Finite Element Analysis For Bending Of Functionally Graded Material Plates

Functionally gradient material (FGM) is a new type of gradient composite material, which consists of two or more than two kinds of components. The volume content of each component varies continuously with the position. It can eliminate the discontinuity of material properties of traditional composite induced by abrupt interface. So it has a lot of superiority in various engineering fields. Due to the wide application of functionally gradient material plate in the modern structure engineering, the study on the mechanical properties of FGM plate has become a quite active research direction. In this paper, based on the classical, first-order shear deformation plate theories and three-dimensional elasticity theory, the bending problem of FGM rectangular plates was studied by using finite element method. Research based on the two plate theories mainly discusses the transform relation between the solutions of FGM and homogenous plates. Moreover, the study on the basis of three-dimensional elasticity theory chiefly focuses on checking the results from the two former plate theories under the given boundary conditions. The research work basically includes:(1) An analysis for the static bending problem of functionally graded material rectangular plates was presented based on the classical thin plate theory. Firstly, the basic equations of finite element method about the bending of FGM plate were deduced, from which a computing program of finite element method is formulated by using MATLAB. Then with the help of the program, numerical solutions of bending problem of FGM rectangular plate under specific load and boundary conditions were obtained. The effects of the variation of the volume fraction index and the boundary conditions on the bending solution were examined for the plates subjected to either uniformly distributed or concentrated loads. Finally, the transform relation between the bending solutions of FGM and homogenous plates is numerically verified by the finite element results.(2) Based on the first-order shear deformation theory, basic equations of finite element method for the bending problem of functionally gradient plate were derived. A computing program of the finite element solution procedure for bending of functionally gradient moderate thick plate was compiled in MATLAB language. By using this procedure, investigation on the bending behavior of FG medium thick plate under uniformly distributed load or concentrated load was carried out. Through comparing the solution of the first-order shear deformation theory to that of classical plate theory effects of shear deformation related to the span-thickness ratio and boundary constraints were investigated. Then, for rectangular plates with the four edges simply supported, an analytical transform relation between the bending solution of moderate thick FGM rectangular plate and that of the corresponding homogenous thin plate was deduced. Numerical results show that this relationship holds precisely. Finally, a numerical measure of integral function in the transform relation under other given boundary condition was also given.(3) Based on the three-dimensional elasticity theory, selecting eight-node cuboid element, static bending of FGM rectangular plate was investigated by using ANSYS, a general FEM program. Under some specified boundary conditions, three kinds of finite element solutions, resulting from3D elasticity theory, classical plate theory and the first-order shear deformation theory, were compared. This part focus on the analysis of the effect of the parameters such as span-thickness ratio, material property gradient parameter and boundary conditions on the bending solutions and also of the difference among the three kinds of solutions and their suitable range.