is
activated. The GUI has six distinct components:
Utility Menu: Contains functions that are available throughout
theANSYS session, such as file controls, selecting, graphic
controls, andparameters. The ANSYS Help System is also accessible
through thismenu.Main Menu: Contains the primary ANSYS functions
organized byprocessors (Preprocessor, Solution, General
Postprocessor, etc.).Toolbar: Contains push-buttons for executing
commonly used ANSYScommands and functions. Customized buttons can
be created.Input Field: Displays a text field for typing commands.
All previouslytyped commands are stored in a pull-down menu for
easy reference andaccess.Graphics Window: Displays the graphical
representation of the models/meshes created within ANSYS. Also, the
related results are reviewed inthis window.Output Window: Receives
text output from the program. This windowis usually positioned
behind other windows and can be raised to thefront when
necessary.
UTILITY MENU RAISE HIDDEN INPUT LINE
ANALYZING BEAMS
Beams are structural members subjected to transverse loading
.
GRAPHICS AREA USER PROMPT INFO MODEL CONTROL TOOL BAR
ANSYS memory management ANSYS executable memory is the memory
required for ANSYS program. ANSYS workspace is the memory required
to run in addition to the ANSYS executable memory . Real memory is
the amount of actual , physical memory (RAM) available through
memory chips on your machine . System virtual memory is simply a
portion of computers hard disk used by the system to supplement
physical memory .
Workspace is the memory ANSYS needs to run. Default is 512 MB in
Windows and UNIX machines . Database space is used to work with
ANSYS database . For example model geometry , material properties ,
loads etc. Defaults to 256 MB on windows and UNIX machines .
Scratch space is where all internal calculations are done . For
example element matrix formulation , frontal solution , Boolean
calculations and so on .
ANSYS basics PICKING AND PLOTTING It is often advantageous to
plot only certain entities in the model .Within the utility menu
> plot , you will see geometric , finite element and other
entities can be plotted .
The plot ctrls menu is used to control how the plot is to be
displayed : Plot orientation , zoom , colors , symbols , annotation
, animation etc
Mouse clicks Ctrl + left mouse button pans the model Ctrl +
middle mouse button zooms the model and spins the model Ctrl +
right mouse button rotates the model .PICKINGPicking allows you to
identify model entities or locations in the graphics window .
Picking operation typically involves the use of the mouse and
picker menu .
Left mouse button picks or unpicks the entity or location
closest to mouse pointer . Middle mouse button does an apply and
saves time . Right mouse button toggles between pick and unpick
mode
COORDINATE SYSTEMS
The ANSYS program has several types of coordinate systems, each
used for a different reason: Globalandlocalcoordinate systems are
used to locate geometry items (nodes, keypoints, etc.) in space.
Thedisplaycoordinate system determines the system in which geometry
items are listed or displayed. Thenodalcoordinate system defines
the degree of freedom directions at each node and the orientation
of nodal results data. Theelementcoordinate system determines the
orientation of material properties and element results data.
Theresultscoordinate system is used to transform nodal or element
results data to a particular coordinate system for listings,
displays, or general postprocessing operations (POST1).
GLOBAL COORDINATE SYSTEM The global reference system for the
model May be cartisian (0) , cylindrical (1) , spherical (2)
LOCAL COORDINATE SYSTEM A user defined system at a desired
location , with ID number 11 or greater May be cartisian ,
cylindrical or spherical May be rotated about X,Y,Z axis
DISPLAY COORDINATE SYSTEM Can be changed to show and list
entities in multiple coordinate systems Default is global Cartesian
Used mostly for listing and plotting models in non-cartesian
systems Active coordinate system in ANSYS is default to global
Cartesian SELECT LOGIC FUNCTION Suppose you want to do the
following: Plot all areas located in the second quadrant Delete all
arcs of radius 0.2 to 0.3 units Apply a convection load on all
exterior lines Write out all nodes at Z=3.5 to a file They all
operate on a subset of a model . Select logic allows you to select
a subset of entities and operate only on those entities .Utility
menu > select > entities
Criteria by which to select :By num/pick: to select based on
entity numbers or by pickingAttached to : to select based on
attached entities . For example select all lines attached to the
current subset of areas .By location : to select based on x,y,z
location . For example select all nodes at X=2.5 . X,Y,Z are
interpreted in active coordinate systems By attributes : to select
based on material number , real constants set number etc Different
attributes are available for different entities Exterior : to
select entities lying on exterior By results : to select entities
by results data e.g. nodal displacements
TYPE OF SELECTION From full : selects a subset from the full set
of entities Reselect: select a subset from current subset Also
select: adds another subset to current subset Unselect: deactivates
a portion of current subset Invert: toggles the active and inactive
subsets Select none : deactivates the full set of entities Select
all: reactivates the full set of entities
REACTIVATING THE FULL SETUtility menu > select everything
COMPONENT MANAGER Components are user named subsets of entities
. The name can be used in dialogue boxes or commands in place of
entity numbers .A group of nodes , elements or key points , or
lines , or volumes can be defined as a component . Only one entity
type is associated with component .Components can be selected or
unselected . When you select a component , you are actually
selecting all of the entities in that component .Component manager
is used to create , display , list and select components and
assemblies Utlity menu > select > component manager
Creating a component could be done by Utility menu > select
> component manager Click on create component icon All of the
currently selected entities will be included in the component , or
you can select the desired entities at this step Enter a name upto
32 characters letters , numbers and _(underscores) are
allowedCreating an assembly Highlight the components for the
assembly Click on the create assembly icon and enter a name
Checking the box next to a component under the assembly number will
also put a component in a assembly
General analysis procedure Every analysis involves four major
steps
1> Preliminary decisions -Which analysis type ?- What to
model ?-Which element type ?
Depending on the physics of the problem analysis type should be
decided , the loads involved and output desired .For example if
load is pressure on bodies , or contact of two bodies then analysis
type will be structural . If loads applied is heat , temperature
than analysis type will be thermal.
Modeling may not necessary be full geometry . Depending upon
symmetry in geometry and loading conditions we can model or model .
Or model can be imported from other CAD modules also .
Selection of element type is very important step . Selection of
element depends upon shape function of element which depicts the
behavior of element . Lower order element gives less accuracy and
low computational time . Higher order element gives higher accuracy
and higher computational time .
2> Preprocessing -Define element type-Defining material
properties-Create or import the geometry model-Mesh the
geometry
Defining element type ANSYS has library of more than 180
elements . To select right element type we need to know the element
shape function and behavior .
Defining material properties
Defining material properties : We dont need to define system of
units in which we are working . Simply decide units you will use ,
then make sure all of your input is consistent .
-for example , if the model geometry is in inches , make sure
that all other input data material properties , real constants ,
loads etc are in inches .
Creating geometry
There are 2 approaches for modeling in ANSYS top down approach
and bottom up approach .
In this method, first keypoints are created, and then other
higher order entities such as lines, areas, and volumes are created
by using these keypoints, refer to Figure 1, 2, 3, and 4.
In this method, the model is created using the geometric
primitives such as fully-definedkeypoints, lines, areas, and
volumes. Figure 5 shows the frustum of a cone created using the
top-down construction method.
