Snap-through analysis of thermally postbuckled graphene platelet reinforced composite beam

Abstract

Present investigation deals with the snap-through phenomenon in a thermally pre-buckled or post-buckled reinforced composites beam. Composite laminated beam is reinforced with graphene platelets (GPLs) where the weight fraction of GPLs may vary in each layer. The governing equations of the beam are obtained by means of the first order shear deformation beam theory and the von-Kármán type of kinematic assumptions. The conventional Ritz method with Chebyshev polynomials is used to discretize the governing equations and establish a set of non-linear equations dealing with the response of a beam under the action of thermal and mechanical loads. Furthermore, the case of uniform temperature elevation in the beam and uniform lateral pressure is considered. At first, the response of the beam under uniform temperature elevation is obtained. Depending on the magnitude of temperature rise, beam may remain flat or undergo thermal post-buckling. Using the displacement control strategy, the non-linear eigenvalue problem is solved. After that the response of the pre-buckled or post-buckled beam subjected to uniform lateral pressure in large deflection is evaluated. Due to the possibility of snap-through phenomenon, the cylindrical arch-length technique is employed. At first, two comparison studies are provided to assure the validity and efficiency of the developed formulation. After that, novel numerical results are given to discuss the effects of temperature change, weight fraction of GPLs, distribution pattern of GPLs and boundary conditions. It is shown that the limit loads of the snapping phenomenon and the intensity of the snap-through phenomenon are highly dependent to the mentioned factors.