Nonlinear Thermoelastic Static Vibration and Buckling Behaviour of Functionally Graded Shell Panel

Abstract

Functionally graded material (FGM) has created the interest of many researchers due to its tailor-made material properties. FGMs are the advanced form of composites that exhibit an inhomogeneous character especially designed for the high-temperature applications such as aircraft engines, rocket heat shields, thermal barrier coatings, heat exchanger tubes, etc. This material has been developed by taking the gradual variation of metal and ceramic constituents in a very efficient manner to suit the needs of the engineering structure. The effective material properties of the FGM follow the rule-based grading of two counterparts as discussed above, metals and ceramics. Shell structures made of FGMs are subjected to different kind of loading during their service life, and the structural responses (deformations, buckling/post-buckling, and linear/nonlinear natural frequencies) are affected considerably due to that. In this regard, a general nonlinear mathematical model has been developed for the FGM doubly curved shell panel using Green-Lagrange geometrical nonlinear kinematics in the framework of the higher-order shear deformation theory. The effective material properties of FGM shell panels are evaluated using Voigt’s micromechanical model via the power-law distribution. The material properties each constituent are assumed to be temperature-dependent. In addition, to achieve the true flexure of the structure, all the nonlinear higher-order terms are included in the mathematical model. The system governing equation of the FGM structure is obtained using the variational principle, and the direct iterative method is employed to compute the desired nonlinear responses in conjunction with suitable isoparametric finite element steps. The convergence behaviour of the proposed numerical model has been checked and validated further by comparing the responses with those available published literature. The linear and the nonlinear flexural, free vibration and the buckling responses of the FGM single/doubly curved shell panels are examined under thermo-mechanical loading. Finally, the effects of different geometrical and material parameters, support conditions, loading types on the deflection, frequency and critical buckling load parameter of the FGM single/doubly curved shell panels are examined and discussed in detail. This is also believed that the present study would be beneficial to the analysis and the design of FGM structure and/or structural component for real-life problems.