For analysing a model, you do not need the same model as the
actual component. So, before creating the model, you need to
consider the following points to decide which features to be
modeled and which ones to be ignored while performing an
analysis
The minor details that are not important to the analysis can be
avoided in the model.
For symmetric models, you need not to create the complete model.
The main advantages of symmetric model are that you can create the
model easily and generating the finer mesh to get better
results.
There are four types of symmetrical models that are discussed
next
Axisymmetric models are symmetric about their central axes; for
example, cylinders, cones, bulbs, and so on,
In a rotational symmetric model, the repetitive segments are
arranged about the central axis
In a repetitive symmetric model, the repeated segments are
arranged in a straight line
Keypoints are created in the active coordinate system. Keypoints
are the base points for creating other geometric entities such as
line, area, and volume
This option is used to create keypoints using the X, Y, and Z
coordinates. To do so, choose this option; the Create Keypoints in
Active Coordinate System
Modeling > create > keypoints > in active cs
This option is used to create a keypoint on a line in ratio
This option is used to create a keypoint at any existing node To
create a keypoint, choose the On Nodes option from the Keypoints
node; the Create KP on Node dialog box will be displayed and you
will be prompted to select the node on which you want to create the
keypoint
Lines are used to define areas. Some of the line elements; for
example, beams are defined by lines
This option is used to create a straight line between two
keypoints using the global cartesian coordinate system
This option is used to create a straight line between two
keypoints using the active coordinate system
This option is used to create the straight line between two
keypoints on an area
This option is used to create a line tangent to an existing
line. To create a tangent line,choose the Tangent to Line option
from the Lines node; the Line Tangent to Line dialog box will be
displayed and you will be prompted to select a line that will be
tangent to a new line
This option is used to create a line that will be tangent to two
existing lines
This option is used to create a straight line that will be
normal (at 90-degree) to the existing line
This option is used to create a straight line that will be
normal (at 90-degree) to two existing lines
This option is used to create a straight line that will be at a
specified angle to the existing line
You can create an arc by choosing Preprocessor > Modeling
> Create > Lines > Arcs from the Main Menu; the options to
create arcs will be displayed under the Arcs node
This option is used to create an arc using three keypoints
This option is used to create circular arcs using center point
and radius
To create a fillet between two intersecting lines, choose
Preprocessor > Modeling >Create > Lines > Line Fillet
from the Main Menu; the Line Fillet dialog box will be
displayed
You can create an area by connecting keypoints or lines. To do
so, choose Preprocessor > Modeling > Create > Areas from
the Main Menu; the options to create areas will be displayed
To create arbitrary using the Arbitrary option, choose
Preprocessor > Modeling > Create > Areas > Arbitrary
from the Main Menu
This option is used to create an area by specifying
keypoints
This option is used to create an area using the shape of an
existing area
Area created using the Through KPs The overlaid area created
option1
This option is used to create an area using the existing
lines
This option is used to create an area by skinning a surface
through guiding lines
Area created using the By Lines options Area created using the
By Skinning opt
This option is used to create an area offset to an existing
area
The Create Area by Offset From Base Area dialog boxAn offset
area created
Figure shows the rectangular areas. Its various options are
discussed next
This option is used to create a rectangular area on a workplane
by specifying two opposite corners
The Rectangle by 2 Corners The rectangular area created
This option is used to create a rectangular area on a
workplane
This option is used to create a rectangular area on a workplane
by specifying the X andY coordinates of two diagonal points of a
rectangle
The Create Rectangle by Dimensions dialog box
Figure shows the circular areas and its various options
Options for creating the circular areas
This option is used to create a solid circular area on a
workplane
This option is used to create a annular circular area on a
workplane
This option is used to create a partial annulus circular area on
a workplane
The partial annulus circular area
This option is used to create a solid circular area on a
workplane
This option is used to create a solid circular area on a
workplane by specifying the outerradius, inner radius, starting
angle, and ending angle in the graphics area
The Circular Area by Dimensions dialog box
This option is used to create a triangular area on a
workplane
The options to create polygon The Triangular Area dialog box The
triangular area
Meshing in ansys
Element order Element order refers to the polynomial order of
the elements shape functions.
What is shape function ? It is a mathematical function that
gives the shape of results within the element . Since FEA solves
for DOF values only at nodes we need the shape function to map the
nodal DOf values to points within the element . The shape function
represents the assumed behavior for a given element How well each
assumed shape function matches the true behavior directly affects
the accuracy of solution .When you choose an element type you are
implicitly choosing and accepting the element shape function
assumed for that element type . Therefore check the element shape
function before selecting the element .
Linear elements Quadratic elements
Linear variation of quantities
Highly sensitive to element distortion
Acceptable if you are interested in nominal stress results
Quadratic variation of quantities
Can represent curved edges and surfaces more accurately than
linear elements . Not as sensitive to element distortion
Recommended if you are interested in highly accurate results
Mesh densityThe fundamental premise of FEA is that as the number
of elements(mesh density ) is increased , the solution gets more
and more accurate , however solution time and CPU usage also
dramatically increases .
Controlling Mesh densityAnsys provides many tools to control
mesh density both on local and global level .
Global controls Smart sizing Global element sizing Default
sizing
Smart sizing This option determines element sizes by assigning
divisions on all lines , taking into account curvature of line ,
its proximity to holes and other features and element order .To use
smart sizing Goto > mesh tool > turn on smart sizing >
manage meshing density ( 1-10)
Global element sizing This option allows you to specify a
maximum element edge length for the entire model Main menu>
preprocessor> meshing > mesh tool > size controls >
global Using this option with ( smartsizing off) will result in a
uniform element size throughout the volume ( or area ) being meshed
With smartsizing on , this option acts a guide but specified sizes
may be overridden to accommodate line curvature or proximity to
features
default element sizing If you dont specify any controls , ANSYS
uses default sizing , whih assigns minimum and maximum line
divisions , aspect ratio , etc based on element order .
Local controls
Keypoint sizing Line sizing Area sizing
Keypoint sizing Controls element size at keypoints Main menu
> preprocessor > meshing > mesh tool > size controls
set keypoint and set
Setting up different keypoints with different sizes we find
useful to contemplate stress concentration regions . Line sizing
Controls element size at lines Main menu > preprocessor >
meshing > mesh tool ; then select size controls lines and
set
Area sizing Controls element size in the interior of areas .
Main menu > preprocessor > meshing > mesh tool ; select
size controls , areas and set
Types of meshing methods
Free mesh Have no element shape restrictions Suitable for
complex shapes and geometries Smart sizing is preferred Tria and
quad shape for 2d elements and tetra for 3d elements
Mapped mesh Follows regular pattern Not suitable for complex
shapes Smartsizing is not preferred and should be off For areas no.
of edges should be 3 or 4 For volumes no. areas should be 4,5 or 6.
Concatenation This option creates a new line that is combination of
two or more lines . Main menu > preprocessor > concatenate
> lines concatenate
Tri and quad shape for 2d element and brick for 3d elements
Sweep mesh Smart sizing is preferred Only for solids Only brick
shape is available
Volume must be toppologically consistent for sweep meshing eg.
