余能原理基面力元法在桁架大变形分析中的应用

Application of base force element method on complementary energy principle in large deformation analysis of the truss

为了对桁架弹性大变形问题进行针对性研究,对平面二维问题的基面力单元模型进行了改进,把平面四边形四边中节点基面力单元退化为平面二节点桁架基面力单元,推导了桁架大变形余能原理控制方程和单元轴力、节点位移表达式,根据由控制方程得出的桁架大变形问题的非线性方程组,利用Matlab语言编制了基面力元程序,计算了桁架结构几何非线性算例。与大型通用有限元软件ANSYS的计算结果进行了对比分析,所用方法的结果与理论解一致,与ANSYS的计算结果相差较小。因此可得结论:所介绍的基面力元模型是可靠的,可以应用于对桁架结构的几何非线性问题分析,具有较广阔的前景。

In order to pointedly research the large elastic deformation problems of the truss , the model of the plane base force element method is improved. The plane 4-side 4-node base force element is degenerated into the 2-node truss element. The gov-erning equations of the BFEM for large elastic deformation of truss, the expressions of the axial force and the displacements formulation of nodal point are derived. According to the system of nonlinear equations for the large elastic deformation prob-lems of the truss obtained by the governing equations, the base force element program is developed by MATLAB technology. The typical numerical examples of the truss in geometric nonlinearity are calculated. The result is compared with that calculated by the ANSYS finite element software. It shows that the result of the proposed method is in accordance with the theoretical solution, and the difference between the result and that calculated by ANSYS is little. So the conclusion can be made that the model of BFEM given in this paper is reliable, and it can be used for geometric non-linear analysis of truss structure with wide application extension.