拉压不同模量有限元法的收敛性分析

针对力学研究中的不同模量有限元法的收敛性问题,从理论上论述了不同模量问题的剪切弹性模量对数值计算收敛性的影响,提出了一种不仅同主应力符号而且同主应力大小有关的剪切弹性模量的确定方法.在此基础上提出了加速收敛因子η,运用η参与运算,使各种不同模量问题有限元计算的收敛速度加快.

On the Convergence of Finite Element Method with Different Extension-Compression Elastic Modulus

For finite element method with different extension-compression modulus,this paper discusses the influence of modulus of elasticity in shear on the convergence of numerical calculation, and puts forward a method relating not only the sign but also the dimension of the principal stress to the modulus of elasticity in shear. On the above basis, a factor η is proposed to accelerate convergence. By using this η in the numerical calculations of different modulus problems, it is found that the convergence velocity can be obviously accelerated.