Geometrically nonlinear bending mesh-free analysis of functionally graded porous sandwich beam

Abstract

In this work, geometrically nonlinear static bending analysis of sandwich beams with a porous core and two skins made of functionally graded materials using a mesh-free method is presented. The material types of the core and face sheets of the beam are chosen so that the material continuity between the layers is guaranteed. The nonlinear governing equation including geometric nonlinearity is established via the principle of virtual work. This equation is discretized into a system of algebraic equations by the mesh-free approach, which is based on the C1 point interpolation method and polynomial basis functions, and then solved by the direct iterative method. The convergence of the mesh-free method is tested to determine the sufficient mesh level for the analysis. Comparative and comprehensive studies are performed to investigate both the correctness and the influences of several important parameters and boundary conditions on the linear and nonlinear deflections of the beam.