Nonlinear Ansys Technology

ANSYS Nonlinear Technology 18

Powerful new capabilities are aimed at studying complex nonlinear behavior in mechanical systems. By Achuth Rao, Ph.D. Product Manager ANSYS, Inc.

Nonlinearities are common in most real-world problems and represent some of the most challenging aspects of engineering analysis. To help users model and solve these problems, ANSYS has a wide range of features and capabilities for handling the most common types of nonlinearity. Changing status or contact nonlinearity — Many common structural features exhibit nonlinear behavior that is status-dependent. Status changes might be directly related to load, or they might be determined by some external cause. Situations in which contact occurs are common to many different nonlinear applications. Contact behavior, such as separation and sliding with frictional effects, introduces nonlinearity into the analysis. Geometric nonlinearity — If a structure experiences large deformations, its changing geometric configuration can cause the structure to respond nonlinearly. Geometric nonlinearity is

characterized by “large” displacements and/or rotations. Small deflection and small strain analysis assume that displacements are small enough that the resulting stiffness changes are insignificant. In contrast, large strain analysis account for the stiffness changes that result from changes in an element’s shape and orientation. The large strain feature is available in most of the solid elements (including all of the large strain elements) as well as in most of the shell and beam elements. ANSYS also handles two other types of geometric nonlinearities: stress stiffening and spin softening. For thin, highly stressed structures, such as cables and membranes, the out-of-plane stiffness of a structure can be affected significantly by the state of in-plane stress in that structure. Stress stiffness is the coupling between in-plane stress and transverse stiffness. Spin softening softens the stiffness matrix of a rotating body for dynamic mass effects. The adjustment approximates the effects of geometry changes due to large deflection circumferential motion in a small deflection analysis. Spin softening is used in conjunction with prestressing, which is caused by centrifugal force in the rotating body. Material nonlinearity — Nonlinear stress–strain relationships are a common cause of nonlinear structural behavior. Many factors can influence a material’s stress–strain properties, including load history (as in elastoplastic response), environmental conditions (such as temperature) and the amount of time that a load is applied (as in creep response). ANSYS handles numerous material-related factors that cause a structure’s stiffness to change during the course of an analysis ranging from anisotropic behavior, nonlinear stress–strain relationships, dependency on time, rate of strain and certain coupled physics effects such as piezoelectric and Seebeck effects, to name a few.

Nonlinear history tracking option monitors results in real time during solution.

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Plotting Newton-Raphson residuals allows users to readily evaluate convergence difficulties.

Robust Solution Techniques ANSYS employs the Newton-Raphson technique to solve the previously mentioned types of nonlinearities, in which the out-of-balance load (the difference between the restoring forces and the applied loads) is used to perform a linear solution. ANSYS checks for convergence based on force, displacement or other criteria. If convergence criteria are not satisfied, the stiffness matrix is updated and a new solution is obtained. A number of convergence-enhancement and recovery features are offered by default such as line search, automatic load stepping and bisection. For special cases such as nonlinear buckling, ANSYS offers an alternative iteration scheme, the arc-length method, to help avoid bifurcation points and track unloading.

Latest ANSYS Capabilities Recent releases of ANSYS have seen further advances in nonlinearity and solution techniques for handling these types of nonlinear behavior. Manual rezoning — In a finite large-deformation analysis, mesh distortion reduces simulation accuracy, causes convergence difficulties and eventually can terminate an analysis. Rezoning allows you to repair the distorted mesh and continue the simulation. ANSYS offers a manual rezoning procedure that allows users to decide when to use rezoning and what region(s) to rezone, and then to generate a new mesh on the selected region(s). During the rezoning process, ANSYS updates the database as necessary, generates contact elements if needed, transfers boundary conditions and loads from the original mesh and maps all solved variables (node and element solutions) to the new mesh automatically. Analysis then continues on the new mesh, with equilibrium achieved based on the mapped variables.

