PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001 S3-1 MAR120, Section 3, December 2001 SECTION 3 ANALYSIS PROCEDURES.

PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001 S3-1MAR120, Section 3, December 2001

SECTION 3

ANALYSIS PROCEDURES


TABLE OF CONTENTS

Section Page

3.0 Analysis ProceduresOverview ………………………………………………………………………… ………………………………....3-3Distinction Between Perturbation (Linear) And General (Nonlinear) Procedures ………………………….. 3-4Structural Procedures Supported By MSC.Patran Marc Preference………………………………………….

3-7MSC.Marc Analysis Procedures…………………………………………………………………………………..

3-8Structural Analysis Procedures: Linear Static…………………………………………………………………. 3-9Structural Analysis Procedures: Nonlinear Static…………………………………………………………….. 3-10 Structural Analysis Procedures Normal Modes………………………………………………………………. 3-13Structural Analysis Procedures: Frequency Response………………………………………………………. 3-16Structural Analysis Procedures: Buckling……………………………………………………………………… 3-17Buckling: Eigenvalue Problem Formulation…………………………………………….………………………. 3-18Structural Analysis Procedures: Direct Linear Transient…………………………………………………….. 3-19Structural Analysis Procedures: Modal Linear Transient…………………………………………………….. 3-20Structural Analysis Procedures: Nonlinear Transient Dynamics……………………………………………. 3-21 Structural Analysis Procedures Frequency Response………………………………………………………….

3-23Structural Analysis Procedures: Response Spectrum……………………………………………………….. 3-24Structural Analysis Procedures: Creep (Time Dependent Plasticity)……………………………………….. 3-25 Thermal Analysis Procedures: Steady State Heat Transfer…………………………………………………. 3-26 Thermal Analysis Procedures: Transient Heat Transfer……………………………………………………... 3-27More On General And Perturbation Procedures………………………………………………………………...

3-28


OVERVIEW

Discussion of Available Procedures in MSC.Patran

Structural Procedures (MSC.Patran 2001) Thermal Procedures (MSC.Patran 2001) Coupled Thermal-Structural

Procedures (MSC.Patran 2002) Highlights of Theoretical Features Graphical example of analysis for each

procedure


If the structure (1) is deformed after applying a general (nonlinear) procedure it is said that it has arrived to a new base state (2).

A perturbation (linear) procedure leaves the base state unchanged. Thus a modal analysis (for example) of the deformed structure (2) will return different natural frequencies that the same procedure applied to the original structure (1) but leave the base state in (2) unchanged.

A later general procedure will use this base state (2).

Preloaded(new base

state)

Undeformed(original base

state)

The Base State Preloading

DISTINCTION BETWEEN PERTURBATION (LINEAR) AND GENERAL (NONLINEAR) PROCEDURES


If a point of the structure reaches the inelastic region, the curve that represents the stress-strain relation will have in general a slope different to the elastic Young modulus.

A new base state will in general have different points of the structure at different points in the curve. Typically most areas will remain in the elastic region.

A perturbation procedure will use this local tangent to the nonlinear curve as the Young modulus for that part of the structure. As long as the tangent does not separates appreciably from the actual curve, the linear analysis will be correct.

Linear Stress-Strain relation

Nonlinear Materials in Linear Analysis

DISTINCTION BETWEEN PERTURBATION (LINEAR) AND GENERAL (NONLINEAR) PROCEDURES (CONT.)

Linear Perturbation about new base state

E

Nonlinear Stress-Strain relation

new base state


If a nonlinear analysis results in contact or a change in contact conditions between two parts and the condition remains in the new base state, a subsequent perturbation procedure will use the contact as established.

Nonlinear Contact Conditions in Linear Analysis

DISTINCTION BETWEEN PERTURBATION (LINEAR) AND GENERAL (NONLINEAR) PROCEDURES (CONT.)

The contact will not change during or as a result of the linear analysis (the base state is not modified by the perturbation) yet the linear procedure accounts for the contact.

The natural frequencies will often change dramatically due to contact. Therefore the response to a oscillatory excitation may also change dramatically if the new natural frequencies are present in the excitation.


Linear Static Nonlinear Static Normal Modes Euler Buckling Direct Linear Transient Modal Linear Transient Nonlinear Transient Frequency Response Spectrum Response Creep

STRUCTURAL PROCEDURES SUPPORTED BY MSC.PATRAN MARC PREFERENCE


MSC.MARC ANALYSIS PROCEDURES

Thermal procedures supported by MSC.Patran Marc Preference

Steady State Heat Transfer Thermal Heat Transfer


STRUCTURAL ANALYSIS PROCEDURES:LINEAR STATIC

Inertia effects are neglected

Model response defined by linear elastic stiffness at the base state (the state of deformation and stress at the beginning of the step)

For Hyperelastic and Hyperfoam materials: Base step

Contact Conditions cannot change during step


1

2

3

4

STRUCTURAL ANALYSIS PROCEDURES:NONLINEAR STATIC

Solves problems where there are one or more of up to the three forms of nonlinearity:

Material Nonlinearity Geometrical Nonlinearity Boundary Nonlinearity (Contact)

and for which time is not a variable


Incremental-iterative solution with automatic “Adaptive” control or “Fixed” (constant fractional incrementation) control.

