設(shè)計(jì)及學(xué)習(xí)匯總18賽季輪邊ansys

1、Lecture 2:NonlinearChapter OverviewIn this chapter, general tools and procedures useful for achieving convergence and post processing results are introduced. These tools are not specific to a particular source of nonlinearity.Building a Nonlinear ModelObtaining a nonlinear solutionStep ControlsSolve

2、r ControlsRestart ControlsNonlinear ControlsOutput ControlsAnalysis Data ManagementPostprocessing Nonlinear ResultsA. Building a nonlinear modelWhat is different about building a nonlinear model vs. a linear model?In some cases, there will be no difference!A model undergoing mildly nonlinear behavio

3、r due to large deflection and stress stiffening effects might need no modification with regards to geometry set up and meshing.In other cases, you must include special features:Elements with special properties (such as contact elements)Nonlinear Material data (such as plasticity and creep data) Incl

4、ude geometric features (i.e. radius at sharp corners) to e singularities that cause convergence trouble. You might also need to give special attention to:Mesh control considerations under large deflectionElement technology options under large deflection with nonlinear materialsLoad and boundary cond

5、ition limitations under large deflection. Building a nonlinear modelWith regards to meshing, if large strains are expected, the shape checking option may be changed to “Aggressive”For large-deflection analyses, if elements undergo some change in shape, this may reduce the fidelity of the solution.“A

6、ggressive” shape checking offers an improved element quality in anticipation of excessive distortion in a large-strain analysis.The default “Standard” shape checking is suitable for linear analyses.Depending on complexity of geometry, can sometimes cause failures during mesh generationRefer to Mecha

7、nical Intro, pt1 for ways to detect and remedy mesh failures.For any structural element, DOF solution Du is solved at nodes, stresses and strains are calculated at integration points. They are derived from DOF. For example, we can determine strains from displacements via:Where B is called the strain

8、-displacement matrixThe image on the right shows a 4-node quad element with 2x2 integration, integration points shown in red.When we post-process results, stress/strain values at integration points are extrapolated or copied to nodal locations linear results are extrapolated, nonlinear results are c

9、opied. Building a nonlinear models, eu. Building a nonlinear modelWith Element Control set to Manual, users can manually toggle between Full and Reduced Integration SchemesThis option influences the number of integration points within an element.Forcing a full integration order only applies to highe

10、r order elements, which have a uniform reduced integration order by default.It is sometimes helpful to force full integration when only one element exists across the thickness of a part for improved accuracy. Refer to the Element Technology Chapter of the Advanced Materials Course for a detailed dis

11、cussion of options. By default, Mechanical element technology will mesh geometry with higher order elements (with midside nodes).Users have the option to drop midside nodesIn challenging large deflection, bending dominated problems with nearly or fully pressible nonlinear materials, it can sometimes

12、 be advantageous to drop the midside nodes and allow the code to implement enhanced strain formulations automatically. Building a nonlinear model20-Node Hex8-Node HexKept midside nodes(Quadratic shape function)Dropped midside nodes(Linear shape function). Building a nonlinear modelIt is important to

13、 note the orientation of loads and its effect on the structure in large-deflection analyses:LoadDirection Before DeflectionDirection After DeflectionAcceleration (constant direction)Pressure(always normal to surface)Force, Moment, Bolt Load (constant direction)What is different about obtaining a non

14、linear solution?Linear static requires only one pass through the matrix equation solverNonlinear performs a new solution with every iterationB. Obtaining a nonlinear solutionKFuFi = KiuiuF1234KiF = Ku. Obtaining a nonlinear solutionWhat is different about obtaining a nonlinear solution?Analysis Sett

15、ings has many options that need to be considered for a nonlinear run. Step Control - Load steps, Substeps, Autotime steppingSolver Control - Choosing the right Solver typeRestart Controls - resuming a solveNonlinear Controls - N-R convergence criteriaOutput Controls - controlling what data is saved

16、Analysis Data Management deleting/keeping filesIn the following slides, we consider each of these tools. Obtaining a nonlinear solutionStep Controls“Auto Time Stepping” calculates an optimum time step at the end of each substep, based on the response of the structure to the applied loads. User speci

17、fies an initial number of substeps along with a range (minimum and maximum).Auto Time Stepping has the effect of adjusting the load increment (up and down) throughout the solution.Smaller increments when convergence is difficult, larger increments when convergence is easy.TimeLoadDtmaxDtstartDtmin.

