基于SBFE和改进连分式的有限域动力分析

DYNAMIC ANALYSIS OF BOUNDED DOMAINS BY SBFE AND THE IMPROVED CONTINUED-FRACTION EXPANSION

基于比例边界有限元理论框架,通过采用连分式展开和引入辅助变量,将有限域的动力刚度矩阵和质量矩阵采用高阶的矩阵表示.采用改进的连分式法求解比例边界有限元方程中的动力刚度矩阵.通过增加连分式展开的阶数,该求解方法能包含动力分析的主要频率范围.针对结构自由度较多的系统当连分式阶数逐渐增大时,原连分式算法可能会造成矩阵运算病态的问题,提出采用改进的连分式算法能有效地提高数值计算稳定性.通过对一正八边形的自由振动分析及矩形平面的时域分析,算例结果表明改进算法的鲁棒性更强,适合大规模系统的动力分析.

By using the continued-fraction solution and introducing auxiliary variables, the dynamic stiffness and mass matrices of bounded domains are expressed in high-order matrices. The formulation is based on an improved continued- fraction solution of the scaled boundary finite element equation in dynamic~ stiffness. This continued-fraction solution converges over the whole frequency range with increasing order of expansion. Compared to the original approach, it leads to numerically more robust for large-scale systems and arbitrarily high orders of expansion. The eigenvalue problem of a regular octagon is considered. Transient analysis of a bounded rectangular plane is also presented. The results of two numerical examples demonstrate that the proposed method is superior to the original approach and it is suitable for dynamic analysis of large-scale systems.