New insights into nonlinear stability of imperfect nanocomposite beams resting on a nonlinear medium

Abstract

An analysis is performed in this research to study the nonlinear thermal stability of graphene platelet reinforced composite (GPLRC) beams based on the third-order shear deformation model of Reddy and von-Kármán kinematic assumptions. The influences of the three-parameter nonlinear hardening/softening elastic foundation and initial imperfection are also taken into account. GPLs are distributed in the layers of the composite media where the volume fraction of GPLs may be different in each layer, so a piecewise functionally graded media is achieved. The elasticity modulus of the composite media is estimated via the Halpin–Tsai rule which includes the dimensions of reinforcements while the thermal expansion coefficient and Poisson’s ratio are obtained via the simple Voigt’s rule. Three nonlinear and coupled governing equations are established using the concept of static version of the Hamilton principle. Due to the immovability of the edge supports, the equations are reformulated to reach two coupled equations in terms of lateral displacement and cross section rotation. For the case of a beam with both ends simply-supported, a two-step perturbation technique is implemented to extract the closed-form expression which provides the mid-span deflection as a function of temperature elevation. Results of this study are compared with the available data in the open literature with respect to simple cases. After that novel results are given to explore the effects of foundation parameters, beam geometry, GPL weight fraction and GPL patterns. It is shown that for sufficiently soft elastic foundation limit load type of instability occurs and the structure becomes imperfection sensitive.