18、Obtaining a nonlinear solutionStep Controls (contd)Recall that breaking the load into increments improves convergence by bringing the start point within the radius of convergence. If Mechanical has trouble converging, the auto time stepping algorithm will bisect the solution.“Bisection” returns to t

19、he last successfully converged substep and applies the load in a smaller increment (thereby using more substeps within the specified range).Fuustart F1. Obtaining a nonlinear solutionStep Controls (contd)For Auto Time Stepping = Program Controlled (Default), Mechanical will automatically set specifi

20、cations depending on the nature of the nonlinearity in the model.User should always verify that these values are adequate by checking the Solution Information folder at the beginning of the run and watching for bisections.Discussed in more detail in Chapter 6 “Nonlinear Diagnostics” . Obtaining a no

21、nlinear solutionSolver ControlsSolver Type offers two options, Direct and Iterative.This is a reference to the way the code builds the stiffness matrix for each Newton-Raphson equilibrium iteration.Direct (Sparse) solver is more robust and is mended for challenging nonlinear models and with non-cont

22、inuum elements (shells and beams).Iterative (PCG) solver is more efficient (in terms of run time and is mended for large bulk solid models dominated by linear elastic behavior.There can also be different In-Core memory requirements:Sparse requires about 10GB/MDOF, while PCG requires 1GB/MDOFThe defa

23、ult Program Controlled will automatically select a solver based on the problem currently in session. Obtaining a nonlinear solutionSolver Controls (contd)By setting “Large Deflection” = ON, in the Solver Control branch of Analysis Settings, Adjustments are made to the stiffness matrix over multiple

24、iterations to account for changes due to:Large deflection, large rotation Large strain.Stress stiffening Spin softeningSolver Controls (contd):Large Deflection: If an elements orientation changes (rotation), the transformation of its local stiffness into global components will change. Change in orie

25、ntation is also accounted for when Large Deflection analysis is specified.It is possible to have large deflection without large strain.For elements that support large deflection but do not support large strain (previous slide), the mechanical strains are evaluated using linear expressions.XY. Obtain

26、ing a nonlinear solutionSolver Controls (contd):Large Deflection = On will also account for Large Strain.If an elements shape changes (area, thickness, etc.), its individual element stiffness will change.The mechanical strains are evaluated using nonlinear expressionsThis measure is a nonlinear stra

27、in measure since it is a nonlinear function of the unknown final length l . It is also referred to as the log strain. The 3-D equivalent of the log strain is the Hencky strain. Obtaining a nonlinear solutionSolver Controls (contd):Large Deflection = On will also account for Stress Stiffening.If an e

28、lements strains produce an in-plane stress state (membrane stresses), the out-of-plane stiffness can be significantly affected. As the vertical deflection (UY), increases, significant membrane stresses (SX) lead to a stiffening response.This is characteristic of thin structures with bending stiffnes

29、s very small compared to axial stiffnesscables, thin beams, shells and couples in the in-plane and transverse displacementsIt is possible to have stress stiffening without large deflection and/or large strainXYFFuy. Obtaining a nonlinear solutionObtaining a nonlinear solutionRestart Controls facilit

30、atePausing or stopping a run to review results in progress.Changing analysis settings to correct an unconverged solution. Modifying existing Loads. Extending a solution that has already completed.For example, to allow system transients to progress further into time. Adding post processing command ob

31、ject(s) after the model has been fully solved.Restart Controls (contd)With “Generate Restart Points” set to “Program Controlled”Restart files areNot saved for a full stand alone linear analysis. Not saved for a full stand alone nonlinear structural analysis that completes successfully.Retained for t

32、he last successfully converged substep of an plete solve due to a convergence failure or if the solution run is manually interrupted. . Obtaining a nonlinear solutionRestart Controls (Contd)With “Generate Restart Points” set to “Manual”. Obtaining a nonlinear solutionLoad Step: Specifies at what loa

33、d steps to create restart points (Last or All).Substep: Specifies how often the restart points are created within a load step. Last: Create a restart point for the last substep of each load step only. All: Creates restart points for all substeps of each load step. Specified: Creates restart points f

34、or a user specified number (N) of substeps per load step. Where N is defined in “Rate of Recurrence” FieldEqually Spaced: Creates specified number (N) of restart points at equally spaced time intervals within a load step.Where N is defined in “Rate of Recurrence” Field Restart Controls (Contd). Obta

35、ining a nonlinear solutionMax Points to Save per StepDefault is “All” (=999)When the maximum number has been saved for each load step, the first file of that load step will be overwritten for subsequent substeps. . Obtaining a nonlinear solutionRestart Controls (Contd)For example, to write 3 equally

36、 spaced restart files for each load step:SubstepsRestart pointsr1LoadTimer2r4r6 (last converged) LS1LS2r3r5. Obtaining a nonlinear solutionRestart Controls (contd)Restart files are automatically deleted if a full solve completes successfully (default)Retain Files After Full Solve: User has the optio

37、n to keep restart files regardless by setting this field to YES.Under Analysis Data Management, setting Future Analysis to “Prestressed analysis” also forces the restart files to be retained. Similarly, setting Delete Unneeded Files to “No” implies that restart files are to be retained. . Obtaining

38、a nonlinear solutionRestart Controls (contd)At the completion of the run, users can specify the restart point for the subsequent run. If default restart controls were taken, restart will only be available for the last successfully converged substepRestart specifications:Restart Type = ManualRestart

39、Point = Load Step 1, Substep 6Once the restart specifications have been set and the analysis control settings and/or existing loads have been adjusted as needed, execute a solve to begin the solution restart Restart Controls (contd)For an overview of available restart points, select theAnalysis Sett

40、ingsobject and refer to theGraphwindow where restart points are symbolized by triangular markers atop the timeline. TheTabular Datawindow lists the restart points within each load step. Obtaining a nonlinear solutionRestart Controls (contd)Restart points are color coded to distinguish between replay

