一种高效的局部径向基点插值无网格方法

AN EFFICIENT MESHLESS METHOD THROUGH LOCAL RADIAL POINT INTERPOLATION

提出了一种弹性动力分析的高效局部径向基点插值无网格方法(MLRPI).该方法采用径向基点插值形函数近似解变量,运用局部Petrov-Galerkin法推导出了相应的离散方程,并根据波动模拟的精度要求,得到某一结点的动力方程.然后采用Newmark常平均加速度法和中心差分法相结合的显式积分格式进行时域积分,得到每个自由度的一种解耦递推格式.最后,对一平面应变问题进行了求解,比较了该文提出的解耦MLRPI方法、常规MLRPI方法和ANSYS有限元方法的精度和计算时间,结果表明解耦MLRPI方法与常规MLRPI方法的精度相当,但计算效率大大提高.

This paper presents an efficient meshless method through local radial point interpolation （MLRPI） for analyzing elastic dynamic response. The method involves a lumped--mass MLRPI and explicit integration procedures, and avoids solving algebra equation sets required by ordinary meshless methods. The shape functions possess the Kronecker delta function property, thus no additional treatment is needed to impose essential boundary conditions. Numerical examples show that the proposed deeoupled MLRPI has the comparable accuracy with the ordinary MLRPI and the ANSYS software, but has high efficiency.