1、SECTION 12RESOLVING CONVERGENCE PROBLEMS,Overview,Nonlinear Analysis Guidelines Information Available to Help Analysis Troubleshooting: General Analysis Troubleshooting: Criteria Behaviour Analysis Troubleshooting: EXIT Numbers,Nonlinear Analysis Guidelines,Convergence of a nonlinear problem is most
2、ly not simply to do with the convergence tolerance values or the criteria specifiedit is an overall issue of model integrity and representation of reality It is strongly recommended that small tests be performed to gain experience of unknown (to you) element and solution types: To understand its lim
3、itations To ensure that it does provide the required behaviour for the actual simulation to be carried out To prevent expensive “surprises” at the end of a project Single element tests are preferable (where possible) since it is so much quicker and easier to verify the input and to evaluate the resp
4、onse with only a few degrees of freedom There are a number of sources of examples and benchmarks available that may help in this regard The MARC User Guide manual. This contains an increasing amount of worked examples written with the express intention of demonstrating the use of the facilities clea
5、rly The MARC Demonstration Problem manual (volume E). It is in Marc data file format only. The data files associated with this manual can be located in the Marc installation directory The NAFEMS suite of examples. Further information is available on their website (www.nafems.org),Nonlinear Analysis
6、Guidelines,Perform and scrutinise the results from a static linear analysis to check the integrity and behaviour of the basic model. If the nonlinear model already exists For contact analyses, this would mean changing all contact conditions to GLUED For material nonlinearity simply increase the fail
7、ure criteria so that it cannot be reached For geometrically nonlinear analyses turn off Large Displacement as well as any large strain material options Add each of the nonlinearities one by one to determine their effect on the solution and its convergence behaviour. For instance, start with contact,
8、 adding next any geometric nonlinearity and then finally any material nonlinearity, etc. For contact analyses, contact conditions can be set to GLUED The next step would be TOUCHING, but with a separation force of 1e20 If buckling is expected, a linear eigenvalue buckling analysis should be performe
9、d to obtain the linear buckling load. This will act as both a benchmark value to compare against as well as a useful aid in determining the load magnitude to be applied in the subsequent geometrically nonlinear analysis Always use engineering common sense and verify the plausibility of the results b
10、efore making design decisions based upon them,Information Available to Help,The problem begins with error messages like: “Failure to converge to tolerance” (EXIT 3002) “Error encountered in stress recovery” (EXIT 1009/1005) “The time step has become too small due to too many step cut-backs” (EXIT 30
11、09) “Unable to reduce the time step below the minimum value allowed” (EXIT 3015) “Node on the boundary of a deformable body tried to slide out of surface definition in a contact analysis” (EXIT 2400) The main place to look is the end of the OUTPUT file (.out) A successful analysis looks like: * This
12、 is a successful completion to an MSC.Marc analysis, indicating that no additional incremental data was found and that the analysis is complete *MSC.Marc Exit number 3004An unsuccessful analysis looks like: * Analysis has failed to converge to required convergence tolerances. One of several error co
13、nditions has been detected and the run aborted. The output will specify additional messages *MSC.Marc Exit number 3002,Analysis Messages,EXIT Number,Associated message for EXIT number,A typical nonlinear output file section: start of assembly cycle number is 0 wall time = 12.00solver workspace neede
14、d for out-of-core matrix storage = 7612 solver workspace needed for in-core matrix storage = 10114 matrix solution will be in-corestart of matrix solutionsingularity ratio 3.4185E-12end of matrix solutionmaximum residual force at node 7 degree of freedom 1 is equal to 1.156E-04 maximum reaction forc
15、e at node 35 degree of freedom 2 is equal to 2.809E-01 residual convergence ratio 4.117E-04maximum displacement change at node 3 degree of freedom 1 is equal to 1.013E-02 maximum displacement increment at node 3 degree of freedom 1 is equal to 1.013E-02 displacement convergence ratio 1.000E+00failur
16、e to converge to toleranceincrement will be recycled,Analysis Messages,The output file (.out) contains all messages The log file (.log) contains mainly the convergence information The status file (.sts) contains a summary,The Status File,Summary of the convergence behaviour of the analysisThings to
17、look out for: Sudden jumps in the number of cycles (what happened?) Large number of separations throughout (a general contact issue) Large number of separations part way (contact lost? Contact causing local failure? Frictional forces overcome?) Large number of cut-backs throughout (load increment to
