Bending–Extension Coupling at Restrained Ends and the Nonlinear Transient Response of Porous FGM Sandwich Beams in Thermal Environments

Abstract

Abstract

This paper examines the nonlinear transient response of porous FGM sandwich beams with elastically restrained ends under thermal environments. Using a refined higher-order shear deformation theory (HSDT), two configurations are analyzed: symmetric and asymmetric cross-sections with temperature-dependent properties and varied porosity distributions. In asymmetric structures, conventional strong-form approximations omit the boundary moments caused by bending–extension coupling and thermal effects. To address this methodological gap, a multi-term weak-form Galerkin approach is developed, retaining end moments and arbitrary support locations. The formulation is rigorously validated against exact linear solutions and independent nonlinear finite element models. Results demonstrate that section symmetry dictates the validity of strong-form approximations. For asymmetric beams, ignoring thermal bending leads to an overestimation of peak deflections at elevated temperatures, with deviations amplifying when supports act at the neutral surface. Comprehensive parametric evaluations further elucidate the governing influence of end restraint, porosity, layer thickness, foundation stiffness, and initial imperfections on the dynamic response.