模拟弹塑性碰撞的修正SPH方法

从基本的无网格光滑粒子法SPH(Smoothed Particle Hydrodynamics)近似出发,修正了模拟固体力学中大变形弹塑性碰撞的SPH方法.在边界处采用修正的边界条件,弹塑性分析过程中采用增量理论计算应力,迭代过程中用守恒光滑法进行滤波修正消除拉力不稳定.对SPH方法进行了程序实现,给出了杆弹塑性碰撞的算例.计算分析表明,SPH方法节点的影响域较大、精度较相同节点间距有限元法的结果有一定差距,但是通过增加粒子数量可以提高SPH的精度,保持了其简单性和计算大变形的特性.

Simulation of elastic-plastic impact with modified smoothed particle hydrodynamics method

Based on the approximation of smoothed particle hydrodynamics(SPH),the formulations of SPH method,which can numerically simulate the elastic-plastic impact process in solid mechanics,was established.Modified boundary functions were used to simulating the boundary condition.Owing to the tensile instability of traditional SPH,the code cannot get the proper result.The conservative smoothing approach was used in the procedure to filter the result and eliminate the tensile instability.The example of elastic-plastic impact of a pole and the comparison of the result calculated by SPH and finite element method(FEM) were given.The numerical example and analysis that indicated the influencing region of traditional SPH particle is lager than FEM,and the precision of SPH method is lower than FEM at the same scale of particles.The precision of SPH method can be improved by increasing the number of particles.