有限元线法求解非线性模型问题——Ⅳ.弹塑性扭转

ANALYSIS OF NONLINEAR MODEL PROBLEMS BY THE FINITE ELEMENT METHOD OF LINES—Ⅳ. ELASTIC-PLASTIC TORSIN

本文是有限元线法(FEMOL)求解非线性模型问题的系列工作的结束篇,对弹塑性扭转这一材料非线性模型问题进行了分析求解。文中以理想塑性材料的棱柱体的扭转为例,采用FEMOL单元对弹性区进行离散,并利用平凡ODE技巧将未知的结线端点(弹塑性交界点)的位置坐标纳入FEMOL导出的ODE体系中去,从而将问题转化为标准的非线性ODE问题。文中给出的数值算例表明,本法具有简便易行、迭代次数少、解答信息丰富且精度高等优点。

As the final paper in this series of nonlinear application of the finite element method of lines (PEMOL), the present paper applies this method to material nonlinear problems by presenting a FEMOL analysis of the elastic-plastic torsion problem. Firstly, the elastic region of the cross-section is discretized by FEMOL elements. Next the changes of nodal lines at end-points on the elatic-plastic interface are taken as shape variables which are incorporated into the ODE system by using the trivial ODE technique with the supplementary BCs provided by the yield condition of a weakform. As a result, the elastic-plastic torsion problem is transformed into a standard nonlinear ODE problem and then solved by standard ODE solvers. Numerical examples are given to show the good performance of the present approach.