橡胶变形响应的非线性有限元分析

EVALUATION OF RUBBER DEFORMATION RESPONSES BY NONLINEAR FINITE ELEMENT ANALYSIS

由于材料及几何两方面的原因，橡胶有限元分析中具有很强的非线性性质．此外，又因为问题中含有不可压约束条件，使得分析变得更加复杂．其结果，不恰当的单元列式将导致“锁闭”现象，从而得出错误的解答；使用低阶单元会造成压力的不稳定；等等．本文将讨论并比较不同的能量函数及有限元列式，推导本构关系式，并建议一种新的迭代技术．已经通过一些典型例题的解析和数值解。

Finite element analysis for rubber involves strong nonlinearity due to both material and geometrical reasons,and it is more complicated because of the constraint of incompressibility.Hence,inappropriate element formulation may cause locking phenomenon leading to erroneous results,and the use of low order elements may result in pressure instability,etc.The energy function and the finite element formulations for rubber responses under mechanical loadings were examined and compared,available constitutive relations were derived, and an alternative iteration scheme was suggested.By analytical and numerical solutions of some benchmark problems.The excellent numerical characteristics and capability of approximating perfect incompressibility were verified.