Thermally induced post-buckling behavior of FGM sandwich beams including porosities and flexibly constrained ends on Kerr foundations

This paper presents a semi–analytical investigation on the buckling and post-buckling behaviors of functionally graded material (FGM) sandwich beams with porosity exposed to uniform temperature rise (UTR). Two sandwich beam models with FGM face sheets and core layers are examined. The main aim of this study is to examine the combined influences of porosity, elastic constraints of ends, elastic foundations and geometric imperfection on the thermal nonlinear instability of FGM sandwich beams. The properties of constituent materials are considered to be temperature–dependent and the effective properties of porous FGM are estimated by means of a modified rule of mixture. Pores are distributed into FGM through even and uneven patterns. Two ends of beam are simply supported and flexibly constrained against axial displacements. Basic equations are established on the basis of Timoshenko beam theory incorporating von Kármán nonlinearity, initial geometric imperfection and interaction from Kerr foundations. The established equations are treated by employing analytical solutions in combination with Galerkin procedure. By using an iteration algorithm, critical buckling thermal loadings and post-buckling load–displacement paths are determined. A parametric study is performed to elaborate the impacts of porosity, sandwich configuration, volume fraction index, tangential constraints of ends, stiffness of Kerr foundations, and the size of geometric imperfection on the critical temperatures and thermal loading bearing capability of FGM sandwich beams. The results find that the existence of porosity and elastic foundations enhance the stability of the FGM sandwich beams under UTR.