ansys nonlinear convergence best g practices
TRANSCRIPT
ANSYS Nonlinear Convergence Best g
Practices
Peter R. Barrett, P.E.September 27, 2012
Rev. 2/3/2016
© 2016 CAE Associates
Rev. 2/3/2016
ANSYS Nonlinear Convergence Best Practices
Nonlinearities Overview:— Large Deflection— Material Nonlinearities— Contact
Characterize Convergence Difficulty with Examples— Relatively Straight Forward (easy) Problems— Challenging (i.e. really hard) Problems
Step-by-Step Convergence Procedurep y p g1. Rigid body motion2. Force balance not obtained3. Material Instabilities and/or Element formulation error3. Material Instabilities and/or Element formulation error
Q&A
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All Products Exhibit Nonlinearities
Always start with the simplest linear analysis if possible! Always start with the simplest linear analysis if possible!
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Large deflection Affects Stiffness
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Material properties cannot always be assumed to be linear
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Contact is the most common source of nonlinearity and often the most difficult to solve! solve!
SStatus changes, friction, pressurepressure
When where?
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When, where? What is the pressure?
Characterize Convergence Difficulty Easier Problems
D f ti l ti l ll— Deformations are relatively small— Nonlinear strains (plasticity, creep, swelling) are small— Contact status does not oscillate
M d l ll d i lifi d (2D A i t i )— Models are small and simplified (2D, Axisymmetric)— Symmetric boundary conditions are utilized— Displacement based loads
L d lt i t il b t— Loads result in tensile member stresses— Nonlinear buckling to the point of instability (Post buckling not needed)
409 Parts967 Contact Pairs409 Parts967 Contact Pairs409 Parts967 Contact Pairs
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Characterize Convergence Difficulty Harder Problems
V l d f ti— Very large deformation— Large strains with large distortion— Contact chatter and/or loose fitting assemblies
C t t lidi ith hi h f i ti ffi i t— Contact sliding with high friction coefficient— Post buckling response— Large 3D models with complex geometry
N t b d i— No symmetry boundaries— Force based loads
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Pin Insert Model Hard Solution
— Model the entire Pin / socket assembly— Mesh fine enough to capture local
stress concentrations— Use a force based analysis to model
pin insertion and removal— Determine critical locations / load
stepssteps Easier Solution
— Model a single axi-symmetric Pin/Socket assemblyPin/Socket assembly
— Create mapped mesh with refinement on contact surfaces and areas of high stress
— Use a displacement controlled solution— Use auto time stepping and smart
output controls since max stress might
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not occur at the final solution step
Gasket Assembly
Hard Problem Hard Problem— Large model— Complex loading sequence
Multiple bolt loads— Multiple bolt loads— Frictional Contact— Nonlinear material response
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Automatic contact reduces modeling time
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Building Collapse Simulation
Running an analysis dynamically can be used to obtain convergence Running an analysis dynamically can be used to obtain convergence— Evaluating the thermal-structural response of the World Trade Center collapse
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Elastomeric Bearing with Lead Plug
Force Deflection of a Single Truss ElementElement Matches Detailed 3d Model
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Clevis Pin Pullout
Springs can be used to imposed loads and/or prevent rigid body motion
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Surgical Staple – Displ. Controlled Example
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ANSYS Nitinol Material Behavior Complex Material Response requires many substeps for
daccuracy and convergence
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Rubber boot with self-contact
Combined Geometric, Material and Contact Nonlinearities
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Vena Cava Filter
IVC filters are used in case of contraindication to anticoagulation I.e. – it captures clots!
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FSI Example – Vena Cava Filter
Nonlinear structural response coupled with fluid flow
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FSI Example – Vena Cava Filter
StreamlinesStreamlines
Deformation
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My analysis did not converge. Now what?
