ANSYS Nonlinear Convergence Best Practices

Transcription

1 ANSYS Nonlinear Convergence Best Practices Peter R. Barrett, P.E. September 27, 2012 Rev. 2/3/ CAE Associates

2 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 p Convergence Procedure 1. Rigid body motion 2. Force balance not obtained 3. Material Instabilities and/or Element formulation error Q&A 2

3 All Products Exhibit Nonlinearities Always start with the simplest linear analysis if possible! 3

4 Large deflection Affects Stiffness 4

5 Material properties cannot always be assumed to be linear 5

6 Contact is the most common source of nonlinearity and often the most difficult to solve! Status changes, friction, pressure When, where? What is the pressure? 6

7 Characterize Convergence Difficulty Easier Problems Deformations are relatively l small Nonlinear strains (plasticity, creep, swelling) are small Contact status does not oscillate Models are small and simplified (2D, Ai Axisymmetric) ti) Symmetric boundary conditions are utilized Displacement based loads Loads result in tensile member stresses Nonlinear buckling to the point of instability (Post buckling not needed) 409 Parts 967 Contact Pairs 7

8 Characterize Convergence Difficulty Harder Problems Very large deformation Large strains with large distortion Contact chatter and/or loose fitting assemblies Contact t sliding with high h friction coefficient i Post buckling response Large 3D models with complex geometry No symmetry boundaries Force based loads 8

9 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 steps Easier Solution Model a single axi-symmetric Pin/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 not occur at the final solution step 9

10 Gasket Assembly Hard Problem Large model Complex loading sequence Multiple bolt loads Frictional Contact Nonlinear material response 10

11 Automatic contact reduces modeling time 11

12 Building Collapse Simulation Running an analysis dynamically can be used to obtain convergence Evaluating the thermal-structural response of the World Trade Center collapse 12

13 Elastomeric Bearing with Lead Plug Force Deflection of a Single Truss Element Matches Detailed 3d Model 13

14 Clevis Pin Pullout Springs can be used to imposed loads and/or prevent rigid body motion 14

15 Surgical Staple Displ. Controlled Example 15

16 ANSYS Nitinol Material Behavior Complex Material Response requires many substeps for accuracy and convergence 16

17 Rubber boot with self-contact Combined Geometric, Material and Contact Nonlinearities 17

18 Vena Cava Filter IVC filters are used in case of contraindication to anticoagulation I.e. it captures clots! 18

19 FSI Example Vena Cava Filter Nonlinear structural response coupled with fluid flow 19

20 FSI Example Vena Cava Filter Streamlines Deformation 20

21 My analysis did not converge. Now what? First step is to determine the cause: 1. Rigid body motion 2. Force balance not obtained 3. Material Instabilities 4. Element formulation error 5. Combination of items 1-4 above We will examine each in detail including: identifying the problem determining i the cause providing solutions 21

22 Understanding the Solver Output Whether in WB or Mechanical APDL, the first step is to read the output file to determine the origin of the non-convergence 22

23 Rigid Body Motion error messages DOF limit exceeded. Negative main diagonal. Small/Negative Pivot error. MAX DOF INC = A very large number *** WARNING *** CP = TIME= 16:15:15 Smallest negative equation solver pivot term encountered at UX DOF of node 98. Check for an insufficiently constrained model. 23

24 Examples of Rigid Body Motion cont. 24

25 Causes of Rigid Body Motion 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.) 25

26 Find the Rigid Body Motion 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 springs Note the unrealistic 10e-6 displacement scaling 26

27 Use modal analysis to find Rigid Body Motion 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 Animating the zero frequency mode shape illustrates the rigidly moving model. 27

28 Correct the rigid body motion Take advantage of symmetries Axisymmetry Rotational Planar or reflective Repetitive or translational 28

29 Correct the rigid body motion 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 Adding a rigid region and pushing it with displacements will usually converge better than a force loading. 29

30 Correct the rigid body motion 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 Can use adjust to touch ANSYS option, but be careful since the geometry will be changed Increase pinball region Corrects interference fits Add friction 30

31 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! Linear solution 31

32 Correct the rigid body motion Use bonded contact to tie dissimilar element types Example Shells or beams to solids Use MPC contact option to eliminate iterations and penalty stiffness dependency Add/adjust weak spring stiffness Be sure to check reactions to make sure no error is introduced 32

33 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. Ft Contact Target Pdn Fn Pd1,d 2 P P P dn d1 d 2 d d d n t u u t 1 u n 2 Contact Stabilization introduces a viscous damping traction proportional to but opposite to the relative pseudo velocities between the two surfaces along contact normal and/or tangential directions. d n Where: = damping coefficient in normal direction d t = damping coefficient in tangential direction u = pseudo velocity 33

34 Contact Stabilization Damping 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 pin Conventional Adjust to Touch Contact Stabilization Damping 34

35 Correct the rigid body motion Buckling Response Nonlinear stabilization Local instabilities and global instability. Used together th with line search and automatic time stepping Arc-length method Circumvent global instability when forces are applied. Simulate the negative slope portion of a load-vs.-displacement curve. Running a static problem as a "slow dynamic" analysis in ANSYS Running a static problem as a "slow dynamic" analysis in ANSYS/LS-DYNA 35

36 Connections that prevent Rigid Body Motion Automation tools can save a lot of time in tying assemblies together Constraint equations Springs Spot Welds Beam connections 36