Plate with a hole Tet mesh option for non sweepable volumes Go to
meshing > mesh > volume sweep > sweep options Check the
option tet mesh option for non sweepable volumes
3> Solution-loading and solution
Solution You must first define a Load Step containing set of
boundary conditions as stated above.Then for solution part
Goto solution > solve > current LSWhen you click on solve
, ANSYS performs matrix formulations , multiplications , inversions
. For this purpose there are various solvers in ANSYS
Solvers
The function of solver is to solve the system of linear
simultaneous equations representing the structures degree of
freedom. The solution could take anywhere from a few seconds to
several hours depending primarily on the size of model , the solver
selected and speed of your computer .
A linear static analysis with one load step requires only one
such solution , but a non linear or transient analysis may require
tens , thousands or even thousands of solutions.Therefore the type
of solver you select is very important .
The solvers available in ANSYS can be categorized into four
types-1> Direct Elimination2> Iterative3> Distributed
domain4> Distributed ANSYS
How does solver calculate solution ?The calculation takes place
as shown in following steps
1> Formulate individual element matrices2> Assemble global
stiffness matrix3> Sparse direct solver factorizes the stiffness
matrix , and then calculates DOF solution from
backward-substitution.4> Iterative solver starts with an assumed
zero value for all DOF and iterate to convergence (based on an
input tolerance on residual force )
5> Use element matrices to calculate the element solution
Formulate element matrices
Assemble global matrix .full fie
Solve matrix equation .rst/.rth fie
Follow the guidelines below to choose the solver Main Menu >
Solution > Analysis type > Solution Controls then choose
solution options tab
Direct Elimination solvers are further classified into Sparse
(default) FrontalIf the linear static case of [k]{x}={F} ,Direct
solvers factorizes [K] to solve for [k]-1.Then {x}=[k]-1{F}This
factorization is expensive but is done once .
Iterative solvers further classified into PCG ( Pre-conditioned
Conjugate Gradient ) ICCG ( Incomplete Cholesky Conjugate Gradient
) JCG ( Jacobi Conjugate Gradient ) AMG ( Algebraic Multigrid )
Iterative solvers use a preconditioner [Q] to solve the equation
[Q][K]{x}=[Q]{F} .Assume that [Q]=[K]-1 . In the trivial case ,
[I]{x}=[K]-1{F} . However the preconditioner is not usually [K]-1 .
The closer [Q] is to [K]-1 , the better preconditioning is .However
the preconditioner is not usually [K]-1 , so this process is
repeated hence the name , iterative solver .
For iterative solvers , matrix multiplication is performed .
This is much faster than matrix inversion if done entirely in RAM ,
so as long as the number of iterations is not very high iterative
solvers can be more efficient than sparse solvers . The main
difference between the iterative solvers in ANSYS namely PCG , JCG
, ICCG is the type of pre-conditioner used .
Multiple load steps
By using multiple load steps , you can :isolate the structures
response to each loading condition Combine these responses in
desired fashion during post processing , allowing you to study
different what-if scenarios .
There are 2 ways to define and solve multiple load steps :
Multiple solve method Load step file method
Multiple solve methodAn extension of single load step solution ,
where you solve each load step sequentially without leaving the
solution processor Best suited for batch mode When used in
interactive mode this method is useful only for models that solve
quickly
Load step file methodIn this case instead of solving each load
step , you write the load step information to a file called load
step file : Main menu > solution > load step opts > Write
LS file
After writing all load step files you can solve it by Mein menu
> solution > solve > from LS files to read in each file
sequentially and solve
4> Post processing-Review results and check the validity of
solution
Plotting results :ANSYS provides contour plot , vector plot of
results example stresses , strains , deflection , thermal
temperature , flux and so on .General posrproc > plot results
> contour plot > nodal solution >stress von mises
DMX- Maximum displacement SMX- Maximum stress SMN-Minimum
stress
Query picking Query picking allows you to probe the model for
stresses , displacements or other results quantities at any picked
location You can also quickly locate the maximum and minimum values
of the item being queried . Available only through GUI General
postproc > query results > element or sub grid solution
>ok
Path operations Path operations allows you to : Map results data
onto an arbitrary path through the model Perform mathematical
operations along the path , including integration and
differentiation Display a path plot 1>Define a path Points
defining a path you can use existing nodes or locations on the
working plane Path curvature , determined by active coordinate
systems (CSYS) A name for the path General postproc > path
operations > define path > by nodes Pick nodes from desired
path and O.K. Choose a path name
2>Map data onto a path General postproc > path operations
> map onto path Choose desired quantity , such as SEQV Enter a
label for quantity 3>Plot the data General postproc > path
operations > plot path item > on graph Besides plots and
listings there are many other path capabilities Stress
linearization used in the pressure vessel industry to decompose
stress along a path into its membranes and bending components
Calculus functions used in fracture mechanics to calculate
J-integrals and stress concentration fctors . Dot products and
cross products used in electromagnetic analyses to operate on
vector quantities
Error estimations
Variable viewer Variable viewer is a specialized tool allowing
you to post results with respect to time The variable viewer can be
started by simply opening the Time History Postprocessor Main menu
> time history postproc > variable viewer
Go to add data > select desired node > list data / graph
data
Results viewer The results viewer is a specialized
postprocessing menu and graphic system Fast graphics for large
models Easy to use menu system for quick results viewing General
postproc > write PGR file
Module 1 Structural analysis of beams
TYPES OF BEAMS & TYPES OF LOADINGS
Beam:-A structural member which is acted upon by a system of
external loads at right angles to its axis is known as beam.
TYPES OF BEAMS:-There are five types of beams as under:-
1.Cantilever Beam:-Acantilever beamis one whose one end is fixed
and the other end carries a point or concentrated load.
2.Simply Supported Beam:-A simply supported beam is one which
carries two reaction forces at its two ends & a point load at
its mid-point
3.Overhanging Beam:-It is a type of simply supported beam which
overhangs from its supports.An overhanging beam may overhang on one
side only or on both sides of the supports
5.Continuous Beam:-It is a type of overhanging beam which
consists of a numerous reaction forces and point loads
SOLVED EXAMPLE
1> Defining element typesPreprocessor> element type >
add/edit/delete > add > BEAM 188 The BEAM188 element is
suitable for analyzing slender to moderately stubby/thick beam
structures. This element is based on Timoshenko beam theory. The
degrees of freedom at each node include translations in x,y, and z
directions, and rotations about the x,y, and z directions.
