非均质材料无网格Galerkin法

ELEMENT-FREE GALERKIN METHOD FOR NONHOMOGENEOUS MEDIUM

提出了采用无网格Galerkin方法来分析非均质材料。无网格伽辽金法 (EFGM)是近些年发展起来的一种数值算法 ,它采用移动的最小二乘法构造形函数 ,从能量泛函的弱变分形式中得到控制方程 ,该法只需节点信息 ,不需将节点连成单元。在积分网格中 ,取高斯点的材料参数来模拟材料特性的变化。算例的结果显示用该法来分析非均质材料得到的结果精度高 ,表明该方法在非均质材料领域有着广阔的应用前景。

The element free Galerkin method(EFGM) for the stress analysis of nonhomogeneous medium is proposed. EFGM is a new numerical method developed recently. In the method, shape function is constructed by moving least square, control equation is produced from the weak form of variational equation, and only nodal data are necessary, joining nodes into element is not needed. In quadrature elements,variations of material properties are simulated by adopting material parameter of Gauss point.High accuracy achieved in examples shows that EFGM is promising in nonhomogeneous medium.