New exact analytical thermal buckling solutions of composite thin plates with all edges rotationally-restrained

Abstract

This research explores the finite integral transform approach for analytical thermal buckling solutions of composite thin plates with all edges rotationally-restrained, which is difficult to handle by other analytical approaches. Performing the transformations defined on the governing thermal buckling equation and the boundaries investigated, which yields the transform coefficient for the deflection. Incorporating the inversion formula to satisfy the remaining boundary restraints yields sets of homogenous linear algebraic equations, which determines the critical temperature and corresponding mode shapes for plates. In addition, we provide new exact solutions for non-Levy-type plates via setting the rotational restrained coefficient. The precision and efficiency of the present solutions were well validated by precise FEM analysis. It is promising to develop the present approach for seeking more analytical solutions for intractable moderately-thick/thick plate problems. RESEARCH HIGHLIGHTS Finite integral transform approach for new exact thermal buckling analysis of fully rotationally-restrained composite rectangular thin plates is developed. New analytic exact thermal buckling solutions of plates under non-classical/non-Levy-type boundaries are obtained. Comprehensive benchmark numerical and graphical results are presented. The method is promising to explore new analytic solutions for intractable problems of plates based on different shear deformation theories.