18、o large) Large number of cut-backs part-way (what happened?),Troubleshooting Analysis Failure,The figure shows contact occurring on only two nodes before non-convergence Perhaps the other part coming into contact slips away afterwards? Perhaps a more refined mesh on the contacted area is needed?,Get
19、ting Clues,Post process what there is The deformed shape often gives obvious clues as to why the simulation is not converging Exaggerating the deformation is a good way to pick up cracks in the model or localised effects from incorrect contact definition Animating with a reasonable deformation exagg
20、eration can also be of help If convergence is not achievable in the first increment it can be very helpful to specify that Marc continues “proceed when not converged” option This means that a POST results file will be generated Even if an increment fails to converge it may provide a pointer to the p
21、roblem,Ensure consistent units are used throughout model Note: N, MM, Kg are not consistent Reduce the time step. There may be significant nonlinearity occurring at the beginning Usual for contact May suggest an incorrect yield value for material nonlinearity Buckling or significant rotation may hav
22、e occurred Over-large element distortion Make sure that the automatic cut-back capability is invoked If using the “fixed” load incrementation, change to the “adaptive” scheme and include the “automatic” criteria Check that each component of the structure is restrained against rigid body motion Bound
23、ary conditions are the interface between the model and the rest of the world,General,Set “Contact Tolerance Bias” to 0.9 (particularly for shell contact) Set “Contact Tolerance” to 0.0 The rigid surface markers should always point towards the interior of the rigid body. If it does not, MSC.Marc may
24、not detect contact between the rigid surface and the deformable body Contact can be lost or not found because of too large a load increment Refine the mesh in the area of slideline definitions Coarse meshes can produce single point contact and promote instability Necessary to capture the contact int
25、eraction accurately if contact distribution is of importance Analytical surface definition may be incorrect and causing “bulbous” corner/edge contact surfaces Consider smoothing the surfaces in contact if there are sharp features, e.g. insert a radius instead of a sharp corner for corner contact Ini
26、tial indeterminate contact state can lead to chatter model components in contact where possible Remove friction,Contact,Review and reconcile any initial contact over-closures and openings Nodes initially penetrating significantly past the contact zone will be ignored If this situation occurs at begi
27、nning of analysis, node will not be found If it occurs later, the increment will be recycled with modified time step,Contact,If using the stress-free check to make sure that the resulting elements will not be distorted too much when the slave nodes are moved by the program to lie on the master surfa
28、ce.,Contact,Hyperelastic Material Data,Check the material stability for elastomer materials (in “experimental data fitting”) Check that the material data covers the entire strain range: This can cause “elements inside out” errors The analysis may not converge if any part of the model experiences str
29、ains beyond the stability limits of the material Revert to a lower order polynomial fit (e.g. Single-term Mooney) in the experimental data fitting When fitting experimental data, engineering stress/strain data is expected Any material model in which the tangent stiffness is zero or negative will mos
30、t often cause convergence problems(材料模型的接触刚度为零或负值导致收敛问题）,Plastic Material Data,Include Reality,Make sure all appropriate nonlinearities are included Some structures rely on “stress stiffening” effects for stability and would require a large displacement analysis Is geometric nonlinearity required? L
31、arge deformations/rotations may be causing large non-physical strains If large strains are present in the analysis, it is likely, for many materials, that failure is also present (e.g. plasticity) Without material failure included in a large strain analysis, an unrealistic problem is being solved fo
32、r which there may not be a solution It is unusual for a hyperelastic material to be in the small strain environment make sure that a large strain option is requested It is possible for many elasto-plastic analyses to be in the small strain environment but the addition of a robust large strain option
33、 is recommended,Elements,Be aware of the element mechanisms associated with reduced integration elements Always specify assumed strain option for fully integrated 2D and 3D solid elements to eliminate over-stiff solutions in the presence of bending Always specify the constant dilatation option for f
34、ully integrated 2D and 3D solid elements in large-strain plasticity to avoid volumetric locking This is due to over-constraints resulting from the incompressible nature of plastic deformation Alternatively, use reduced integration or Herrmann elements Use Hermann Elements with the hyperelastic mater
