Two-dimensional Isothermal Elasticity And Thermoelasticity Analysis Of Functionally Graded Materials By The Generalized Finite Integration Method

Mechanical performances under different external conditions are usually considered during design of Functionally graded materials(FGMs).In order to save cost,numerical simulation has played an important role in studying FGMs.Among many meshless methods,the generalized finite integration method(GFIM)constructed integration matrix by using piecewise polynomials is a special strong form collocation method.It does not involve Gaussian integral and weighted functions,and possesses high accuracy and stability.In this paper,the GFIM is extended to solve system of partial differential equation,and is used to analyze the 2D isothermal elasticity and thermal elasticity of FGMs.The main works of this paper is as follows.(1)Some research progresses of finite integration method(FIM),FGMs are described.Detail formulations of GFIM and FIM are given.And mapping technique and Durbin’s Laplace inversion technique are introduced into GFIM.(2)The program design procedure of GFIM for solving PDEs is systematically summarized.The influences of the kind of collocation nodal points,the order of piecewise polynomial and the arbitrary functions on the results are discussed.And the accuracy of FIM and GFIM is compared.(3)The novel treatment for constructing relationships among arbitrary terms produced during integration procedure is proposed.The GFIM is extened to solve isothermal and thermal elastic problems of FGMs.In order to validate its feasibility,the results of GFIM are compared with those of FEM COMSOL Multiphysics.The mechanical responses of FGMs with isotropy,orthotropy and different gradient distributions under external conditions are discussed.