2> Define material properties Preprocessor> material
properties > material model > structural > linear >
elastic > isotropic EX=2E5 ( 2*105) PRXY=.33
3> Define section properties Preprocessor> sections >
beam > common sections B=60H=40
4> Modelling keypoints and lines Modelling > Create >
Keypoints > In active c/s Create Keypt No.1 at (1,0,0)
Create Keypt No.2 at (400,0,0)
Modeling > Create > Lines > In active c/s > Select
Keypt. 1 and Keypt 2
5> Meshing Meshing > Mesh tool > Global > Set No. of
element divisions NDIV. = 10 > Mesh > Select line > OK
6> Viewing Elements Utility Menu > Plot Ctrls > Style
> Size & Shape > Check display of element
7> Applying Loads & Boundary Conditions
Solution>Define Loads> apply > structural>
displacement > on keypoins > select leftmost key point >
DOFs to be constrained > all DOF
8> Applying Loads & Boundary Conditions
Solution>Define Loads> apply > structural>
force/moments > on keypoins > select rightmost keypoint
>direction of force moment Fy ,value of force -2500
9> SolutionSolution> solve > current LS(Load
Step)>OK
10> Postprocessing Generalpostproc > Plot Results >
Deformed Shape > Deformed+undeformed
11> Postprocessing Generalpostproc > Plot Results >
Contour plot>nodal solution > stress > Von-Mises
stress
12> Animating Utility Menu > Plot Ctrls > Animate >
Deformed Results > Stress > Von Mises
No of Frames to create = 20
To be performed by students
Analytical methodFem solution in ansys
Beam orientation theory
The cross section of beam is different from section created in
ANSYS s/w . The main reason for this is difference in orientation
of nodal coordinate system and World Coordinate System . To rectify
this problem we need to orient the orientation keypoint to global Y
axis .
Create a third keypoint i.e. keypt no.3 for orientation at
0,40,0
Go to meshing > mesh tool > element attributes > line
> select line > tick on orientation keypoint to yes
Then continue from step no. 5
Practice questions 1:
F = 5000NEX= 2*105 N/mm2PRXY=.33
Practice questions 2:
Modulus of elasticity = 30 * 106 psiPoisons ratio = .33
Practice questions 3:
EX=1*10^7 psiPrxy=.33
Simply supported beams
Determine reaction loads at A & B and also create Shear
force and Bending Moment Diagrams
Modelling > Create > Keypoints > Keypoint no. 1 at
(0,0,0) and keypoint no. 2 (2.5,0,0) and Keypoint no. 3 (5,0,0)
Modelling > Create lines > From Keypoint 1 to 2 and from
Keypoint 2 to 3
Applying Boundary Conditions Solution > Define Loads >
Apply Structural> Displacement > On keypoints > Select
keypoint no. 1 and 2 > restrict Ux,Uy,Uz,Rotx ,Roty degrees of
freedom
Solution Define Loads > Apply > Structural > Force >
On keypoint no. 2 > Fy=-10000
Viewing reaction loads and S.F. and B.M diagrams
General Postproc > List Results > Reaction Solutions >
All Items
General Postproc > Element Table> Define Table > By
sequence num > SMISC 6 > APPLY > SMISC 19
General Postproc > Plot results > Line Element Results
> SMISC 6 , SMISC 19
How to apply Uniformily distributed loads (udl) ?After meshing
goto utility menu > Plot lines You will see 4 lines with
elements (dashed lines)
Go to apply> structural > pressure on beams > select
line all dashed lines of line 3 > okAfter selection colour will
change to dark yellow
Remaining steps are same from step no. 9
Assignment questions
Ex = 1e11 N/mm^2 Prxy =.33
Ex = 1e11 N/m^2 Prxy =.33
Ex = 1e5psi Prxy =.33
How to apply uniformly varying loads ?
Pressure value at node I = 0Pressure value at node j = 5000
Module 2 Structural analysis of trusses
Trussis astructure comprising one or more triangular units
constructed with straight members whose ends are connected at
joints referred to asnodes. External forces and reactions to those
forces are considered to act only at the nodes and result in forces
in the members which are eithertensile orcompressive forces.
Moments (torques) are explicitly excluded because, and only
because, all the joints in a truss are treated asrevolutes.
In truss members the forces on the members are axial (that is,
they act along the axis of the member), putting them in either pure
tension or pure compression.The members are joined together by
pins.Top of Form
Bottom of FormIn trusses loaded by downward forces, the members
along the top (the top chord) are in compression and the members
along the bottom (the bottom chord) are in tension. The members
connecting the top and bottom chords (the web members) may be
tension or compression, depending on their angles and the
distribution of the loads.Top of Form
Bottom of FormThe forces in the members can be calculated in
several ways. The traditional by hand methods are themethod of
jointsand themethod of sections. For truss analysis via computer,
thefinite element methodis the standard technique.
Element type selection LINK 180
DEFINING REAL CONSTANTS Preprocessor > Real Constants >
Add /Edit/Delete > Add > ok > Area= .1
MESHING ( 1 divisions / line )Preprocessor > meshing >
mesh tool > global size > NDIV = 1
OUTPUT defining element table General postproc > element
table > define table > add SMISC ,1 > apply > LS,1
>ok > close
a> Loads on each member SMISC , 1b> Stresses on each
member LS,1
LISTING RESULTS General postproc > list results > element
table date > select SMISC 1 and LS1 > ok
Assignment questions
Cross section is .01m^2Ex=2e11 n/mm^2Prxy=.33
Cross section is .01m^2Ex=2e11 n/mm^2 Prxy=.33Analyzing bicycle
frame
Module 3 Analyzing Plane stress , symmetricity
Plane stress analysis
The normal stresses (x'andy') and theshear stress(x'y') vary
smoothly with respect to therotationangle, in accordance with
thecoordinate transformationequations. There exist acoupleof
particular angles where the stresses take on special values.First,
there exists an anglepwhere the shear stressx'y'becomes zero. That
angle is found by settingx'y'to zero in the above shear
transformation equation and solving for(set equal top). The result
is,
The anglepdefines theprincipal directionswhere the only stresses
are normal stresses. These stresses are calledprincipal stressesand
are found from the original stresses (expressed in
thex,y,zdirections) via,
The transformation to the principal directions can be
illustrated as:
Maximum Shear Stress Direction
Another important angle,s, is where the maximum shear stress
occurs. This is found by finding the maximum of the shear stress
transformation equation, and solving for. The result is,
The maximum shear stress is equal to one-half the difference
between the two principal stresses,
The transformation to the maximum shear stress direction can be
illustrated as:
ELEMENT TYPE : PLANE 182 , 183
Plane 182 shape
Plane 183 shape
Element behavior k3 to plane stress with thickness
Case study1Analyze the geometry given below first without hole
and then with hole , plot von-mises stress and conclude .
Defining real constants Preprocessor>real constants >
add/edit/delete > add > thickness=.001
Creating areas Modeling > create > areas > rectangle
> by dimensions >
MESHING Meshing> mesh tool > turn smart sizing to 5 >
mesh > select area Note = you can select either tri shape or
quad shape for mesh
Applying loads and boundary conditions Loads > apply >
structural > displacement > on lines > select leftmost
line > restrict all DOFLoads > apply > structural >
pressure > on lines > select rightmost line > Load
pressure value=-1
Output Generalpostproc > plot results > contour plot >
stress > von mises
Creating rectangular geometry with hole
First create rectangle of 300,100 After creating rectangle goto
modeling > create > circle >solid circle > assign
following values
Boolean operation Booleans > operate > subtract > areas
> select rectangle > apply > select circle > ok
Perform the remaining steps of meshing , loads , solution and
postprocessing COMPARISON OF CONTOUR PLOTS WITHOUT HOLE WITH
HOLE
How to create vector plots of stress ?Plot results > vector
plot > predefined > stress > principal s
COMPARISON OF CONTOUR PLOTS
COMPARISON OF vector PLOTS
Conclusion of analysis STRESS CONCENTRATION FACTOR (SCF)Failures
such as fatigue brittle cracking and plastic deformation frequently
occur at points of stress concentration. It is for this reason that
stress concentration factors play an important role in design. The
value of SCFs depend on the shape and dimensions of the component
being designed and can be calculated using finite element methods.
