Study on Element Free method for Material and Geometrically Nonlinear Problems

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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.