Study on Element Free method for Material and Geometrically Nonlinear Problems

本研究的目的是发展一种材料和几何非线性问题的无单元方法。本研究结果总结如下：提出了考虑几何非线性的EFGM的新公式。在该公式中，位移函数采用移动最小二乘插值逼近，Drichlet边界条件采用惩罚法。2、基于patch和mapping的概念，提出了enhanced free element Galerkin method （E-EFGM）。用这种方法可以分析由几种材料组成的结构以及弯曲结构。讨论了EFGM应用于弹塑性问题的难点。3、提出了一种新的插值方法——带约束条件的最小二乘法，并将其应用于Batina型无网格法和采用节点积分法的无单元Galerkin法。该方法在不损失精度的前提下，使约束条件的施加变得简单有效。几个数值算例说明了上述方法的有效性。

The purpose of this study is to develop a element free method for material and geometrically nonlinear problems. The results of this study are summarized as follows.1, The new formulation of EFGM considering geometrically nonlinearity is presented. In the formulation, the moving least square interpolation is used for the approximation of the displacement function and penalty method is used to impose the Drichlet boundary conditions.2, The enhanced element free Galerkin method (E-EFGM) is formulated based on the concept of patch and mapping. Using this method, the structure composed of several kind of materials, as well as the curved structure, can be analyzed. The difficulty of the application of EFGM to elastic-plastic problems is also discussed.3, The new interpolation method, the least square method with constraint conditions, is proposed and applied to the gridless method of Batina type and element free Galerkin method using nodal integration method. Using this method, the imposition of constraint condition becomes simple and efficient without loss of accuracy.4, Several numerical examples clarify the validity of the above proposed methods.