Stress concentrations arise from any abrupt change in the geometry
of a specimen under loading. As a result, the stress distribution
is not uniform throughout the cross-section.
Stress concentration factor k in this example may be defined
as:
(1)0
where x is maximum stress appears around stress concentration
point and 0 is nominal applied stress. For linear-elastic material
behaviour SCF has constant value for any nominal loading. Its value
is varying only with the changing of radius of roundness.
Using reflective symmetry in ansys Consider a rectangular plate
with a hole that is symmetrically loaded and has geometrical
symmetricity about line AB . Here we dont need to model whole
geometry instead we can model half of geometry about AB and apply
symmetric boundary condition about line AB .
Applying symmetric boundary condition
Model half geometry as shown above
First create the half geometry as shown above .Goto loads >
apply > structural > symmetric B.C > on lines > select
line ABApply > structural > pressure > on lines >
select rightmost line > -2000
Remaining steps are same as given in above examples Assignment
questions MODULUS OF ELASTICITY = 2E5 N/MM^2POISONS RATIO=.33The
bracket is loaded uniformily over 150mm line with load of 2625
N/mm
The bracket is loaded with a point load of 2000N at center point
P
axisymmetry
Axisymmetric elements are 2-D elements that can be used to model
axisymmetric geometries with axisymmetric loads These convert a 3-D
problem to a 2-D problem Smaller models Faster execution Easier
postprocessing We only model the cross section, and ANSYS accounts
for the fact that it is really a 3-D, axisymmetric structure (no
need to change coord. Systems)
Modeling To model this We just need this: Modeling To model this
We need this
Note: Axisymmetry is always about Y-axis
To model this
We need this
Note: Axisymmetry is always about Y-axis
The pressure vessel shown below is made of cast iron (E = 2e5
N/mm^2, = 0.33) and contains an internal pressure of P = 35 N/mm^2
. You need to apply symmetric B.Cs to solve this problem . You may
create model or model and apply symmetric boundary conditions .
Note: Axisymmetry is always about Y-axis Radial stress is
SXAxial Stress is Sy Hoops stress is SZ
Analytical results Ansys results
Radial stress (SX) = 35 N/mm^2Axial stress(SY)= 45 N/mm^2Hoops
Stress(SZ)= 125 N/mm^2Deflection = .0458 mm
Thin Cylinders Subjected to Internal Pressure:When a thin walled
cylinder is subjected to internal pressure, three mutually
perpendicular principal stresses will be set up in the cylinder
materials, namely Circumferential or hoop stress The radial stress
Longitudinal stressnow let us define these stresses and determine
the expressions for themHoop or circumferential stress:This is the
stress which is set up in resisting the bursting effect of the
applied pressure and can be most conveniently treated by
considering the equilibrium of the cylinder.
In the figure we have shown a one half of the cylinder. This
cylinder is subjected to an internal pressure p.i.e. p = internal
pressured = inside diameter L = Length of the cylindert = thickness
of the wallTotal force on one half of the cylinder owing to the
internal pressure 'p'= p x Projected Area= p x d x L=p .d.
L-------(1)The total resisting force owing to hoop stressesHset up
in the cylinder walls=2 .H.L.t---------(2)BecauseH.L.t. is the
force in the one wall of the half cylinder.the equations (1) &
(2) we get2 .H. L . t=p . d . L H=(p . d) / 2tCircumferentialor
hoop Stress(H)=(p .d)/ 2t
Longitudinal Stress:Consider now again the same figure and the
vessel could be considered to have closed ends and contains a fluid
under a gage pressure p.Then the walls of the cylinder will have a
longitudinal stress as well as a ciccumferential stress.
Total force on the end of the cylinder owing to internal
pressure= pressure x area= p xd2/4Area of metal resisting this
force =d.t. (approximately)becaused is the circumference and this
is multiplied by the wall thickness
Module 3 analysis of tri-axial stress system
Analyzing 3d geometries
3D ElementsElement type : solid 185
Element type : solid 186
Modeling block Modeling > create > volumes Block > by
dimensions Give values for x1,y1,z1 and x2,y2,z2
Modeling solid cylinders Modeling > create >
volumesCylinder > solid cylinder
WP X ,WP Y are center point of base
Modeling hollow cylinders / annulus Modeling > create >
volumesHollow Cylinder > by dimensions
Offsetting workplanes
Utility menu > workplane > offset workplane by
increments
We are required to place WP at (5,5,10) location from
(0,0,0)Specify increment value along x,y,z directions
rotating workplane
1> Set angle to 90 degrees by scrolling bar to right
2> Rotate clockwise or anticlockwise by using these icons
3> Create solid cylinder
Performing Boolean operations Modeling > operate Booleans
> subtract > select bigger volume > ok >select smaller
volume > ok
Similarly you can perform add operation Modeling > operate
> Booleans > add > volumes > pick all
Modeling assignments
Importing files in ansys Utility menu > file > import >
iges
Goto browse > select file
Import cutter.igs file and bracket.igs file from B1 workshop
input files for practice
ASSIGNMENT QUESTIONS 3-D BracketDescriptionApply loads to the
3-D bracket model below and solve using the Sparse iterative
solver. The model has already been meshed with SOLID95 20-noded
bricks, and Youngs Modulus has been set to 30e6 psi
The meshed model is already provided
Connecting RodDescription Apply loads to the connecting rod
(half-symmetry) model below and solve using the SPARSE solver. The
model has already been meshed with SOLID95 20-noded bricks, and
Youngs Modulus has been set to 30e6 psi.
Meshed model is already provided
Module 4 Dynamic analysis
Dynamic analysis Why dynamic analysis ? Static analysis doesnt
take into account variation of load w.r.t time . Output in the form
of stress , displacement etc w.r.t time could be predicted by
dynamic analysis In static analysis velocity and acceleration are
always zero . Dynamic analysis can predict these variables w.r.t
time/frequency . To determine natural frequency of components . It
is the basic design property and is useful for avoiding resonance ,
reducing noise .
STATIC ANALYSIS DYNAMIC ANALYSIS
Force is static ( dead wt )Force varies w.r.t. time
/frequency
Displacement is static Displacement is function of
time/frequency
No velocity and acceleration due to constant or fixed
displacement F=KX
Velocity and acceleration develops due to variation of
displacement Damping force , inertia force due to velocity &
acceleration
Dx/dt=0
D2x/dt2=0
Hence x and x terms are zero and equation reduces to F=Kx
Solution time is less Solution time is high
Output- stress , displacement Output stress , displacement,
velocity , acceleration w.r.t. time /frequency
MODAL ANALYSISThe purpose of conducting modal analysis is to
determine natural frequency and corresponding mode shapes .
