MLPG混合配点法在材料不连续问题中的应用

Treatment of Material Discontinuity in the Meshless Local Petrov-Galerkin Mixed Collocation Method

基于MLPG混合配点法提出了分析结构中存在材料不连续性问题的方法。通过移动最小二乘近似构造形函数,采用配点法建立系统平衡方程,推导了系统刚度矩阵和载荷力向量。采用直接插值法和罚函数法添加了本质边界条件和自然边界条件,利用直接插值法在材料界面上添加平衡条件。通过对包含2种材料的一维杆的求解,证实了MLPG混合配点法求解材料不连续问题的有效性,而且结果具有较高的精度。

This paper propose a method of analyzing structure with material discontinuity in the MLPG mixed collocation method.The shape functions are constructed using Moving-Least-Squares approximation and the collocation method is adopted for establishing the system equations.The traction and displacement boundary conditions are imposed into the system equations while the equilibrium equations on the material interface are added into the system equations directly.The effectiveness of treatment of material discontinuity in the MLPG mixed collocation method is proved by solving a one-dimensional bi-material rod.