A Theoretical Analysis Of FGM Plates And Shells Based On Physical Neutral Surface

Functionally gradient materials (FGM) are both macroscopically and microscopically heterogeneous composites which are normally made from a mixture of ceramics and metals with continuous composition gradation from pure ceramic on one surface to full metal on the other. This leads to a gradual and smooth change in the material profile as well as the effective physical properties, making them distinguish from the conventional fiber-matrix composites and preferable in many engineering applications, especially in high temperature environments such as aerospace structures, fusion reactors and nuclear industry. In this paper, the concept of physical neutral surface and classical laminated plate and shell theories are employed to formulate the basic equations of the FGM plates, cylindrical shells and double curved shallow shells. In this theory, stretching-bending coupling effects are decoupled, governing equations and boundary conditions have the simple forms, so analysis and solution procedure of FGM plats and shells are simplified.In linear analysis, FGM plates and shells behaviors, which include bending, vibration, bucking, are discussed using analytical method based on physical neutral surface theories. With increased material constant, deflections of FGM plate and shell are decreased, but frequency and critical bucking loading are increased.In nonlinear analysis, FGM plates and shells behaviors, which include large deflection bending, large deflection vibration, post-bucking, are discussed using Galerkin variational method. It can be concluded thatIn nonlinear bending analysis of FGM plates, cylindrical shells and double-curved shallow shells, if there is no thermal loading, behaviors of FGM plates and shells are intermediate to that of plates and shells made of pure ceramics and metals in mechanical loading, but this is not true while thermo-mechanical loading are applied. Under the same thermal loading, simply support plates have larger initial deflection, and clamped shells have small initial deflection, but clamped plates have not except for in post-bucking state. When geometry parameter of FGM shells is larger than critical geometry parameter, in which are related with material constant, thermal loading and boundary condition, the maximum deflection has a sudden jump with the increased mechanical loads.Under simply support and clamped boundary conditions, deflections of plates are increased with increased mechanical loading. Deflections of simply support plates are larger than clamped plates with or without thermal loading. Deflections of plates with thermal loading are larger than deflections of plates without thermal loading. Under thermal loading, simply support plates have initial deflection, but clamped plates has not except for in post-bucking state. In nonlinear bending analysis of FGM cylindrical and double curved shallow thin shells, the maximum deflection has a sudden jump with the increased mechanical loads.In large deflection vibration analysis, when vibration amplitude is closed to zero, nonlinear frequency is closed to linear frequency, frequency of FGM plates are increased with increased vibration amplitude, but frequency of FGM shells are complex with increased vibration amplitude.In post-bucking analysis, deflection of simply support plates is closed to zero, when boundary pressure is closed to critical pressure. Deflection of simply support plates increased with increased boundary pressure. With increased thermal loading, clamped FGM plates have bifurcation buckling behavior, but simply support plates has not. Under the same thermal loading, heat resistance of ceramics is better than that of metals, but if material constant is properly selected, that of FGM can be better than that of ceramics, so superiority of FGM can be best presented.Physical neutral surface plate and shell theories about FGM have more merits in the engineering application, because they are easier and simpler than classical laminated plate and shell theories based on geometric middle surface.