余能原理基面力元法在桁架弹塑性分析中的应用

基面力元法(BFEM)是一种新型的有限单元法,是以"基面力"来描述一点的应力状态。为了编制适用于桁架弹塑性分析的MATLAB基面力元程序,以余能原理基面力元法为基础,将基面力元法的平面4节点的实体单元模型向桁架单元进行退化,列出了退化桁架单元的柔度矩阵、单元轴力和节点位移的具体表达式,并对其控制方程进行了必要的处理。根据退化的桁架单元模型,采用增量法的思想和线性强化弹塑性模型,以三杆超静定桁架和复杂静定桁架为算例进行了计算。将计算结果与大型有限元分析软件ABAQUS的T2D2计算结果进行了对比分析,发现所用方法与ABAQUS的计算结果高度吻合,进一步验证了基面力理论的正确性和程序的适用性。

Application of base force element method with complementary energy principle for elasto-plastic truss analysis

Base force element method(BFEM) is a new type of finite element method, which uses the "base force" as fundamental variables to describe the stress state at a point. In order to compile a base force element program for the elasto-plastic analysis of truss using MATLAB language, based on the BFEM with complementary energy principle, the solid element of the plane 4 nodes in BFEM is degenerated into the truss element. The concrete expressions of the flexibility matrix, axial force and displacement of the degenerated truss elements are derived, and necessary modification of the governing equations is conducted. According to the degenerated truss element model, the idea of incremental method and linear strengthened elasto-plastic model are adopted for calculation by using 3-pole indeterminate truss and complicated static determinacy as samples. It is found that through comparison of the calculated results and the results from T2D2 of ABAQUS, the calculated results using the method are in highly agreement with those obtained with ABAQUS, which further verifies the correctness of the base force element method and the applicability of the program.