Nonlinear consecutive dynamic instabilities of thermally shocked composite circular plates on the softening elastic foundation

Abstract

In this research, the nonlinear dynamics of a clamped circular composite plate placed on a softening elastic foundation under rapid thermal loading is investigated. In this situation, based on the amount of temperature supplied to the structure and the coefficients of softening elastic foundation, two instabilities may happen one after the other. The structure will thermally buckle and deform dynamically if the applied temperature exceeds a critical level. If the softening coefficient of the elastic foundation is critical, the structure will completely lose its stability after a certain deformation range. A polymer containing graphene platelets (GPL) makes up the system. Based on various functions, the volume fraction of fillers varies along the thickness. The system’s nonlinear dynamic equations are obtained by applying Hamilton’s principle and the Von-Kármán theory. The transient heat conduction equation is solved by the cubic B-spline collocation (CBSC) and Crank–Nicolson procedures. The CBSC and the Newmark methods are used to solve spatially and temporally dependent governing nonlinear differential equations. Also, the Newton–Raphson method is used as a powerful tool to solve nonlinear algebraic equations. The temporal evolution, phase-plane, and post-buckling-to-maximum deflection paths are demonstrated to analyze the instabilities of the plate.