不可压缩和近乎不可压缩粘弹性问题的有限单元法

本文首先从Herrmann泛函出发,导出了不可压缩和近乎不可压缩粘弹性问题的新的本构关系,然后根据虚功原理建立了相应的有限元公式。最后编制了平面问题的有限元分析程序VFAPINP,并计算了实例。计算结果表明所介绍的分析方法和计算程序解决了泊松比趋近或等于0.5时粘弹性应力分析问题,特别适用于固体推进剂的应力分析。

A Finite Element Method for Incompressible and Nearly- Incompressible Viscoelasticity

The constitutive relation valid for incompressible and nearly-incompessible viscoelastic body is derived based on Herrmann Functional, and a finite element formulation is obtained by invoking the principle of virtue-work. A computer program VFAPINP is developed, which can be used for the solution of plane problems, and one test example is done using the program. All the results show that the approach and the computer program presented here are valid for the problem of stress analysis of viscoelastic problem when Poisson's ratio approaches 0. 5 or equals to 0. 5 and can be used to the strength analysis of solid propellant grain.