基于Hamilton体系的弹性力学问题的比例边界有限元方法

比例边界有限元方法是求解偏微分方程的一种半解析半数值解法。对于弹性力学问题,可采用基于力学相似性、基于比例坐标相似变换的加权余量法和虚功原理得到以位移为未知量的系统控制方程,属于Lagrange体系。但在求解时,又引入了表面力为未知量,控制方程属于Hamilton体系。因而,本文提出在比例边界有限元离散方法的基础上,利...

A Hamiltonian-based derivation of scaled boundary finite element method for elasticity

The scaled boundary finite element method (SBFEM) is a semi-analytical and semi-numerical solution approach for solving partial differential equation. For problem in elasticity, the governing equations can be obtained by mechanically based formulation, Weighted residual formulation and principle of virtual work based on Scaled-boundary-transformation. These formulations are described in the frame of Lagrange system and the unknowns are displacements. In this paper, the discretization of the SBFEM and the dual system to solve elastic problem proposed by W.X. Zhong are combined to derive the governing equations in the frame of Hamilton system by introducing the dual variables. Then the algebraic Riccati equations of the static boundary stiffness matrix for the bounded and unbounded domain are derived based on the hybrid energy and Hamilton variational principle in the interval. The eigen-vector method and precise integration method can be employed to solve the algebraic Riccati equations for static boundary stiffness matrice.