The increments represent load incrementation rather than time incrementation.

Advanced optional user control include various criteria to drive the Adaptive procedure.

STRUCTURAL ANALYSIS PROCEDURES: NONLINEAR STATIC (CONT)


Basic method based on Newton-Raphson and related techniques (discussed later)

Additional methods based in the Arclenth method (discussed later)

Generally, coupled nonlinear equations for each degree of freedom

Basic statement of equilibrium: Balance between internal forces {I} and external forces {P}:

{K}{u} - {P} = 0

{I} = [K]{u}

Generally, coupled nonlinear equations for each degree of freedom

STRUCTURAL ANALYSIS PROCEDURES: NONLINEAR STATIC (CONT)


Uses eigenvalue techniques to extract the frequencies of vibration of the structure

Generally,

(-2[M] + [C] + [K]){} = 0

where: = circular frequency = mode of vibration

associated to

[M],[C],[K] = Mass, Damping, and Stiffness Matrices

Basic method based on Newton-Raphson

STRUCTURAL ANALYSIS PROCEDURES: NORMAL MODES


In this metal forming example a tube is (step 1) deformed plastically, then (step 2) unloaded. Subsequently one may (step 3) extract the natural frequencies and associated modes. In the same job we may (step 4) apply other loads on a nonlinear static procedure thus deforming the tube past its previous base state and possibly without producing additional plastic strain yet reaching another base state. Without unloading we would (step5) extract the natural frequencies corresponding to the base state reached at the end of the previous nonlinear step 4.

STRUCTURAL ANALYSIS PROCEDURES: NORMAL MODES (CONT)

Uses the stiffness of the base step, so that small vibrations of a preload condition (previous step) can be modeled.


STRUCTURAL ANALYSIS PROCEDURES: NORMAL MODES (CONT)

A number of “Linear Perturbation” procedures require having run a previous Natural Frequency step.These are:

Modal Linear Transient Frequency Response Spectrum Response Viscoelastic (Frequency Domain)

In MSC.MARC, [C]=0 for the

purpose of computing Methods available: Inverse Power

Sweep and Lanczos algorithms Example: One- and Two-DOF

Spring-Mass-Dashpot Systems


For the cantilever beam shown here (figure at top), and a cosine (Harmonic) forcing function presented as a tip load, the Frequency Response procedure finds a solution that matches the theory. The first natural frequency is 325 Hz

Plotting the tip displacement magnitude as a function of the frequency of the harmonic excitation (figure at bottom) one can clearly see the static solution and the resonance when the first natural frequency is reached.

Resonance

Static solution = 0

STRUCTURAL ANALYSIS PROCEDURES: FREQUENCY RESPONSE


buckling

STRUCTURAL ANALYSIS PROCEDURES: BUCKLING

Classical “Euler” buckling. Eigenvalue and critical load estimates.

“Stiff” Structures. (they carry loads primarily by axial or membrane actions)

“Snap-through” problems. (they have large displacements/rotations and small strains)

These should not be solved with this procedure. Instead, use the Nonlinear Static procedure with the RIKS method option.


Bifurcation buckling is useful for “Stiff” structures. The method is not suitable if large geometry changes occur prior to buckling. Material is assumed to be linear elastic before buckling.

The method can provide misleading results if the structure is imperfection sensitive.

If results are questionable, run a Nonlinear Transient Dynamics analysis or preload the structure with a Nonlinear Static procedure.

BUCKLING: EIGENVALUE PROBLEM FORMULATION

Structure under “dead load” P0, stiffness [K0]

A “live” load is added, equal to lDP. As long as the response is stiff and linear elastic, the stiffness changes to [K0] + l[DK]

This poses the eigenproblem:([K0] + l[DK]){v} =

{0} Nontrivial solutions lcr define the

Critical Buckling Load P0 + lcrDP


I M u·· C u· K u + +=

STRUCTURAL ANALYSIS PROCEDURES: DIRECT LINEAR TRANSIENT

Integrates equations of motion through time

Various integration methods available: Newmark, Houbolt, Central Difference, Fast Explicit, Single Step Houbolt


Computationally inexpensive

where = Eigenmode = amplitude of

mode

STRUCTURAL ANALYSIS PROCEDURES: MODAL LINEAR TRANSIENT

Provides the model response as a function of time based on a given time dependent loading

The number of modes used is a matter of user judgment

More Modes = More Accurate Less Modes = Less Expensive

qu nn

q

na


STRUCTURAL ANALYSIS PROCEDURES: NONLINEAR TRANSIENT DYNAMICS

Same definitions as for Nonlinear Static, except:

Internal forces here include inertial and damping forces, not just stiffness forces

}]{[}]{[}]{[}{ uKuCüMI


STRUCTURAL ANALYSIS PROCEDURES: NONLINEAR TRANSIENT DYNAMICS (CONT)

Same time operators used for Direct Linear Transient, Fixed Increments.

