The Analytical Solution And The ES-PIM Numerical Simulation Method For Sandwiches Cantilever Beam

Most phenomenon in nature such as in mechanical, mechanics, electronics and other fields can be described in the form of differential equations. We want to solve these equations for the analytical solution. While for the most of the practical problems, we can achieve the numerical solution instead of the analytical solution. So most numerical methods have been developed, such as Finite Element Methods, Finite Difference Methods, Finite Volume Methods, and recently Meshfree Methods. Based on the Finite Element Methods, Guirong Liu and his coworkers have developed a series of numerical methods according to the different background meshes, the shape functions and the integration domain. These method have been used to solve some shortcomings of the Finite Element Methods.Finite element method is one kind of numerical methods to solve the partial differential e-quations. FEM originates from the solid mechanics and gradually has been extending to different areas, such as heat conduction, fluid dynamics, and electromagnetic, etc.In this work, an edge-based point interpolation for material discontinuous problem is for-mulated. And we have applied this method to solve the sandwich cantilever beam problem. To test ES-PIM solution of this problem, we also calculated the analytic solution and the FEM solution of the the sandwich cantilever beam problem. By means of Matlab, we can get the high accuracy and efficient of the ES-PIM. The article consists of following parts:Chapter one introduces the background,development, and the research methods of the FEM.Chapter two gives the statement about the theory of elasticity of the material discontinuous problem, and also introduces the method of edge-based point interpolation.In chapter three, the analytic solution of the sandwich cantilever beam problem is illus-trated,which based on the the theory of elasticity.In chapter four, we apply the ES-PIM method to the sandwich cantilever beam problem, and give the solution of the Matlab program.At last, we make a brief summary of this paper.