First step is to determine the cause: First step is to determine the cause:1. Rigid body motion2. Force balance not obtained3 Material Instabilities3. Material Instabilities4. Element formulation error5. Combination of items 1-4 above
We will examine each in detail including:— identifying the problem
d t i i th— determining the cause— providing solutions
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Understanding the Solver Output
Whether in WB or Mechanical APDL the first step is to read the output file Whether in WB or Mechanical APDL, the first step is to read the output file to determine the origin of the non-convergence
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Rigid Body Motion error messages DOF limit exceeded. Negative main diagonal. Small/Negative Pivot error. MAX DOF INC = “A very large number”
*** WARNING *** CP = 11.703 TIME= 16:15:15Smallest negative equation solver pivot term encountered at UX DOF of node 98. Check for an insufficiently constrained model.
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Examples of Rigid Body Motion cont.
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Causes of Rigid Body Motion
Insufficient supports— Insufficient supports— Individual parts of an assembly are not supported. This is the most common
form that is found in a contact analysis where rigid body motion occurs in the parts not associated with any supports.
— Insufficiently connected dissimilar element types (i.e. beams to solids, etc.)
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Find the Rigid Body Motion
Plot the unconverged or last converged displacement solution and verify Plot the unconverged or last converged displacement solution and verify displacement scaling
— The example below is a converged solution where the rigid body motion is only restrained by weak springsrestrained by weak springs
— Note the unrealistic 10e-6 displacement scaling
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Use modal analysis to find Rigid Body Motion
If it is not clear what constraint is required to eliminate rigid body motion a If it is not clear what constraint is required to eliminate rigid body motion, a modal analysis can be performed.
— A modal analysis determines the vibration modes including rigid body motion.Each rigid body mode is predicted as a zero frequency mode— Each rigid body mode is predicted as a zero frequency mode
— Animating the zero frequency mode shape illustrates the rigidly moving model.
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Correct the rigid body motion— Take advantage of symmetries
— Axisymmetry— Rotational— Planar or reflective— Repetitive or translational
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Correct the rigid body motion
Isolate the error by creating a smaller simpler model – KISS!Isolate the error by creating a smaller simpler model KISS!— Make a 2d Sector model— Delete/Suppress parts or fix DOF until you get an answer
Add supports and/or use displacement controlled solution Add supports and/or use displacement controlled solution— Adding a rigid region and pushing it with displacements will usually converge
better than a force loading.
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Correct the rigid body motion
Use bonded contact for debugging Use bonded contact for debugging— If interfaces are all in compression, one might be able to leave as bonded— Modify to standard contact one pair at a time
Adjust the parts to all start in contact Adjust the parts to all start in contact— Can use adjust to touch ANSYS option, but be careful since the geometry will
be changed Increase pinball region Increase pinball region
— Corrects interference fits Add friction
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Correct the rigid body motion Avoid mistakes from wrong assumptions
— Make sure to include large deflections when displacements are significant• You can never get the wrong answer by adding large displacement effects
— Check Displacement Scaling
Large deflections included!
Li l ti
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Linear solution
Correct the rigid body motion
Use bonded contact to tie dissimilar Use bonded contact to tie dissimilar element types
— Example Shells or beams to solidsUse MPC contact option to eliminate— Use MPC contact option to eliminate iterations and penalty stiffness dependency
Add/adjust weak spring stiffnessBe sure to check reactions to make sure no— Be sure to check reactions to make sure no error is introduced
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Correct the rigid body motion Add Contact Stabilization Damping Rigid body motion often can occur in the beginning of a static analysis due
to the fact that the initial contact condition is not well established.
FnFn
Contact
Ft
dudP nndn
Target
Contact
22
11
udPudP
td
td
Pdn
Pd1,d2
Contact Stabilization introduces a viscous damping traction proportional to b t it t th l ti d l iti b t th t fbut opposite to the relative pseudo velocities between the two surfaces along contact normal and/or tangential directions.
