无网格伽辽金法在板弯曲问题中的应用

无网格伽辽金法采用移动最小二乘近似试函数,形函数一般不具有插值特性,本质边界条件需要特殊处理.本文采用替换式拉格朗日乘子法施加本质边界条件,为提高精度,对修正泛函使用罚函数法再次施加本质边界条件.此方法没有增加未知量的数目,而且刚度矩阵仍具有对称正定带状特点.数值算例表明了该方法的合理性及数值稳定性.

Application for Board- bending of Element- free Galerkin Method

In the Element- free Galerkin Method, shape function is constructed by the moving least square approximation. But the essential boundary condition cannot be applied directly because the shape function does not satisfy, the Kronecher- δ condition. The paper employs alternative Lagrange multiplier method to enforce the essential boundary condition, and the penalty function is employed again in order to improve the accuracy. This method does not increase the number of the unknown variables, and the stiffness matrix is still symmetry and stripness. The result shows that this method is reasonable and stable.