Application of the VIM to thermal buckling of composite beams on an elastic foundation

Abstract In this paper, thermal buckling analysis of composite laminated beams resting on a two-parameter elastic foundation is carried out by means of the variational iteration method (VIM). The solution procedure is based on the first-order shear deformation beam theory of Timoshenko combined with the von Karman type of geometrical non-linearity. Both edges of the beam are assumed to be axially restrained while may possess various out-of-plane boundary conditions. The elastic foundation is modelled via the two-parameter Pasternak medium which takes into account the vertical interaction of the elements. The governing equilibrium equations are obtained by means of the virtual displacement principle. Stability equations are then obtained by means of the adjacent equilibrium criterion. These equations are uncoupled to extract individual equations in terms of lateral displacement. The resulted differential equations are solved via the VIM. The study examines the VIM in obtaining the closed-form analytical solutions for thermal buckling of composite laminated beams. Furthermore, it is shown that for some special materials with negative thermal expansion coefficient, buckling may occur under cooling rather than heating or it may not occur at all.