Where: = damping coefficient in normal directiondd n
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= damping coefficient in tangential direction= pseudo velocityu
d t
Contact Stabilization Damping
Example: Consider a fixed pin interfacing with a hole in plate with initial Example: Consider a fixed pin interfacing with a hole in plate with initial radial clearance and under a force based load
— Stabilization captures localized stress distribution more accurately because it does not change the shape of the pindoes not change the shape of the pin
Conventional Adjust to Touch Contact Stabilization Damping
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Correct the rigid body motion
Buckling Response— Nonlinear stabilization
• Local instabilities and global instability. U d t th ith li h d• Used together with line search and automatic time stepping
— Arc-length method• Circumvent global instability when g y
forces are applied. • Simulate the negative slope portion
of a load-vs.-displacement curve.R nning a static problem as a— Running a static problem as a "slow dynamic" analysis in ANSYS
— Running a static problem as a "slow dynamic" analysis inslow dynamic analysis in ANSYS/LS-DYNA
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Connections that prevent Rigid Body Motion
Automation tools can save a lot of time in tying assemblies together Automation tools can save a lot of time in tying assemblies together
Constraint equations
Springs
Spot Welds
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Beam connections
Examples of Force equilibrium not obtained
Definition: Definition:— Convergence value is greater than criterion after min. load increment and max.
number of iterations are solved
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Equilibrium Iterations
A nonlinear structure is analyzed using an iterative series of linear A nonlinear structure is analyzed using an iterative series of linear approximations, with corrections.
ANSYS uses an iterative process called the Newton-RaphsonMethod. Each iteration is known as an equilibrium iteration.
F
Load
3 4 A full Newton-Raphson
1
23
iterative analysis for one increment of load. (Four iterations are shown.)
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u Displacement
Convergence Procedure
The difference between external and internal loads {Fa} {Fnr} is called The difference between external and internal loads, {Fa} - {Fnr}, is called the residual. It is a measure of the force imbalance in the structure.
The goal is to iterate until the residual becomes acceptably small; less than the criterion, where the solution is then considered converged.
When convergence is achieved, the solution is in equilibrium, within an acceptable toleranceacceptable tolerance.
Fa
{{Fa} {Fnr}
Fnr{
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u
Newton Raphson Residuals
Plot Newton Raphson Residuals to determine critical contact pair Plot Newton Raphson Residuals to determine critical contact pair— Note that these controls need to be activated prior to the solution
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Causes of Force balance not obtained
Contact Stiffness is too large Contact Stiffness is too large Load is stepped too rapidly For small load increments, MINREF criterion exceeded Material instability Buckling
Definition of non-convergence, sum of R (unbalanced forces)
t b l 5% f thnever gets below .5% of the sum of F (sum of external loads, reactions, etc.))
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Ideal Load Stepping
Convergence after 3 to 5 iterations each substep Convergence after 3 to 5 iterations each substep— Use more substeps to reduce iterations, use less if only one or two are
needed. (One exception: If contact without friction is the only nonlinearity, sometimes one substep with lots of iterations can be an efficient solution pmethod)
LoadLoadLoad Step 2
Load Step 123 4
Load Step 1
Substeps1
2 equilibriumiterations
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“Time”
Causes of Force balance not obtained Contact Stiffness is too large. Note: In V16 and beyond default stiffness
h b d d b b t f t f 10 f i ihas been reduced by about a factor of 10x from previous versions. Oscillation of contact status & force balance caused by contact stiffness.
