有限元法中单元划分优化及约束反力求解策略  

Optimization Method of Element Division and Solution Strategy of Constraint Forces in Finite Element Method

作　　者：张国智[1] ZHANG Guozhi(College of Mechanical and Electrical Engineering,Xinxiang University,Xinxiang 453003,China)

机构地区：[1]新乡学院机电工程学院,河南新乡453003

出　　处：《新乡学院学报》2023年第9期42-45,共4页Journal of Xinxiang University

基　　金：新乡市重大科技专项(21ZD009);2021年新乡学院课程思政示范课程。

摘　　要：针对复杂形状问题的有限元的单元优化及速解,研究了有限元法中单元划分优化及约束反力求解策略。在分析对象的几何形状的基础上,提出了将物体划分为由若干个全等图形和相似图形的单元优化划分方法,并给出了二维典型单元的单元刚度矩阵的计算公式。同时,针对基于刚性有限元法快速求解约束反力的问题,提出了基于整体刚度矩阵伪逆直接求解约束反力的方法。对典型复杂零件的单元划分的结果表明,单元刚度矩阵计算量减少了83%。对机床支撑筋板螺栓设计的计算结果表明,基于整体刚度矩阵伪逆直接求解约束反力可快速、精确实现螺栓的设计。将提出的单元优化划分方法和直接求解约束反力的求解方法有机结合,可有效提高有限元的计算效率和计算精度。Aiming at the element optimization and fast solution of finite element method for complex shape problems,the element division optimization and solution strategy in finite element method were studied.Based on the analysis of the geometric shape of the object,an optimal method for partitioning the object into congruent and similar shapes was proposed,and the calculation formulas for the element stiffness matrices of typical two-dimensional were given.At the same time,aiming at the problem of fast analytical solution of constraint forces based on rigid finite element method,a direct solution method of constraint forces based on the pseudo inverse of the global stiffness matrix was proposed.Through the element division of typical complex parts,the results show that the calculation amount of the element stiffness matrix is reduced 83%.Through the calculation of bolt design for machine tool support rib plate,the results show that directly solving constraint forces based on the pseudo inverse of the overall stiffness matrix can quickly and accurately achieve bolt design.The organic combination of the proposed unit optimization partitioning method and the direct solution method for constraint reactions can effectively improve the computational efficiency and accuracy of finite element analysis.

关 键 词：单元划分优化 全等图形 相似图形 刚性有限元法 伪逆 筋板 螺栓 

分 类 号：TH123[机械工程—机械设计及理论]