0
FUNDAMENTAL FREQUENCY Fundamental frequency is the first natural
frequency of component .
NATURAL FREQUENCY Natural frequency is the frequency with which
an object once disturbed will vibrate on its own without any
external excitation.
Circular frequency
Where k is constant M is mass Cyclic frequency
After solving k/m we get as EI / ALl4
Engineering application of modal analysis 1> To avoid
resonance When natural frequency of component becomes equal to
frequency of external excitation , it results in amplitude build up
, this phenomenon is known as resonance and causes failure .
2> Physical significance of mode shape Suppose natural
frequency we got is 30 Hz and mode shape is in y direction . If an
external excitation is applied at 30Hz along y direction then
resonance will occur but if external excitation of 30 Hz is applied
along x direction then no resonance will occur .
How to avoid resonance ? To avoid resonance either external
excitation frequency should be changed or natural frequency of
component . Generally we do not have any control on external
excitation frequency and hence practical approach is to alter
natural frequency.
Natural frequency depends on mass (inversely proportional) and
stiffness (directly proportional ) . In practice natural frequency
is altered by changing stiffness rather than mass.
How to change stiffness?
1> Changing the support ( boundary conditions )
Additional support of shaft by one or more bearing increases
stiffness and results in higher natural frequency .2> Add
ribs/stiffners , change thickness , use stiffer material etcWhen
changing the boundary conditions is not possible , other
alternatives like adding ribs , increasing thickness or to use
stiffer materials ( higher E).
Steps involved :-
Preprocessor > material properties > material models >
specify density
Solution > analysis type > new analysis > modal
Solution > analysis options Mode extraction method BLOCK
LANCOZNo. of modes to extract 10No. of modes to expand - 10
When asked for frequency range leave blank as we dont know about
upper and lower limits START FREQUENCY=0END FREQUENCY=0
Several mode extraction methods are available in ANSYS: Block
Lanczos (default) Subspace PowerDynamics Reduced Unsymmetric Damped
(full) QR Damped Which method you choose depends primarily on the
model size (relative to your computer resources) and the particular
application.
CASE STUDY 1
EX=2e5MpaPRXY=.33Density=7830e-9 100mm
300mm
Determine the first 10 natural frequencies of rectangular plate
with 30mm thickness . There are 3 cases 1> Only left end
fixed2> Both end fixed 3> Take E=5e5 Mpa
S.No CASE 1 CASE 2 CASE 3
1
2
3
4
5
6
7
8
9
10
Conclusion :
CASE STUDY 2
Extract the first ten modes of the u-bracket model using the
Block Lanczos method. List the frequencies and plot the von Mises
stress for all the modes. Next, plot the mode shape for the first
mode and then animate it.Material Properties: EX = 30,023,280 psi
PRXY = 0.29 DENS = 7.346344e-3Boundary Conditions: Fix topmost area
(area 17)
Material Selected Structural SteelYoungs Modulus(E)
2.0e+005MpaPoissons Ratio 0.3Density 7.85e-006Kg/mm^3Tensile
Ultimate Strength 460 MpaTensile Yield Strength 250 MpaCompressive
Yield Strength 250 Mp
Determine first 10 natural frequencies of above given components
.
Module 5thermal analysis
Thermal analysis Heat transfer is defined as energy in transit .
Analysis of a system using the laws of heat transfer is named as
Thermal Analysis . Thermal analysis is investigation of the part or
system to calculate heat transfer rate and temperature distribution
.
Element types available in ansys
1-d 2-d 3-d
Link 31Plane 55Brick 8 node 278
Link 33Plane 7720 node 279
All thermal elements have 1 dof/node i.e. temperature .
Thermal loads Convection Heat flux Temperature Heat flow Heat
generation
Output Temperature distribution Thermal flux Thermal
gradient
Types of heat transfer
1> Pure ConductionThe transfer of heat is from a high
temperature to lower temperature . In solids heat transfer is due
to lattice vibration ( translational and rotational ) Fouriers law
governs conduction heat transfer
The temperature gradient been assigned with negative sign as
temperature gradient vector is in opposite direction of heat flow .
The direction of heat transfer will be opposite to temperature
gradient , since net energy is transferred from high temperature to
low temperature .
Heat fluxHeat flux is defined as the amount of heat transferred
per unit area per unit time from or to a surface.
Temperature gradient Atemperature gradientis aphysical quantity
that describes in which direction and at what rate thetemperature
changes the most rapidly around a particular location
Pure conduction case Determine the temperature distribution and
vector plots of heat flux and thermal gradient for the following
fig. Thermal conductivity k=10 W/m K
T=200oc
T=10o0c
T=1000c 20m
10m t=100oc
Selecting element type:Preprocessor > element type > plane
77
Defining material propertiesPreprocessor > material
properties > material models > thermal > conductivity >
isotropic ; KXX=10
Defining loads Loads > define loads > apply > thermal
temperature > on lines ; select 3 lines and apply temperature of
373 (100+273)k and top line with 473 (200+273)
Postprocessing ( plotting temperature plot , thermal flux and
thermal gradient )General postproc > plot results > contour
plot > nodal solution > dof solution > nodal
temperature
Vector plot > predefined > flux and gradient > Thermal
flux
Vector plot > predefined > flux and gradient > Thermal
gradient
Postprocessing ( path operations )1. Defining a path General
postproc > path operations > define path > By nodes Click
2 nodes and choose a path name
Map onto path > dof solution > temperature
Plot path items > on graph > temp
2> Convection Convection heat transfer is due to molecular
movement of fluid such as air or water , when the fluid is caused
to move away from source of heat , carrying energy with it .
Many industrial thermal problems are convective in nature .
Basic governing equation is for convection is Newtons law of
cooling
mixed conduction/convection)Mixed
convection/conduction/insulated boundary condition example is
constrained as shown below . Determine the temperature distribution
and vector plots of heat flux and thermal gradient .
Applying convection Loads > define loads > apply thermal
> convection > on lines/areas > Film coefficient=10Bulk
temperature=100
Problem 3Temperature distribution in a fin cooled electronic
component .This analysis involves heat generation , conduction and
convection Physical prolemAll electronic items generate heat during
the course of their operation . To ensure optimal working of
component , the generated heat needs tobe removed and thus the
electronic component be cooled . This is done by attaching fins to
the device which aid in rapid heat removal .Problem definition For
the sake of simplicity we assume tht electronic circuit is made of
copper with thermal conductivity of 386 W/mK . Also it generates
heat at the rate of 10e6 W. The enclosing container is made of
steel with thermal conductivity of 20 W/m K . The fins are made of
thermal aluminium with thermal conductivity 180 W/m K . There is
convection along all boundaries except the bottom which is
insulated . the film coefficient is 50W/m2 k and Bulk temperature
is 200C .