— A typical range of ANSYS penalty stiffness is .01 to 10 times the ANSYS i t l tiff l hi h i f ti f t i l d h b t tinternal stiffness value which is a function of material and mesh but not geometry
F=KU
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Causes of Force balance not obtained Load is stepped too rapidly
U Mi M d t ti b t t l t i Y Use Min, Max and starting substep control to improve convergence. You cannot get the wrong answer by adding too many substepsLoad
TimeIncorrect
Strain Energy
tmaxtstart tmin
Rule of Thumb:The more nonlinearities, the more substeps required
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Overcome the Force Unbalance
Nonlinear Solution Corrective Action ANSYS WB Mechanical offers a toolbox of options under the analysis
settings branch for achieving successful convergence. — Step Control - Load steps and substepsp p p— Nonlinear Controls - N-R convergence criteria
— Contact Settingsg
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Overcome the Force Unbalance
Reduce Normal Stiffness Factor Reduce Normal Stiffness Factor
Increase the number of Substeps Increase the number of Substeps— General Rule – more nonlinearities – use more substeps
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Overcome the Force Unbalance
Change contact stiffness update• Recommend using iteration based adjustments• Try Aggressive Update for tough problems
Ramp on the interference fit
Use Higher Order Elements• Especially with curved surface contact
Refine the mesh• The more points in contact the better the convergence
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Overcome the Force Unbalance
Increase the MINREF criterion• If the criterion is very small this will not effect the solution accuracy
Extend the Stress-Strain curve
Adjust the convergence tolerance• If the unbalance force difference is very small this can increase solution speed
i ifi tlsignificantly
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Review Initial Contact Settings and eliminate gaps
See the ANSYS output file or run CNCHECK before solving See the ANSYS output file or run CNCHECK before solving
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Adjust Contact Pinball Region
Default pinball region is different based on analysis type (see below) Default pinball region is different based on analysis type. (see below) — Increase for large initial penetrations
Default PINB*
Contact Classification
Contact Surface Behavior
Initial Penetration Behavior KEYOPT(9)
3 x Depth** Rigid/Flex Standard Default (Include Everything)4 x Depth Rigid or Flex Standard Include Everything/with Ramped effects2 x Depth Flex/Flex Standard Default (Include Everything)
0.50x Depth Flex/Flex Bonded or No Separation Default (Include Everything)0.75x Depth Rigid/Flex Bonded or No Separation Default (Include Everything)p g p ( y g)1.00x Depth Rigid/Flex Bonded or No Separation Include Everything/with Ramped effects
**Depth = Underlying element depth (for solid elements)* Values are for NLGEOM,ON and are reduced by 50% for NLGEOM,OFF
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Depth Underlying element depth (for solid elements)**Depth = 4 x element thickness (for shells and beams)
Surface Projection Based Contact
More accurate distribution of contact stresses More accurate distribution of contact stresses. Satisfies moment equilibrium when an offset exists between contact and
target surfaces with friction. Can help ith contact con ergence Can help with contact convergence.
Better handling of sliding contact. KEYOPT,<contact element type>,4 ,3
Default Contact Settings Surface Projection Contact
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Examples of Material Instabilities
Depending upon the size of the residual these can be caused by large Depending upon the size of the residual these can be caused by large force unbalance or can be a result of incorrect material properties
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Causes of Material Instabilities
Force balance not obtained Force balance not obtained— Material law cannot handle large load and/or time increment. If the force
unbalance is very large, the material model might not be the problem— Element distorted shape results in negative volume calculation Check theElement distorted shape results in negative volume calculation. Check the
mesh, but again with very large force unbalances the material model might not be the problem
Too large of plastic or creep strain increment— Max. increment can be adjusted as part of cutback controls, but typically force
balance is the controlling criterion and thus this is rarely changed.
Elements with mixed u-P constraints not satisfied— Modify the Volumetric Constrainty
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Causes of Element Formulation Errors
Element Shape distortion Element Shape distortion Excessive strain Volumetric locking (PLESOL,NL,HPRES) Hourglass modes
— Using Higher order elements or change to enhanced strain to eliminate reduced integration issues in lower order elementsintegration issues in lower order elements
Buckling— Reduce rate of loading
V l f b l Very large force unbalance
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Correct Element Formulation Errors
Mechanical APDL commands Mechanical APDL commands— Use CHECK command for overall verification including missing elastic
properties, unconstrained model, and element shape checks.— MCHECK command can help you identify defects in the mesh such as holes orMCHECK command can help you identify defects in the mesh such as holes or
cracks.
