基于拉氏变换的弹性动力学插值型重构核粒子法

插值型重构核粒子法的形函数具有离散点插值特性和不低于核函数的高阶光滑性，因而不仅可以直接施加本质边界条件，同时也保证了较高的计算精度．本文将弹性动力学方程作拉氏变换后，在变换域内用插值型重构核粒子法求解，最后再借助Durbin数值反演方法求得时间域的解．针对典型的弹性动力学问题，给出了插值型重构核粒子法的数值算例，并验证了本文方法的有效性．

Interpolating Reproducing Kernel Particle Method with Laplace Transform for Elastodynamics

Because the shape function of the interpolating reproducing kernel particle method has a point interpolation property and high-order smoothness no less than the kernel function, the essential boundary conditions can be imposed directly and the high numerical accuracy can be guaranteed as well. Based on the Laplace transform, the transient elastodynamic equation is transformed and the interpolating reproducing kernel particle method is utilized to calculate the response in the transformed domain. To determine the response in the time domain, the inverse Laplace transform algorithm of Durbin is utilized. Numerical examples for typical elastodynamic problems are presented, which shows that the interpolating reproducing kernel particle method is effective for elastodynamics.