Nonlinear dynamic analysis of imperfect functionally graded material double curved thin shallow shells with temperature-dependent properties on elastic foundation

Abstract

This paper presents an analytical investigation on the nonlinear dynamic analysis of functionally graded double curved thin shallow shells using a simple power-law distribution (P-FGM) with temperature-dependent properties on an elastic foundation and subjected to mechanical load and temperature. The formulations are based on the classical shell theory, taking into account geometrical nonlinearity, initial geometrical imperfection, temperature-dependent properties and unlike other publications, Poisson ratio is assumed to be varied smoothly along the thickness $\nu =\nu (z)$ . The nonlinear equations are solved by the Bubnov-Galerkin and Runge-Kutta methods. The obtained results show the effects of temperature, material and geometrical properties, imperfection and elastic foundation on the nonlinear vibration and nonlinear dynamical response of double curved FGM shallow shells. Some results were compared with those of other authors.