Study On Adaptive Meshfree Method In Solid Mechanics

In recent years, the meshfree method has been becoming the focus of research inthe field of computational mechanics. Meshfree methods employ specialapproximation theories that allow the construction of shape functions without theneed of element. Because nodes can be moved, inserted and deleted freely, themeshfree methods are particularly suitable for adaptive analysis.The research of this thesis is on adaptive element free Galerkin method (EFGM).This method uses moving least-squares (MLS) approximation and global Galerkinformulation. It requires a background mesh for domain integration. An adaptiveprocedure based on background mesh is developed for this meshfree method. Itcomprises a background cell energy error estimate and a local domain refinementtechnique. The essence of error estimates is to use the difference between the valuesof the projected stress and these given directly by the EFG solution. Global and localenergy errors are computed in background cell as the basic measure of errorestimation. A technique based on Delaunay triangulation algorithm is implemented inbackground mesh generation and domain refinement to improve the solution of theelement free Galerkin method.The method is used to solve linear elastostatic and elastodynamic problems withhigh gradient phenomena such as stress concentration and stress wave. The results ofstress concentration problems show that this method can reduce the error of numericalsolutions. In this thesis, the adaptive meshfree method is creatively used to trackstress wave propagation in the forefront. The examples show the adaptive procedurepresented in this method can improve the results of stress wave problems effectively.