Open Access
Finite element methods for nonlinear elastostatic problems in rubber elasticity
J. T. Oden,Eric B. Becker,T. Miller,T. Endo,E. B. Pires +4 more
- 01 Mar 1983
pp 39-70
2
TL;DR: In this article, a number of finite element methods for the analysis of nonlinear problems in rubber elasticity are outlined, including the augmented Lagrangian method, continuation or incremental loading methods, and associated Riks-type methods which have the capability of incorporating limit point behavior and bifurcations.
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Abstract: A number of finite element methods for the analysis of nonlinear problems in rubber elasticity are outlined. Several different finite element schemes are discussed. These include the augmented Lagrangian method, continuation or incremental loading methods, and associated Riks-type methods which have the capability of incorporating limit point behavior and bifurcations. Algorithms for the analysis of limit point behavior and bifurcations are described and the results of several numerical experiments are presented. In addition, a brief survey of some recent work on modelling contact and friction in elasticity problems is given. These results pertain to the use of new nonlocal and nonlinear friction laws.
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Citations
Nonlinear finite element modeling and analysis of a truck tire
Seokyong Chae
- 16 Jun 2006
TL;DR: For an efficient full vehicle model simulation, a multi-body system (MBS) simulation is frequently adopted so that the dynamic and steady-state responses of the sprung mass can be shortly predicted when the vehicle runs on an irregular road surface such as step curb or pothole.
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The Application of Newton's Method to the Problem of Elastic Stability
TL;DR: The numerical solution of problems of elastic stability through the use of the iteration method of Newton is examined in this paper, where it is found that if the equations of equilibrium are completed by a simple auxiliary equation, problems governed by a snapping condition can, in principle, always be calculated as long as the problem at hand is properly formulated.
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Discrete approximations related to nonlinear theories of solids
TL;DR: In this paper, a generalized arc-length is introduced in the configuration-load space in order to facilitate the incremental computations near limit points, and the arc length is used as the loading parameter in some illustrative problems.
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Numerical analysis of continuation methods for nonlinear structural problems
TL;DR: Continuation methods are considered in this paper as the collection of methods needed for the computational analysis of specified parts of the solution field of "under-determined" equations Fx = c where F: Rm → Rn, m >; n. is given and any suitable m−n of the variables x, are designated as parameters.
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