Glue operationIt attaches 2 or more entities creating common
boundary between them
Without fin with fins
CONCLUSION The vector plot of geometry with fins shows that heat
is dissipates through fins and serves as a channel for heat
dissipation with increased surface area .
transient thermal analysis
Transient thermal analysis determines temperatures and other
thermal quantities that vary over time. Engineers commonly use
temperatures that a transient thermal analysis calculates as input
to structural analyses for thermal stress evaluations. Many heat
transfer applications-heat treatment problems, nozzles, engine
blocks, piping systems, pressure vessels, etc.-involve transient
thermal analyses.A transient thermal analysis follows basically the
same procedures as a steady-state thermal analysis. The main
difference is that most applied loads in a transient analysis are
functions of time. To specify time-dependent loads, you first
divide the load-versus-time curve into load steps.
O/P DESIRED : 1> TEMP VS TIME GRAPH 2> ANIMATION OF TEMP
DISTRIBUTION OVER TIME
STEPS involved :DEFINING element typePreprocessor > element
type > add/edit > thermal mass > solid > 20 node
279
The element is defined by 20 nodes with a temperature degree of
freedom at each node. DEFINING MATERIAL PROPERTIES Preprocessor
> material properties > material models > thermal
conductivity =10 ; density = 7830 ;specific heat = 2.01
Solution New analysis > transient > full
Solution > solution controls ; make following settings Time
at end of load step=5000No. of sub steps=100Automatic time stepping
is OFFIn frequency write every Nth substep
In non-linear tab set line search to ON
Defining thermal loads and initial conditions
Solution > define loads > settings > reference
temperature > 300
Solution > define loads > apply > thermal >
temperature > on areas > select left most area > 500
Solution > define loads > apply > thermal >
convection >on areas > select all area except leftmost Film
coefficient=10Bulk temperature = 305
Solution > solve > current LS
PostprocessingGeneral postproc > results summary
Here we have got collection of 100 result sets as we have
assigned no. of substeps to be 100 , the S/W has performed this by
breaking load step into 100 substeps . Result summary shows all the
results at different time intervals Read results > by pick >
select any of result set > read
Plot results > contour plot > nodal solution > dof
solution > nodal temperature
Plotting temperature vs time graph Goto timehistory postproc
> add > select any node > graph data
Temp vs time plot
Module 6Structural non analysis
Non linear analysis
A nonlinear analysis is needed if the loading on a structure
causes significant changes in stiffness. Typical reasons for
stiffness to change significantly are: Material non linearity
Strains beyond the elastic limit (plasticity) Geometric non
linearity Large deflections, such as with a loaded fishing rod
Contact non linearity Contact between two bodies
When a load causes significant changes in stiffness, the
load-deflection curve becomes nonlinear. The challenge is to
calculate the nonlinear displacement response using a linear set of
equations.
One approach is to apply the load gradually by dividing it into
a series of increments and adjusting the stiffness matrix at the
end of each increment. The problem with this approach is that
errors accumulate with each load increment, causing the final
results to be out of equilibrium.
ANSYS uses the Newton-Raphson algorithm: Applies the load
gradually, in increments. Also performs equilibrium iterations at
each load increment to drive the incremental solution to
equilibrium. Solves the equation [KT]{Du} = {F} - {Fnr} [KT]=
tangent stiffness matrix{u}= displacement increment{F} = external
load vector{Fnr} = internal force vector Iterations continue until
{F} - {Fnr} (difference between external and internalloads) is
within a tolerance.Some nonlinear analyses have trouble converging.
Advanced analysis techniques are available in such cases
This process is repeated for each load increment until the full
external load has been applied. One or more load steps to apply the
external loads and boundary conditions. (This is true of linear
analyses too.) Multiple substeps to apply the load gradually. Each
substep represents one load increment. (A linear analysis needs
just one substep per load step.) Equilibrium iterations to obtain
equilibrium (or convergence) at each substep. (Does not apply to
linear analyses.)
Time and Time Step
Each load step and substep is associated with a value of
time.Time in most nonlinear static analyses is simply used as a
counter and does not mean actual, chronological time
By default, time = 1.0 at the end of load step 1, 2.0 at the end
of load step 2, and so on. For rate-independent analyses, you can
set it to any desired value for convenience. For example, by
setting time equal to the load magnitude, you can easily plot the
load-deflection curve.
The "time increment" between each substep is the time step Dt.
Time step Dt determines the load increment DF over a substep. The
higher the value of Dt, the larger the DF, so Dt has a direct
effect on the accuracy of the solution. ANSYS has an automatic time
stepping algorithm that predicts and controls the time step size
for all substeps in a load step.
Solved Example In this example, we will investigate the behavior
of a cantilever beam under largerdeflection. When the model
undergoes larger deflection, the basic analysis that is oftenused
in ANSYS is no longer sufficient. The load has to be broken down in
to small steps(load steps) and the stiffness matrix is then updated
each tim using the the result from theprevious load step.
Theoretical details on geometric nonlinearity can be found in the
classhandout, hence, we will only focus on how to perform such
analysis using ANSYS here.The model to be analyzed in this example
is illustrated in Figure 1.
Material properties Geometric propertiesLoading
E = 1 x 106 psi
L=100inB=2inH=2.5P=400lb
Loading , meshing , modeling steps will be same as in case of
linear analysis
Goto solution > solution controls
Analysis options : large displacement staticAutomatic time
stepping :ONNumber of substeps : 100Maximum number of
substeps:1000Min. number of substeps :1
Goto nonlinear tab > line search on
ANSYS File StructureSeveral files are created during a typical
ANSYS analysis. Some of thesefiles are in ASCII format while the
others are binary. Brief descriptions ofcommon file types are given
below.
2.5.1 Database FileDuring a typical ANSYS analysis, input and
output data reside in memoryuntil they are saved in a Database
File, which is saved in the WorkingDirectory. The syntax for the
name of the Database File isjobname,db. Thisbinary file includes
the element type, material properties, geometry (solidmodel), mesh
(nodal coordinates and element connectivity), and the resultsif a
solution is obtained. Once the Database File is saved, the user
canresume from this file at any time. There are three distinct ways
to save andresume the Database File: Use the Utility Menu. Click on
SAVE JOB or RESUMJDB button on the ANSYS Toolbar. Issue the command
SAVE or RESUME in the Input Field.
2.5.2 Log FileThe Log File is an ASCII file, which is created
(or resumed) immediatelyupon entering ANSYS. Every action taken by
the user is stored sequentiallyin this file in command format
(ANSYS Parametric Design Language(APDL)). The syntax for the name
of the Log File, which is also saved inthe Working Directory,
isjobname.log. If jobname.log already exists in theWorking
Directory, ANSYS appends the newly executed actions instead
ofoverwriting the file. The Log File can be utilized to: Understand
how an analysis was performed by another user. Learn the command
equivalents of the actions taken within ANSYS.
2.5.3 Error FileSimilar to the Log File, the Error File is an
ASCII file, which is created (orresumed) immediately upon entering
ANSYS. This file captures all warningand error messages issued by
ANSYS during a session. It is saved in theWorking Directory with
the following syntax for the name: jobname.err. Ifjobname.err
already exists in the Working Directory, ANSYS appends thenewly
issued warning and error messages instead of overwriting the
file.This file is particularly important when ANSYS issues several
warning anderror messages too quickly during an interactive
session. The user can thenconsult the Error File to discover the
exact cause(s) of each of the warningsor errors.