35、ials MSC.Marc uses the global X-axis as the axis of symmetry for axisymmetric elements,The figure shows the mesh before (top) and after (bottom) deformation. Elements on the left stretched more readily due to plastic necking. The analyst anticipated this and refined the mesh towards the left. A unif
36、orm mesh would have produced a poorer simulation.,Specify a mesh so that the shape of the elements is reasonable throughout the entire analysis Anticipate how the mesh will deform For example, make element sides shorter in the direction that will be elongated the most,Elements,If the analysis is sti
37、ll recalcitrantremove nonlinearities to try and isolate the cause of the problem For contact analyses, this would mean changing all contact conditions to GLUED For material nonlinearity simply increase the failure criteria so that it cannot be reached For geometrically nonlinear analyses turn off la
38、rge displacement as well as any large strain material options As a last resort, and with a good reason Turn on non-positive definite (gives a slower equation solution) Turn on quasi-static inertial damping Some specific clues can be found by looking at the behaviour of the convergence ratios during
39、the solution,General,Convergence Criteria Behaviour,Monotonic Divergence: Material failure, e.g. point loads/supports causing massive localised failure Contact lost because of too large a load increment or wrong contact settings Refine the mesh in the area of slideline definitions. Coarse meshes can
40、 produce single point contact and promote instability Analytical surface definition may be incorrect and causing “bulbous” corner/edge contact surfaces Buckling has occurred without arc-length methods requested Reduce load step to reduce the amount of nonlinearity occurring in an increment Convergen
41、ce criteria too slack? Tighten the convergence criteria, particularly for geometric nonlinearity the solution may be drifting too far from the true equilibrium position Were the rigid contact bodies extended sufficiently far?,Convergence Criteria Behaviour,Slow Convergence: Not uncommon in contact a
42、nalyses whilst contact is being established Convergence tolerance too tight? Use full Newton-Raphson to obtain full quadratic convergence characteristics Friction issues Check the relative sliding velocity is an appropriate value (1-10%) Use “stick-slip” model Unfeasibly large friction coefficients
43、(tangential “chatter”) Elements (bars, beams, springs) that are simulating “stiff” members can cause round-off issues if their stiffnesses are arbitrarily large. Evaluate stiffnesses from “real” geometry and materials Follower force with the stiffness contribution gives a better convergence rate and
44、 may help in the presence of large rotations,Convergence Criteria Behaviour,Slow Convergence (cont.): Gap elements can produce slow displacement norm convergence behaviour Both the iterative and incremental displacements associated with a high stiffness spring are tiny This causes the displacement n
45、orm calculation of: (iterative displacement ) / (displacement increment) to produce extremely small numbers The changes occurring in the displacement values are lost because of machine precision Analytical contact surface definitions give a continuous normal and better convergence and would be bette
46、r than a discrete surface definition for a coarse mesh A poorly conditioned system leads to consistently slow convergence Large:Small element sizes Stiff:Soft materials Poor quality element shapes,Convergence Criteria Behaviour,Oscillating Convergence: A typical response Settling of contact use “ite
47、rative penetration detection” a recommended distance tolerance and bias values Threshold material failure,Convergence Criteria Behaviour,Oscillating Divergence: Buckling is occurring; either real or numerical Catastrophic material failure (e.g. point loads/supports causing localised failure) Extreme
48、 friction parameters with a large load increment An element mechanism may have been excited in a reduced integration element. The remedy is to use a fully integrated element Refine the mesh in the area of slideline definitions. Coarse meshes can produce single point contact and promote instability C
49、hattering Non-Convergence: No friction with contact and rubber materials can cause chattering in some geometric configurations. This is prevented by a small amount of friction,Fixed Non-Convergence: If the concrete (or similar “softening”) material model is being used, slacken the residual convergen
50、ce norm “Locking” can occur in highly constrained structures in a materially nonlinear analysis in which massive plastic strain is developed (plasticity is assumed incompressible) The effective plastic strain magnitude should be displayed to check this Linear tri/tet displacement elements are notori
51、ously guilty of this numerical phenomenon The Hermann and the reduced integration elements were designed to eliminate such behaviour The very large pressures associated with hyperelastic analyses can cause ill-conditioning (and, hence, slow convergence) if the “full” initial stress stiffness matrix is selected In this case, either the “none” or “tensile only” options would be recommended The initial stress selection is not related to accuracy, just the rate of convergence,
