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.

在当前的工作中，我们根据三种不同的特性，研究了功能梯度（FG）多孔纳米复合材料梁的静态响应，这些梁具有内部孔和石墨烯血小板（GPLs）增强相的均匀或不均匀分层分布。模式。本文结合非局部应变梯度理论和新颖的三角二变量剪切变形梁理论，开发了有限元方法，以研究非局部应力和应变梯度对FG结构的综合影响。通过引入三节点梁单元，解决了该问题的控制方程。我们对纳米复合材料梁的弯曲行为进行了全面的参数研究，尤其关注它们对GPL增强材料的重量分数和分布模式的敏感性，以及非局部比例参数，几何特性和边界条件。根据结果​​，似乎孔隙率分布和GPLs模式对纳米复合梁的结构行为具有有意义的影响，其中对于材料中非均匀和对称的孔隙率分布和GPLs分散模式达到了最佳响应。