轴对称体扭转问题的轴对称有限元模拟解

SIMULATING TWIST PROBLEMS OF AXISYMMETRICAL BODIES BY AXISYMMETRICAL PROBLEMS

轴对称体的轴对称问题与扭转问题一向被认为是两个互相不能模拟的问题.前者的未知量与方程多于后者,形式也不相同.本文提出一种退化模拟方法.能够把扭转问题模拟为轴对称问题的一类特殊情况来解.一般的结构分析程序都能够分析轴对称问题,但轴对称体的扭转问题通常作为三维问题处理.按本文提出的方法,可用结构分析程序的轴对称分析功能模拟扭转分析.本文还给出模拟计算的算例.计算结果表明与理论解完全一致.本文对退化模拟的材料本构关系进行了研究,建议在数值计算时以各向异性材料的轴对称问题模拟任何材料的扭转问题.当限定用各向同性材料的轴对称问题来模拟时,采用了罚系数法.

It used to be considered that an axisymmetrical problem and a twist problem of an axisymmetricalbody cannot be simulated by each other,because the number of unknown variables in an axisymmetricalproblem is greater than that in a twist problem,and the governing equations are not the same.This pa-per proposes a degencrated analogy method,by which the twist problems of axisymmetrical bodies canbe simulated by axisymmetrical problems with finite element programs.An ordinary structural analysis method can be used to analyze an axisymmetrical problem,but atwist problem of axisymmetrical bodies is treated as a 3-dimensional problem usually.According to the method proposed in this paper,the analysis of a twist probiem can be simulated by the analysis of anaxisymmetrical body with a structural analysis program.The example of analysis computation is alsogiven.The computed result is in agreement with the theoretical result.In this paper,the constitutive relation of the degenerated analogy problem is given.The authorssuggest that a twist problem of a body made of any materials is simulated by an axisymmetrical problemof a body made of orthotropic material.If you have to use some program for the axisymmetrical prob-lem to be limited to isotropic materials the penalty coefficient method can be used to solve the problem.