Third order thermomechanically coupled laminated plate: 2D nonlinear modeling, minimal reduction, and transient/post-buckled dynamics under different thermal excitations

Abstract

In the framework of a unified 2D continuum formulation of the fully coupled thermomechanical laminated plate with von Karman nonlinearities, a consistent model with third order shear deformability and cubic temperature distribution along the thickness is proposed. Focusing on symmetric cross-ply laminates, an effective minimal dimension reduction is then pursued by expressing both in-plane displacement components and shear angles in terms of transverse displacement and thermal variables via kinematic condensations. The ensuing compact reduced order model with different coupling features allows to account for nonlinear mechanical and thermal phenomena, along with their interactions, under a variety of thermomechanical assumptions, boundary conditions and excitations. Upon proper validation in linear free dynamics and critical buckling, numerical investigation of the nonlinear dynamic response under different thermal conditions is accomplished, focusing on the variable features of its transient and post-buckled response, where the thermomechanical interaction plays a meaningful role.