37 Examples of Force equilibrium not obtained Definition: Convergence value is greater than criterion after min. load increment and max. number of iterations are solved 37

38 Equilibrium Iterations A nonlinear structure is analyzed using an iterative series of linear approximations, with corrections. ANSYS uses an iterative process called the Newton-Raphson Method. Each iteration is known as an equilibrium iteration. Load F 1 4 A full Newton-Raphson 2 3 iterative analysis for one increment of load. (Four iterations are shown.) u Displacement 38

39 Convergence Procedure The difference between external and internal loads, {F a } - {F nr }, 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 tolerance. {F a } {F nr } F { a F nr u 39

40 Newton Raphson Residuals Plot Newton Raphson Residuals to determine critical contact pair Note that these controls need to be activated prior to the solution 40

41 Causes of Force balance not obtained 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) never gets below.5% of the sum of F (sum of external loads, reactions, etc.) 41

42 Ideal Load Stepping 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 method) Load Load Step equilibrium iterations Load Step 1 Substeps Time 42

43 Causes of Force balance not obtained Contact Stiffness is too large. Note: In V16 and beyond default stiffness has been reduced d 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 internal stiffness value which h is a function of material and mesh but not geometry F=KU 43

44 Causes of Force balance not obtained Load is stepped too rapidly Use Min, Max and starting ti substep control to improve convergence. You cannot get the wrong answer by adding too many substeps Load Time Incorrect Strain Energy t start t min t max Rule of Thumb: The more nonlinearities, the more substeps required 44

45 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 substeps Nonlinear Controls - N-R convergence criteria Contact Settings 45

46 Overcome the Force Unbalance Reduce Normal Stiffness Factor Increase the number of Substeps General Rule more nonlinearities use more substeps 46

47 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 47

48 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 significantly ifi 48

49 Review Initial Contact Settings and eliminate gaps See the ANSYS output file or run CNCHECK before solving 49

50 Adjust Contact Pinball Region 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 effects 2 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) 1.00x Depth Rigid/Flex Bonded or No Separation Include Everything/with Ramped effects * Values are for NLGEOM,ON and are reduced by 50% for NLGEOM,OFF **Depth = Underlying element depth (for solid elements) **Depth = 4 x element thickness (for shells and beams) 50

51 Surface Projection Based Contact More accurate distribution of contact stresses. Satisfies moment equilibrium when an offset exists between contact and target surfaces with friction. Can help with contact convergence. Better handling of sliding contact. KEYOPT,<contact element type>,4,3 Default Contact Settings Surface Projection Contact 51

52 Examples of Material Instabilities Depending upon the size of the residual these can be caused by large force unbalance or can be a result of incorrect material properties 52

53 Causes of Material Instabilities 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 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 Constraint 53

54 Causes of Element Formulation Errors 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 elements Buckling Reduce rate of loading Very large force unbalance 54

55 Correct Element Formulation Errors 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 or cracks. 55

56 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, : l ln 1 1 Always extend your material law will beyond expected strain levels 56

57 Element Selection Use Higher Order elements for curved surface contact for faster, more accurate results 20 node bricks 57

58 Solver Type and Tolerance Suggest using Direct (Sparse) solver unless PCG is significantly faster per iteration 58

59 Correct Element Formulation Errors Add intermediate substeps 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 Change Element type / formulation Use shell or beam elements Faster and more efficient solutions where applicable Test with 1 Element model Change the HyperElastic material model Modify creep law or coefficients Start mesh shape so that deformed elements become more square 59

60 Element type selection 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 Shell elements Slender structures (twisted pipe model) 60

61 Remesh the model part way through the analysis Rezoning Automatically map existing stresses and strains so that the solution history is preserved 61

62 Change material models 62

63 Hyperelastic material models Yeoh is very robust for large strain problems such as seals 63

64 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 64

65 Element Shape Robust well shaped elements can improve solution convergence and time 65

66 Mesh Controls Numerous controls are available to locally modify the mesh to reduce stress gradients through multiple elements Example showing the value of symmetry 66

67 Mesh refinement Automated mesh refinement will increase the solution quality and sometimes speed Automated mesh refinement in workbench is generally only used in linear analyses 67

68 Element Formulation 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 metal plasticity with higher order elements 2D Plane Stress Elastic material or Metal Plasticity with lower order elements 2D Plain Strain Elastic material or Metal Plasticity with lower order elements Fully incompressible hyperelasticity with higher h or lower order elements Default URI Enhanced Strain Simplified Enhanced Strain B-Bar with Mixed u-p 68

69 You have a solution! How do you make the solution more efficient? Change the mesh Refine areas of steep gradient 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? 69

70 Improve Performance in Subsequent Analyses 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 bisection Force Residual vs. Iterations Time vs. Cumulative Iteration 70

71 Thoroughly investigate your results List and plot results to check to make sure you solved the problem intended and that the results make sense 71

72 Check the quality of your results - forces First check should always be a free body diagram Applied loads Matching reaction forces 72

73 Check the quality of your stress results Comparing average vs. un-average stresses can provide an estimate of mesh error 73

74 Understand the data generated Displacements are based on original coordinate system Stresses and strain component data rotate with the elements 74

75 Need more information? Additional Information on all of these topics is available in the ANSYS Help or through mentoring or training classes 75