Simple formulas for thermal post-buckling of square plates using Green-Lagrange strain-displacement relations

Abstract

In this paper, simple intuitive formulas are derived, to predict the thermal post-buckling behavior of square plates, undergoing large lateral deflections. Most of the earlier work on this topic, used the von-Karman nonlinear strain-displacement relations, that are valid for the moderately large lateral deflections. In this study, the rigorous Green-Lagrange nonlinear strain-displacement relations, which do not have this restriction on the magnitude of the lateral deflections are used, to formulate the post-buckling problem. This formulation makes use of the tensile loads developed, if the normal inplane edge displacements are restrained to move in the plane of the plate, due to the large lateral deflections. The effectiveness of this approach is shown by Woinowsky-Krieger, while studying the nonlinear vibrations of beams. The intuitive formulation is validated indirectly, by considering a column, and a square plate, bending in one direction only, as the corresponding post-buckling results are not readily available. Finally, the simple formulas derived for the first time, to predict the thermal post-buckling behavior of the simply supported and clamped square plates.