Highly efficient mesh-free approach to simulate the non-linear bending analysis of FG porous beams and sandwich beams with FG face sheets

Abstract

The main objective of the present work is to propose a coupling of the Radial Point Interpolation Method (RPIM) with variable shape parameter to High Order Continuation Method (HOCM) for analyzing the geometrically non-linear behavior of porous Functionally Graded (FG) isotropic and sandwich Timoshenko beams by taking into account the non-linear shear deformation. The FG and FG Sandwich Beams (FGSB) effective material properties are assumed to vary continuously in the thickness direction according to a power-law index. The porosity is modeled as the stiffness reduction criteria and included in the mixture rule. The strong form of the non-linear equations governing porous FG and FGSB beams are obtained using the principle of virtual displacements in the framework of First-Order Shear Deformation Theory (FOSDT). The HOCM is used to compute the solution of the non-linear problem by a transformation to recursive succession of linear problems using Taylor series expansion. The continuation technique is used to obtain the complete solution path in a step by step manner. The effectiveness and accuracy of the proposed coupling is brought out through numerical examples which concern porous FG isotropic and FG sandwich beams. The optimal parameters have been defined according to the stability analysis of the proposed solver, and then used to investigate the effect of boundary conditions, showing the effect of the power-law index, effect of geometric imperfections, and face sheet-core-face sheet thickness ratios on deflections. The validation is done by comparing the obtained results to those available in the literature and/or those computed using Finite Element Method (FEM).