不可压缩粘弹性有限元法及其对推进剂药柱应力分析的应用

AN FEM FOR NEARLY-INCOMPRESSIBLE VISCOELASTICITY AND ITS APPLICATION IN PROPELLANT GRAIN STRESS ANALYSIS

由于固体推进剂具有近似不可压缩的特点 ,利用位移法有限元求解这类材料的力学问题不可能得到满意的结果。本文根据 Herrmann变分原理导出一种适用于不可压缩和近似不可压缩粘弹性物质的新的本构关系式 ,介绍了相应有限元公式 ,并开发了用于平面问题分析的计算机程序 VFAPINP。计算结果表明 ,本方法和程序可以用于所有泊松比的粘弹性问题的计算 ,尤其适用于固体推进剂药柱的应力分析。

Since solid propellant exhibit nearly-incompressible material behaviour,the displacement formulation of the finite element method is unable to give acceptable solution to mechanical problems of these materials.This paper introduces a new constitutive relation based on Herrmann variational theorem for incompressible and nearly-incompressible viscoelasticity.The corresponding finite element formulation is presented here and a computer program VFAPINP is developed for solution to plane problems.The results show that the approach and the computer program are valid for stress analysis of viscoelastic materials with all admissible values of Poisson′s ratio and particularly for the propellant grain stress analysis.