基于MLPG法的动态断裂力学问题

利用无网格局部Petrov-Galerkin(MLPG)方法分析了受瞬态载荷作用的动态断裂力学问题.采用移动最小二乘近似函数为试函数,并利用罚函数法施加本质边界条件.同时,利用纽马克法进行时间积分.最后求解了双缺口板尖端附近的应力场,以及Ⅰ型和Ⅱ型应力强度因子随时间的变化关系.算例表明:利用MLPG方法分析受瞬态常压力作用的动态断裂力学问题是可行的和有效的,且具有效率高和容易分析的特点.

An Analysis of the Dynamic Fracture Problem by the Meshless Local Petrov-Galerkin Method

The dynamic fracture problem under an impulsive load was analyzed using the meshless local Petrov-Galerkin method. The moving least squares (MLS) approximation was adopted to approximate displacement functions, and the penalty function method was used to impose the displacement boundary conditions. The Newmark method was applied in the time integration scheme. The stress fields near the crack tip of a double notched plate and time histories of dynamic stress intensity factors (DSIF) for mode-I and mode-II were obtained. The numerical example shows that the local Petrov-Galerkin method is feasible and effective to analyze the dynamic fracture problem under the impulsive load, and has advantages of higher precision, higher efficiency and easy implementation.