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Nonlinear diagnostics — The nonlinear diagnostics tool in ANSYS can help you find problems in your model when a nonlinear analysis has difficulty converging. Typically, nonlinear analysis fail to converge for the following reasons: ■

Too large a distortion

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Elements contain nodes that have near-zero pivots (nonlinear analysis)

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Too large a plastic or creep strain increment

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Elements in which mixed u-P constraints are not satisfied

Tracking nonlinear residuals — As part of the nonlinear diagnostics, ANSYS allows tracking of the Newton-Raphson residuals during nonlinear iterations. Plotting the residual forces helps identify regions of high residual forces. Such a capability is useful when you experience convergence difficulties in the middle of a load step, in which the model has a large number of contact surfaces and other nonlinearities. Tracking the nonlinear residuals allows one to focus on the nonlinearities in area of interest, instead of having to deal with the entire model. Nonlinear diagnostics also allows one to identify elements that violate certain convergence criteria, such as plastic/creep strain increments and the like. The nonlinear history tracking option allows one to monitor results of interest in real time during solution. Before starting the solution, you can request nodal data, such as displacements or reaction forces at specific nodes. You also can request element nodal data, such as stresses and strains at specific elements, to be graphed. Brake squeal analysis — The QR damped eigenvalue extraction method now can be used in problems with friction nonlinearities, in which an unsymmetric stiffness matrix may be produced. An example of this type of problem is brake squeal analysis, in which the combination of ANSYS contact elements and the QRDAMP eigensolver provide an easy-to-use, efficient

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means of determining unstable modes. ANSYS offers a two-step procedure in which the nonlinear unsymmetric stiffness terms due to frictional sliding in a static analysis are included in the eigensolution. In brake squeal analysis, the effect of the coefficient of friction (as well as other parameters) can be varied to see the effects on different modes and the coupling between modes. This can help to determine which modes (frequencies) will be unstable and a source of audible discomfort. Coupled physics — Due to interaction of various physics, coupled physics analysis is inherently nonlinear in nature. The interaction between various physics is typically either as a load or as a change in the stiffness of the other physics. This type of interaction makes the coupled system of equations nonlinear. ANSYS offers two types of coupled physics capabilities: direct coupled physics and sequential coupled physics. The direct method usually involves just one analysis that uses a coupled-field element type containing all necessary degrees of freedom. Coupling is handled by calculating element matrices or element load vectors that contain all necessary terms. An example of this is a coupled physics analysis using the PLANE223, SOLID226 or SOLID227 elements. Users can define material properties for these elements to model interaction such as piezoelectric, piezoresistive, Seebeck/Peltier effects and the piezocaloric effect. The sequential method involves two or more sequential analysis, each belonging to a different field. The ANSYS Multi-field solver, available for a large class of coupled analysis problems, is an automated tool for solving sequentially coupled field problems. It is built on the premise that each physics is created as a field with an independent solid model and mesh. Coupled loads automatically are transferred across dissimilar meshes by the solver. The solver is applicable to static, harmonic and transient analysis, depending on the physics requirements. Any number of fields may be solved in a sequential (or mixed sequential/simultaneous) manner. An application of the ANSYS Multi-field solver (MFX-Multiple code solver) used for simulations with physics fields distributed between more than one product executable is the ANSYS Multiphysics and ANSYS CFX coupling for advanced FSI analysis. The solver uses iterative coupling in which each physics is solved either simultaneously or sequentially, and each matrix equation is solved separately. The solver iterates between each physics field until loads transferred across the physics interfaces converge.

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Sequential analysis between ANSYS CFX and ANSYS Multiphysics provides for nonlinear coupled physics analysis of a MEMS micro-pump.

In addition to some of the recent advances mentioned in this article, ANSYS continues to enhance its nonlinear capability. The next version of ANSYS will have further advances in areas of contact nonlinearity (line-surface contact, cohesive zone model using contact elements), material nonlinearity (Gurson’s material, anisotropic hyperelasticity), element or geometric nonlinearity (higher order shell, rebar elements) and convergence enhancement techniques (stabilization). I

The author wishes to thank development and technical support personnel at ANSYS, Inc. and the various thirdparty solutions providers for their efforts and contribution to this article.

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Volume 7, Issue 3 2006