Nonlinear thermomechanical static and dynamic analysis of sandwich beams with CNT-reinforced composite core and elastically restrained ends

This paper presents a semi-analytical approach to investigate the nonlinear static and dynamic responses of sandwich beams constructed from carbon nanotube (CNT) reinforced composite core and homogeneous face sheets. CNTs are distributed into polymer matrix through uniform and functionally graded patterns. The properties of constituents are assumed to be temperature-dependent and effective properties of nanocomposite core are estimated by means of extended rule of mixture. Elasticity of tangential constraint of two ends is considered to cover all possible situations of in-plane boundary conditions. Motion equations are established on the basis of Timoshenko beam theory taking into account von Kármán nonlinearity, initial geometric imperfection and interaction from elastic foundations. Analytical solutions and Galerkin method are employed to solve motion equations and derive a nonlinear ordinary differential equation for sandwich beams with simply supported ends. In the nonlinear dynamical analysis, fourth-order Runge-Kutta scheme is employed to trace the temporal displacement paths. Parametric studies are performed to assess various influences on the nonlinear static and dynamic responses of sandwich beams. It is found that there is exists a relatively value of thickness of face sheets for which the static and dynamic deflection are the smallest. The results also detect that tangential constraints of ends result in decrease and increase in the deflection at lower and higher temperatures, respectively.