一种新的有限域动力刚度改进连分式求解算法

An improved continued fraction solution algorithm for dynamic stiffness of bounded domain

比例边界有限元法仅需离散边界,网格划分灵活,且易于采用高阶单元,是结构动力分析的理想方法。针对有限域动力问题,基于广义特征值分解对动力刚度表示的比例边界有限元方程进行模态变换。通过选取特定的因子矩阵,简化了改进连分式算法的求解流程,提出了一种新的有限域动力刚度改进连分式求解算法。在动力刚度连分式渐近解的基础上引入辅助变量,建立了有限域动力问题的运动方程,其系数矩阵对称稀疏,可以利用现有的有限元求解器求解。正八边形板和重力坝算例表明,新算法具有良好的数值稳定性和计算精度,适用于实际工程问题的动力响应分析。

The scaled boundary finite element method is an ideal method for dynamic analyses of structures.It requires the only discretization of the boundary,which leads to flexible mesh generation and easy employment of high-order elements.Based on the generalized eigenvalue decomposition,the scaled boundary finite element equation in dynamic stiffness for the bounded domain dynamic problem was transformed.Choosing a specific factor matrix,an improved continued fraction solution algorithm with simplified solution procedure was proposed.Introducing the auxiliary variables,the motion equation with sparse and symmetric coefficient matrices for bounded domain was established.It can be solved by using the existing finite element solver.Numerical examples including a regular octagon plate and a gravity dam were analyzed.Good numerical stability and computational accuracy of the new algorithm were demonstrated.This algorithm is suitable for dynamic response analyses of realistic engineering problems.