Analysis Of Small Deformation Of Thin Plate& Thin Shell With Element-free Galerkin Method (EFG)

With the wide application of plane & shell structures ,the exact analysis of such structures become very important. However , the analysis goes more difficult and the expenses come higher as more accuracy is demanded , especially the structures has crack and/or is multi-material made. The new type of numerical method called mesh-free method is being developed quickly in the area of computational mechanics in recent years. Element-free Galerkin Method (EFG) is a well-developed method in most mesh-free method. Comparing with traditional numerical method: Finite Element Method(EFM) , Nodes of the Element-free Galerkin (EFG) method have less degree of freedoms which makes programme easier . EFG method very advantageous for dealing with cracks and/or multi-material interface because it merely requires to generate node belong crack and material interface. Moreover, EFG computation model is much easier to build. This make EFG more valuable for analysis of thin plate that has cracks and/or is multi-material made. Using EFG method, the present paper analyzes small strain bending problems of thin plate that has one crack, two cracks, and two materials with one crack at material interface . For thin plate,the shear deformation in the neutral surface is ignored, only worrying about bending deformation. So node only has displacement freedom perpendicular to the plane of the plate. The curvature can be obtained directly to construct EFG alignment. Gauss quadratures is used . The integrals are evaluated with Gauss quadratures by subdividing the domain into subdomains . The characteristics of material is considered in the process of numerical integration. The essential boundary conditions are enforced by full transformation method. For thin shell , the shear tensile deformation and bending deformation in the the plane of the shell . The parameter coordinates of the shell middle surface is employed . On base of Simp shell theory. The strain in the plane is deduced from the first fundamental form of deformed shell middle surface and the curvature is deduced from then second fundamental form of deformed shell middle surface . The EFG alignment is then constructed . Based on SC (the stabilized conforming nodal integration method by Chen and his coworkers, the nodal integration of derivative of the approximant is implement. In this paper, displacement boundary conditions are treated by the full transformation method , and rotation boundary condition by penalty function method. Numerical results show that the above method is accurate,convergent ,stable and can efficiently solve small deformation of thin plate & thin shell.