Several Studies Of Functionally Graded Annual Sector Plate

Functionally graded materials(FGMs),as a kind of new composite materials developed in the last two or three decades,whose structure and composition vary continuously in space.Compared with traditional homogeneous or laminated materials,FGMs have more superior mechanical properties in the aspects of avoiding and reducing local stress concentration and relieving thermal stress.Beams,plates and shells,as the most common structures,are wildly used in engineering applications and a large number of papers have been published on the mechanical problems of functionally graded beams,plates and shells.In this paper,three-dimensional elasticity solutions are presented for a transverse isotropy functionally graded annular sector plate subjected to tangential force X,normal force Y and concentrated couples M_X,M_Y and M_Z that are applied at one of its radial edges.The other radial edge is fixed and the two arc boundaries are free.There are no loads on the top and bottom surfaces of the plate.The material parameters can vary along the thickness direction in an arbitrary fashion.The main research contents and innovations are as follows:1)According to the study of Yang,et al(2012),the complex variable method is used to solve the problem.Four analytic functions with several undetermined constants are constructed based on Mian and Spencer(1998)displacement expansion formula of bending problem for functionally graded plate,among which how to construct these four analytic functions is one of the key points in this paper.2)Based on the situations for the plate subjected to concentrated forces and concentrated couples,combing solving conditions,corresponding boundary conditions and end conditions are founded to determine these undetermined constants so as to accomplish the analysis,in which the correct and reasonable boundary conditions and end conditions is the another key point of this paper and it is also a innovative result.3)When the material elasticity parameters are the constants,transverse isotropy functionally graded annular sector plate can be degenerated into homogeneous transversely isotropic and homogeneous isotropic annular sector plate and the corresponding internal force analytical solutions are obtained.4)The ANSYS software is used to simulate and analyze the annular sector plate.The simulation results are compared with the three-dimensional elasticity solutions and the corresponding conclusions are drawn.