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Correct Element Formulation Errors Make sure to use the correct material input Make sure to input True Stress vs. Log Strain
— Conversion from engineering data , :
11ln Always extend your material law will beyond
expected strain levels
1 1ln l
p
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Element Selection
Use Higher Order elements for curved surface contact for faster more Use Higher Order elements for curved surface contact for faster, more accurate results
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20 node bricks
Solver Type and Tolerance
Suggest using Direct (Sparse) solver unless PCG is significantly faster per Suggest using Direct (Sparse) solver unless PCG is significantly faster per iteration
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Correct Element Formulation Errors
Add intermediate substepsp Rezoning
— Generally only used for very large strain cases like forming operations or seals Adjust the starting mesh shapes – this is the most common solution Adjust the starting mesh shapes this is the most common solution Change Element type / formulation Use shell or beam elements
Faster and more efficient sol tions here applicable— Faster and more efficient solutions where applicable Test with 1 Element model
— Change the HyperElastic material modelf ff— Modify creep law or coefficients
Start mesh shape so that deformed elements become more square
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Element type selection
Select the appropriate element type to maximize results efficiency and Select the appropriate element type to maximize results efficiency and quality
Simple is almost always better and definitely easier to debug
Complex 3-D geometries
Slender structures (twisted pipe
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Shell elements (twisted pipe model)
Remesh the model part way through the analysis
Rezoning Rezoning— Automatically map existing stresses and strains so that the solution history is
preserved
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Change material models
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Hyperelastic material models
Yeoh is very robust for large strain problems such as seals Yeoh is very robust for large strain problems such as seals
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The value of the one element test case
Testing nonlinear material models— Make sure the material converges for all stress / strain levels expected with the
one element model before running full model— Especially critical step for hyperelastic and creep analyses
Testing of macros and user-defined routines Evaluation of the impact of large aspect ratios, skew angles or warped
elements
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Element Shape
Robust well shaped elements can improve solution convergence and time Robust well shaped elements can improve solution convergence and time
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Mesh Controls
Numerous controls are available to locally modify the mesh to reduce Numerous controls are available to locally modify the mesh to reduce stress gradients through multiple elements
— Example showing the value of symmetry
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Mesh refinement
Automated mesh refinement will increase the solution quality and Automated mesh refinement will increase the solution quality and sometimes speed
— Automated mesh refinement in workbench is generally only used in linear analysesanalyses
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Element Formulation
Solver Output records the element technology being activated based on Solver Output records the element technology being activated based on the element order chosen (midside nodes) and the material association. Workbench uses higher order 2d elements by default
Elastic material or Elastic material or metal plasticity with higher order elements
Default URI2D Plane StressElastic material or Metal Plasticity with lower order elements
Default URI
Enhanced Strain2D Plain StrainElastic material or Metal Plasticity with
Enhanced Strain
Fully incompressible hyperelasticity with h h l
lower order elements Simplified Enhanced Strain
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higher or lower order elements B-Bar with Mixed u-P
You have a solution!
How do you make the solution more efficient? How do you make the solution more efficient? Change the mesh
— Refine areas of steep gradientC h t l— Coarsen areas where stresses are low
— Adjust initial element shapes to create better deformed shapes Change the Substep settings
— Add substeps to reduce bisections— Reduce substeps where convergence takes 1 or 2 iterations max.
Include Material Nonlinearities?
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Improve Performance in Subsequent Analyses
The Force Convergence graph clearly indicates that starting with more The Force Convergence graph clearly indicates that starting with more substeps would eliminate the 27 iterations performed before the first bisection. Reducing the starting number of substeps might eliminate this bisectionbisection
Force Residual vs. Iterations
Time vs. Cumulative Iteration
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Thoroughly investigate your results
List and plot results to check to make sure you solved the problem List and plot results to check to make sure you solved the problem intended and that the results make sense
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Check the quality of your results - forces
First check should always be a free body diagram First check should always be a free body diagram
Applied loads
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Matching reaction forces
Check the quality of your stress results
Comparing average vs un-average stresses can provide an estimate of Comparing average vs. un-average stresses can provide an estimate of mesh error
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Understand the data generated
Displacements are based on original coordinate system Displacements are based on original coordinate system Stresses and strain component data rotate with the elements
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Need more information?
Additional Information on all of these topics is available in the ANSYS Help Additional Information on all of these topics is available in the ANSYS Help or through mentoring or training classes
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