Linear and nonlinear static bending of sandwich beams with functionally graded porous core under different distributed loads

Abstract

Abstract In this investigation, linear and nonlinear bending analyses of sandwich beams with functionally graded cores are determined under different types of distributed loads. These sandwich beams are composed of two isotropic faces and a porous core with different gradients of internal pores. The governing formulation used to describe the beam’s linear and nonlinear behavior is constructed from Reddy s third-order shear deformation theory and nonlinear strain–displacement relations of von Karman. The Gram-Schmidt orthogonalization procedure is adopted to generate numerically stable functions for the displacement field to solve the beam problems with various boundary conditions. Then, the Ritz method is utilized to find out linear and nonlinear bending results in conjunction with the iterative technique . The accuracy of our solutions is validated, and our numerical results agree well with some cases available in the literature. New results of the sandwich beams based on several effects of porosity coefficient, slenderness ratio , loading types, porous distributions of the core, etc., are presented in graphical and tabular forms , serving as a benchmark solution for future studies.