大规模宽频弹性动力学分析的快速定向压缩边界元法

Fast Directional Boundary Element Method for Large Scale Wideband Elastodynamic Analysis

发展一种大规模宽频弹性动力学分析的快速定向压缩边界元法.证明弹性动力学核函数具有定向低秩特性,为采用快速定向压缩算法提供理论基础.根据S波的波数,将节点之间的相互作用划分为低频相互作用和高频相互作用,并将后者进一步划分为与多个楔形区.在楔形区上,可以采用核函数的定向低秩特性进行快速计算.低频相互作用与核无关快速多极边界元法中计算方法相同,不同方向楔形区上的变换矩阵可以采用坐标系旋转的方法进行快速计算.可对任意频率进行快速谐响应分析.数值算例表明:该方法可以将宽频弹性动力学问题计算复杂度降低到O(Nlog~αN).与卷积求积边界元法相结合,也可以应用于弹性动力学瞬态分析.

A fast directional boundary element method for large scale wideband elastodynamic analysis is developed. Directional low rank property of elastodynamic kernels is shown which serves as the theoretical basis of its fast directional algorithm. By only considering S-wave number, interactions of different nodes are divided into low-frequency interactions and high-frequency interactions, and the latter is further divided into interactions with directional wedges on which the directional low rank property is applied. Low-frequency interactions are computed in same manner with that in kernel independent fast multipole BEM for elastodynamics, and translation matrices for different directional wedges are calculated efficiently by coordinate frame rotations. Thus harmonic responses for any frequencies can be computed efficiently. Numerical examples show that the computational complexity for wideband elastodynamic problems are successfully brought down to O(Nlog^αN). It can also be applied to transient elastodynamic analysis combined with convolution quadrature method.