2.5.4 Results FilesThe results of an ANSYS analysis are stored
in a separate Results File. Thisfile is a binary file and,
depending upon the Analysis Type, the file'sFUNDAMENTALS OF ANSYS
29extension takes a different form. The following syntax applies to
the ResultsFile name for the selected Analysis Type:Structural
analysis: jobname.rstThermal analysis: jobname.rthFluids analysis:
jobname,rfl
Module 7 Ansys workbench
ANSYS workbench developed by ANSYS Inc. USA is a computer
aidedFinite Element Modeling and Finite Element Analysis tool . In
the GUI of ANSYS workbench user can generate 3D and FEA models
perform analysis and generate results of analysis .You can perform
variety of tasks ranging from Design Assessment to Finite Element
Analysis too complete product optimization Analysis by using ANSYS
workbench .
STARTING ANSYS WORKBENCH To start ANSYS workbench choose Start
> Programs /All programs > ANSYS 14.0> Workbench
The workbench window helps streamline an entire project to be
carried out in ANSYS workbench . In this wwindow one can create ,
manage and view the workflow of the entire project created by using
standard analysis systems
The workbench window mainly consists of Menu Bar , Standard tool
bar , tool box window , project schematic window and status bar
.
Toolbox window This is located on left in workbench window . The
toolbox window lists standard and customized templates or the
individual analysis components that can be used to create projects
. To create a project drag a particular analysis or component
systems from toolbox indow and drop it into the project schematic
window .
Analysis system toolboxThis is displayed expanded in the toolbox
window by default . It contains pre-defined templates for different
types of analysis that can be carried out in ANSYS workbench . Each
predefined component consists of all the components that are used
to perform a particular type of analysis .
Different types of analysis systems are discussed below .Design
assessment : This analysis system is used to perform a combined
solution for static and transient structural analysis . It also
performs post-processing through a script using additional data
associated with geometry
Electric: This analysis system is used to analyze steady state
electric conduction
Explicit Dynamics This analysis system is used to identify the
dynamic response of a component under stress wave propogation , or
time-dependent loads or impacts .
Fluid flow (CFX) This system allows users to carry out flow
analysis of compressible and incompressible fluids .It is also used
to analyze heat transfer in fluids Fluid flow (FLUENT) Like CFX
FLUENT is also used to carry out fluid flow analysis of
compressible and incompressible fluids and their heat transfer
analysis .
Harmonic Response Harmonic response is the response of a system
under a sustained cyclic load . This is used to analyze a system
working under periodic or sinusoidal loads . This analysis helps in
determining whether a particular structure will be withstanding
resonance , fatigue , and other effects of forced civration .
IC engine This analysis systems helps to determine the
performance of the whole system of an IC engine . It takes into
consideration the various fluid properties , moving components ,
and electric and electronic components inside an engine .
Linear Buckling This analysis systems is used to evaluate the
buckling strength of a system under external loads .
Magnetostatics This analysis system is used to analyze the
magnetic field developed due to the presence of a temporary or
permanent magnet .
Modal This analysis system is used to study the dynamic
properties of model , subjected to vibration , determines frequency
and mode shapes .
Random vibration This analysis system is used to determine
reaction of a structure or a component to changing frequencies of
vibrations . Many components experience vibrations which are random
in nature . This analysis systems is used to determine the response
of structure that are exposed to such random vibrations
Random vibration This analysis system is similar to random
vibration analysis system and is used after transient analysis is
done .
Rigid dynamics This analysis system is used to determine the
response of a rigid bodies or mechanisms consisting of rigid bodies
. Response of a robot mechanism is an example of rigid dynamics
.
Static structural This analysis system is used to determine the
response of a structure subjected to static loading conditions .
The loads in this case are assumed to produce no or negligible time
based loading characteristics . Using this type of analysis
displacement , stresses and deformation of structures under static
loading conditions can be determined .
Steady state thermalThis analysis system is used to determine
temperature , thermal gradient , heat flow rates and heat fluxes
under the influence of thermal loading which remains constant with
time and are static in nature .
Thermal electric This analysis system is used to simulate
thermal and electric fields .
Transient structural This analysis system is used to determine
response of structures under the action of time dependent variable
. Using this analysis , time-varying displacement , stresses and
strains can be determined .
Transient thermalThis analysis system is used to determine the
temperature and other thermal variables of a structure that vary
over time .
Component system toolboxThis toolbox is displayed in the
collapsed state in the toolbox window . To expand component system
toolbox , click on (+) sign located on the left of the component
systems title bar . The components displayed in the component
system are basic blocks of a project and form only a part of
analysis system such as geometry , mesh etc .
Custom system toolboxBy default custom system toolbox is also
displayed in collapsed state in toolbox. To expand this node (+)
sign displayed on left of custom system title bar . the system is
used to carry out standard coupled analysis in which the input and
output data of one analysis are used as input for the next analysis
. For example pre-stressed modal system is used to carry static
tructural analysis followed by a modal analysis . Similarly
FSI:Fluid flow (CFX) -> static structural custom system is used
to carry out a fluid flow analysis in CFX followed by a static
structural analysis.
Design exploration toolboxBy default design exploration toolbox
is displayed in collapsed manner in the toolbox window . Expand
this toolbox by following the procedure discussed earlier . The
options in the design exploration toolbox are used to explore a
component , so that the design of component can be further
optimized by changing the design variables based on performance of
the product .
Project schematic windowThe project schematic window helps
manage an entire project . It displays the workflow of entire
analysis project . To add an analysis system into the project
schematic window , drag the analysis system from the toolbox window
and drop it into the green-colored box displayed in the project
schematic window .Alternatively double-click on an analysis systems
in toolbox indo to include it in the project schematic window .
Each time you drag and drop an analysis system or an item into
project schematic window a system is formed . Each system consists
of cells which are used to carry out various tasks within a system
. You can add more than one systems in project schematic window and
can even share data available in cells from one system to other
system .
Menu bar Menu bar is located on top of the workbench window and
contains various options such as file , view , tools and so on .
This option enable you to control and manage the files of the
current project .
Standard tool bar The standard toolbar is collection of the
frequently used tools in ANSYS workbench . The various tools
available in the standard toolbar are New , open , save , save as ,
import , reconnect , refresh project , update project .
Contact analysis
While working on assemblies, the first question would be whether
or not the contact stresses are important. If not, then we can just
bond the surfaces together and can have coarse mesh and be done
with it. But if contact stresses are important and more over
surfaces are opening and closing then we need to look more into
other types (NL) of contacts and finer meshing techniques. The
following types are available in ANSYSMechanical
1. Bonded
2. No Separation
3. Rough
4. Frictionless
5. Frictional
1. Bonded:Both surfaces are bonded like glue. They are not
allowed to separate. Not allowed to Slide. Surfaces will be
together irrespective of gap, penetration, loading and behavior of
other parts/ contacts. We always have some tolerance in our
designs. For example you may have five thousands of gap between two
parts. But if you do not want to move those parts with respect to
each other, you can use bonded contact. It DOES NOT matter how much
is the