41、able (blue triangles) and a non-replayable (red triangles). Repayable points are ones which will produce the exact solution when run from start to finish. Non-replayable points appear if you modify a load or analysis for a given step and restart from that step. The restart will solve, but if you lat

42、er solve without restarts, keeping the modifications for the entire step, non-replayabe points are those which might not be available. Obtaining a nonlinear solution. Obtaining a nonlinear solutionRestart Controls (contd)Below is a summary of loads supported for restartsLoads must already exist in t

43、he Project Tree from the start of the analysisAdding a new load into the project tree will nullify a restartNonlinear ControlsTolerances on Convergence are calculated automatically. They are used during the Newton-Raphson process to dictate when a model is Converged or “balanced”The default converge

44、nce criterion works very well for most engineering applications.For special situations, users can override these defaults to Tighten or loosen the convergence tolerance.A tighter tolerance gives better accuracy, but can make convergence more challenging. Obtaining a nonlinear solutionRecall that the

45、 Newton-Raphson method iterates to a converged solution using the equation KTu = F - FnrThe program solves this equation repeatedly until the residual (force imbalance), F - Fnr, es acceptably small.The largest acceptable value for the residual is called the force convergence criterion.FuThe solutio

46、n is converged when Residual CriterionCriterion. Obtaining a nonlinear solutionExpressed mathematically:If |R| (eR Rref) Then the solution is converged.Where:R =Fa - Fnr is the residual vector |R| = (SR2i)1/2, is a vector norm of the residual (A norm is an operator that reduces a vector to a single

47、scalar value) (eR Rref) is the Force convergence criterioneR is a tolerance factor and Rref is a reference force valueRref is the norm of all applied forces and reactions, |F| (automatically scaling the criterion to the magnitude of load). Obtaining a nonlinear solutionNonlinear Controls (Contd)In a

48、ddition to force balance, a moment balance will also be included if rotational degrees of freedom (DOF) are present in the model (i.e. when beam and/or shell elements are present for example). . Obtaining a nonlinear solutionNonlinear Controls (contd)Balance checks on displacement and/or rotational

49、DOF values can also be added as a supplement to force/moment balances. When Joints are present in a model, these additional constraints will be added automatically.When nonlinear contact is present, these supplemental checks can sometimes be overly restrictive and can cause unnecessary divergence. U

50、ser can remove as necessary. Obtaining a nonlinear solution. Obtaining a nonlinear solutionThe Force Convergence graph displays a plot of the force criterion and residual forces (“force convergence”) vs iteration. When the residual is less than the criterion, the solution is converged.ResidualCriter

51、iaSimilar plots are available for moment convergence and for displacement and rotational DOF convergence when applicable. Obtaining a nonlinear solutionEach converged substep is highlighed on this Force Convergence Graph with a vertical green dotted line.Each converged loadstep is highlighed with a

52、blue dotted line. Obtaining a nonlinear solutionNonlinear Controls (contd)If you add any convergence criteria, the program deletes all the default criteria!For example, if you override program control by adding a displacement convergence check, the force convergence check will be deleted. Make sure

53、you reestablish the force convergence check.After redefining convergence criteria, you should always confirm the specifications reported in the Solution Information branch to ensure intended balance checks are active. Obtaining a nonlinear solutionNonlinear Controls (contd)Why must you re-establish

54、a force convergence criterion?Relying on displacement convergence alone can in some cases lead to erroneous results.Big ResidualBecause displacement-based checking is a relative measure of convergence, it should only be used as a supplement to force-based convergence.Force-based convergence provides

55、 an absolute measure of convergence, as it is a measure of equilibrium between the internal and external forces.Nonlinear Controls (contd)The Minimum reference value (MINREF) is a safety feature that prevents your solution from trying to converge to a zero tolerance.If free-body (unconstrained) syst

56、ems or mechanisms have no external forces, the criterion (eR * |F|2) will be zero. If the criterion is zero, the solution will never converge!In such cases, the program redefines the criterion to be (eR * MINREF). Where eR is the convergence tolerance value.The default value that WB-Mechanical uses

57、for MINREF depends on the physics of the problem. Obtaining a nonlinear solution. Obtaining a nonlinear solutionNonlinear Controls (contd)Line Search is an additional tool intended to enhance convergence behavior. When active, line search multiplies the displacement increment by a program-calculated

58、 scale factor between 0 and 1, whenever a stiffening response is detected, typical in a contact application.By default, the program turns Line Search ON when contact elements are present. You can override the default to turn it on or off explicitly. Obtaining a nonlinear solutionConvergence criteria

59、 guidelines:Default convergence criteria work well most of the time.You should rarely need to change the criteria.To tighten or loosen a criterion, dont change the default reference value, but instead change the tolerance factor by one or two orders of magnitude.Do not use a “l(fā)oose” criterion to eliminate convergence difficulties.This simply allows the solution to “converge” to an incorrect result!Tightening the criterion requires more equilibrium iterations.Review any MINREF warning messages during solution. Make sure the minimum re