A Legendre-Ritz solution for bending, buckling and free vibration behaviours of porous beams resting on the elastic foundation

Abstract

By using high-order deformation theory, this paper presents a novel approach for analysing the mechanical behaviours of functionally graded porous beams resting on a Winkler-Pasternak elastic foundation. The governing equations are derived from the Lagrange principle. Legendre-Ritz polynomial functions, which possess the simplicity of algebraic polynomials and the efficiency of orthogonal polynomials, are developed to solve the problem. Three boundary conditions accompanied by two porosity types, including symmetric and asymmetric distributions of beams, are considered. The effects of porosity, boundary condition, foundation parameter, span-to-height ratio, and distribution type on the mechanical behaviours of porous beams are investigated. Some new results are presented for the first time as a benchmark for future studies.