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

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 K acute accent arm acute accent an. 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.

Automated summary

This study investigates the linear and nonlinear bending behaviors of sandwich beams with functionally graded cores under various distributed loads. The formulation used is based on Reddy's theory and von Karman's nonlinear strain-displacement relations. Numerically stable functions for displacement fields are generated using the Gram-Schmidt orthogonalization procedure, and linear and nonlinear bending results are found using the Ritz method and iterative technique. The accuracy of the solutions is validated, and new results based on different factors like porosity coefficient and loading types are presented for future studies.