Bending analysis of functionally graded porous nanocomposite beams based on a non-local strain gradient theory
Tarek Merzouki, Houari Mohammed Sid Ahmed, Aicha Bessaim, Mohamed Haboussi, Rossana Dimitri, Francesco Tornabene
Abstract
In the present work we study the static response of functionally graded (FG) porous nanocomposite beams, with a uniform or non-uniform layer-wise distribution of the internal pores and graphene platelets (GPLs) reinforcing phase in the matrix, according to three different patterns. The finite-element approach is developed here together with a non-local strain gradient theory and a novel trigonometric two-variable shear deformation beam theory, to study the combined effects of the non-local stress and strain gradient on the FG structure. The governing equations of the problem are solved introducing a three-node beam element. A comprehensive parametric study is carried out on the bending behavior of nanocomposite beams, with a particular focus on their sensitivity to the weight fraction and distribution pattern of GPLs reinforcement, as well as to the non-local scale parameters, geometrical properties, and boundary conditions. Based on the results, it seems that the porosity distribution and GPLs pattern have a meaningful effect on the structural behavior of nanocomposite beams, where the optimal response is reached for a non-uniform and symmetric porosity distribution and GPLs dispersion pattern within the material.