Non-linear dynamic analysis of FGM plates and shells with a degenerated shell finite element

Abstract

In this work, the nonlinear time history response and dynamic-buckling of functionally graded material (FGM) shell structures in thermal environments with temperature-dependent material properties are studied. The effective properties of the functionally graded material are assumed to be temperature-dependent and can vary through the thickness only. To overcome shear and membrane locking, an efficient modified reduced integration is adopted. An implicit conservative/decaying time integration scheme and a curved 8-node degenerated shell element are used for the time and spatial discretization respectively. The shell element is formulated in the framework of the Total Lagrangian Formulation with thermal strains/stresses taken into account using the Green-Lagrange geometric nonlinearity. Numerical results obtained here, show that the developed curved shell element with the implicit conservative time integration scheme is capable of solving nonlinear dynamic-buckling and large displacement dynamic problems of FGM shell structures in severe thermal environments. The effects of the constituent material, material gradient, parameters of structural geometry and thermo-mechanical loadings on the dynamic behavior are then investigated. In particular, the effects of the power-law indexes and temperature gradient through-thickness on the nonlinear static, dynamic and dynamic-buckling phenomena are presented and discussed.