基于比例边界有限元法的高阶透射边界应用

摘要

基于比例边界有限元法和连分式展开推导了无限域弹性动力分析的求解方程,实现了一种局部的高阶透射边界.采用改进的连分式法求解无限域的动力刚度矩阵,克服了原连分式算法可能会造成矩阵运算病态的问题.该局部高阶透射边界在时域里表示为一阶常微分方程组,其稳定性取决于其系数矩阵的广义特征值问题.如果出现虚假模态,采用移谱法来校正系数矩阵以消除虚假模态.通过两个算例验证了该高阶透射边界的精确性、鲁棒性.%For an unbounded domain,a local high-order transmitting boundary is implemented based on the scaled boundary finite element method and the continued-fraction expansion.An improved continued-fraction expansion is employed to solve the dynamic stiffness matrix equation of an unbounded domain.Compared to the previous approach,it is numerically more robust for large-scale systems and arbitrarily high orders of expansion.The equation of this boundary is a system of first-order ordinary differential equations in the time domain.The stability of the high-order boundary depends on the general eigenproblem of the coefficient matrices.Possible spurious modes can be eliminated using the spectral shifting technique.The accuracy and the robustness of the high-order transmitting boundary are verified by two numerical examples.