| Functionally graded material(FGM)is a new kind of composite material,which is different from the traditional composite material,the composition of FGM can change continuously along the space and there is no obvious material interface,so the stress concentration of the traditional composite material at the interface can be avoided.In addition,functionally graded materials can also be designed to meet the special needs of the structure,so they can be used in various engineering fields.At present,with the wide application of functionally graded materials,the study of mechanical properties of functionally graded materials(FGM)plates has long been the focus of researchers,and the balance of plates is one of the basic issues worth studying.Based on the three-dimensional elastic theory,the equilibrium of transversely isotropic functionally graded circular and elliptical plates subjected to different loads is studied in this paper.Based on the generalized England-Spencer plate theory and the complex function method,the theoretical expressions of transversely isotropic functionally graded plates are established.On this basis,the following research works are carried out respectively:(1)A three-dimensional analytical solution of a transversely isotropic FGM elliptic plate with fixed supports under uniform loads is obtained.The expression of the mid-plane displacement of the plate satisfies the fixed boundary conditions.Then,the expressions of four analytic functions corresponding to this problem are obtained by using the complex variable function method.The validity and accuracy of this method are verified by comparing with the existing analytical solutions.The numerical results show that the gradient index,the ratio of thickness to radius and semiminor axis ratio have important effects on the response of FGM elliptic plates.(2)The three-dimensional analytical solution of static bending of FGM circular plate under biharmonic function load is obtained.By expanding the transverse loads on FGM circular plates in the form of Fourier series along the circumference direction,the unknown constants involved in the analytical functions are determined by using boundary conditions similar to those in classical plate theory.The validity and accuracy of this method are verified by numerical examples.The results show that the gradient factor and load form have important influence on the bending behavior of FGM circular plates.(3)Three-dimensional elastic solutions of FGM circular plate and annular plate under boundary axial force and couple moment are obtained respectively.By making the inner diameter of FGM annular plate tend to zero,the accuracy of this method is verified by comparing with the solution of FGM circular plate problem.The numerical results show that the material gradient factor has a significant effect on the elastic field of FGM circular plates.The thickness to radius ratio of the plate has an effect on its displacement,while the effect on the dimensionless normal stress can be neglected.The theory of functionally graded plates presented in this dissertation can be applied to solve the equilibrium problem of material parameters varying continuously along the thickness direction.The upper and lower surfaces of the plate satisfy the boundary conditions accurately,and the side of the plate satisfies the boundary conditions similar to those in classical plate theory.Therefore,the analytical solutions of functionally graded plates based on three-dimensional elasticity theory can be used as reference solutions to check various semi-analytical solutions and numerical solutions used in the analysis of similar plates.In addition,according to the specific engineering application objectives,the optimal design of FGM circular and elliptical plates can also be achieved by using the three-dimensional analytical solution in this paper. |
PDF Full Text Request