基于余能原理的有限变形问题有限元列式

Finite element formulation for finite deformation problem based on complementary energy principle

利用基面力概念,推导了一种基于余能原理的有限变形问题显式有限元列式,可应用于结构的大位移、大转动问题。以基面力为状态变量来表达单元的余能,将有限变形情况下的单元余能分解为变形余能部分和转动余能部分,利用Lagrange乘子法推导出余能原理有限元的控制方程,编制了相应的非线性有限元程序。通过算例分析,说明该列式和程序的可靠性和精确性。

Using the concept of base forces, an explicit finite element formulation for the finite deformation is presented based on complementary energy principle, which can be used for large displacements and large rotations problem of structures. The complementary energy of an element is described by taking the base forces as state variables, and the complementary energy in large deformation case contains deformation part and rotation part. The control equations of finite element method of complementary energy principle are derived using Lagrange multiplier method. A nonlinear finite element procedure is developed. Several examples are analyzed to illustrate the reliability and accuracy of the formulation and the procedure.