平面桁架的几何非线性有限元分析

Finite Element Analysis of Geometric Nonlinearity for Plane Truss

平面杆系结构的几何非线性分析方法有多种。以平面桁架为例,从杆的平衡方程出发,直接利用变分方法导出杆单元在大转动、小应变条件下的考虑几何非线性的单元切线刚度矩阵,依照此原理编制了相应的有限元程序。算例表明,推导结果是正确的,该程序可用于平面桁架的几何非线性分析。

There are many methods for geometric nonlinearity finite element analysis of plane truss. Starting from geometric and physical relations of plane truss, the authors have successfully derived non-linear tangent stiffness matrix of plane truss element with large displacement. Based on this theory, program has been worked out, numerical results of high accuracy for plane truss is thus obtained. Computations indicate that formulations for the nonlinear element are effective and that the nonlinear solution is convergent. The method and its program could be used for engineering designers to accurately analyze plane truss,