On Coupled Problems Of Functionally Graded Materials Plates And Shells

As nonhomogeneous materials, functionally graded materials (FGMs) were first introduced by a group of Japanese scientists to address the needs of aggressive environment of thermal shock. Since then, FGMs have received more and more attention. Nowadays, FGMs have extended their first applications in aerospace to electronics, chemistry, optics, biomedicine, acoustics, nuclear engineering, civil engineering and the like. Research on the behavior of FGM structures not only benefits the development of mechanics of nonhomogeneous materials, but also satisfies the needs of practice.The inhomogeneity of FGM makes it very difficult to analyze the FGM structures. Most of the present works on FGM structures employed kinds of assumptions or theories derived for the homogeneous materials, which may become doubtful for FGM structures. So, we employ an elasticity method, i.e. state space method, to analyze the simply-supported FGM beams, plates and cylindrical shells. For FGM, the coefficient matrix of the state equation is not constant and is very difficult to solve directly. The FGM plates/shells are then approximated by a laminate model. Since no assumptions are introduced on the deformations or stress fields in the analysis, the presented results can serve as benchmarks for clarifying the reliability of various approximate theories or numerical methods. We find that the inhomogeneity of FGM will affect the response of FGM structures effectively, which will be crucial to the design in the practice.As new smart structures, piezoelectric FGM structures have gained much interest recently. The interface between the piezoelectric actuator or sensor layers and the FGM layers, however, may become debonding during the service time. In some cases, weak bonding is particularly introduced to achieve some particular aims. A linear spring-layer model is adopted in this paper to simulate the weakness of bonding and the effect of bonding is discussed.Finally, a generalized refined theory suggested by Soldatos is employed to analyze the cylindrical bending of single- or multi-span FGM plates under various boundary conditions. Since the shape function of displacements is determined by the elasticity equations of equilibrium, it can be self-adjusted with the gradient index, which makes this theory more suitable for analyzing FGM structures. To improve the efficiency of calculations, the state space method is adopted to derive the shape function and solve the equations governing the FGM plate deformation. The numerical comparisons between several theories show that the inhomogeneity of FGM will decline the accuracy of the classical thin plate theory, the first-order shear...