In addition, Adaptive Incrementation is available for Newmark, Fast Explicit, and Single Step Houbolt time integration methods.


Excitation must be Stationary, thus

and ergodic (different samples of the excitation yield the same time average)

STRUCTURAL ANALYSIS PROCEDURES: FREQUENCY RESPONSE

Steady State Response to a continuous excitation containing a specified set of frequencies.

Requires previous Normal Modes analysis.

))(())(( txftxf


STRUCTURAL ANALYSIS PROCEDURES: RESPONSE SPECTRUM

Inexpensive approach to estimating the peak response of a model subjected to “base motion”. Behavior is assumed to be linear.

total response = relative response excitation + base motion

Useful for seismic analyses of buildings

Setting up in MSC.Patran requires the input of a non-spatial Field (frequency dependent) representing the Spectrum.

}]{[}]{[}]{[}]{[ buMuKuCüM

}{}{}{ bt uuu


STRUCTURAL ANALYSIS PROCEDURES: CREEP (TIME DEPENDENT PLASTICITY)

Analysis of materials described in the CREEP Material form.

Explicit and Implicit procedures. Adaptive or Fixed incrementation. Relative and Absolute accuracy control.


A non-physical “time” incrementation is used to allow

management of prescribed temperatures and fluxes through

the analysis and control the output accordingly

THERMAL ANALYSIS PROCEDURES: STEADY STATE HEAT TRANSFER

Independent from stress and deformation state

May include conduction, boundary convection and radiation

May include gap radiation, conductance, and heat generation between contact surfaces

May be linear or nonlinear

“Steady State” means that the rate of change of temperature is null all over the domain.


THERMAL ANALYSIS PROCEDURES: TRANSIENT HEAT TRANSFER

Temperature rate is significant Time incrementation

corresponds to physical time. Automatic time incrementation

optional user control Transient results may be used

for a sequentially coupled thermo-structural transient analysis (the stress and deformation depend on the transient temperature field but the opposite is not necessarily true).


MORE ON GENERAL AND PERTURBATION PROCEDURES

A General analysis procedure is one in which nonlinear effects are included. The response is generally nonlinear, but one may obtain a linear response using a nonlinear procedure.

The starting condition of a general step is the ending condition from the

last general step Total time increases throughout the general, nonlinear analysis Each step also has its own time, which begins at zero in each step The “step time” may have actual physical meaning or not Nonlinearity requires us imagining what will happen to properly planned

meshing, loading, and sequencing.


Example:

Step 1: Nonlinear Static: Apply P = 500 Lb load (with contact condition)

Step 2: Natural Frequency extraction

Step 3: Nonlinear Static: Heat the beam (Thermal Expansion, changing area of contact)

Step 4: Natural Frequency extraction

Where does the contact happen?

To the right of the circle’s top.

A Perturbation analysis procedure is one in which a linear response is computed about a “base state”. The response is always linear, but the base state may be the result of a previous nonlinear step.

1. To the left of the circle’s top ?

2. On the circle’s top ?

3. To the right of the circle’s top ?

MORE ON GENERAL AND PERTURBATION PROCEDURES(CONT.)


A Nonlinear Transient Dynamics step may not be interrupted to perform a perturbation analysis. Before performing a perturbation analysis, the structure must be brought into

static equilibrium.

Nonlinear effects may only be included in the base state for a linear perturbation step


The starting condition of a perturbation step is the ending condition from the last general step - if there was any - or the undeformed structure. This is the “base state”.

The ending condition of a perturbation step will be ignored by subsequent perturbation steps. That is, the structure reverts to the “base state” at the end of the perturbation step.

The step time of linear perturbations is never accumulated into total time

Procedures that are General: Nonlinear Static Nonlinear Transient

Dynamic



Plasticity and other inelastic effects are ignored during the perturbation

Hyperelastic properties will be used by their value at the base state

Contact conditions cannot change during the perturbation

Frictional slipping is not allowed during the perturbation

Purely perturbation analysis cannot be simulated with alternative general procedures but may be preloaded to a modified base state.

The following procedures are considered “purely” linear perturbation analyses:

Bifurcation Buckling Natural Frequency Modal Dynamics Response Spectrum Direct Steady State

Dynamics Modal Steady State

Dynamics



Other analyses may be performed in principle by either general or perturbation procedures, although using alternative procedures

Creep (Requires preloading with Nonlinear Static) Buckling Collapse using Arc Length method (Nonlinear Static procedure)

PAT328, Section 3, March 2001MAR120, Lecture 4, March 2001 S3-1 MAR120, Section 3, December 2001 SECTION 3 ANALYSIS PROCEDURES.

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