Static stability of beams subjected to nonuniform axial compressive and shear loads is essential in many industrial applications, such as aircraft, automotive, mechanical, civil and naval. Thus, this article tends to investigate and optimize critical buckling loads of thin/thick sandwich functionally graded (FG) beam with porous core, for the first time. The proposed model is developed to consider a sandwich beam with three layers, which has top and bottom FG layers reinforced by single-walled carbon nanotubes (SWCNTs) and core porous layer with various porosity distributions. The variable in-plane compressive load is described by different distributed functions. Parabolic higher-order shear deformation theory of Reddy is adopted to describe kinematic displacement field and consider both thin and thick structures. The equilibrium governing variable-coefficient differential equations are obtained in detail by generalized variational principle. Equilibrium equations are solved numerically by differential quadrature method to get critical buckling loads. Numerical results are illustrated to examine influences of porosity function, porosity percentage, distribution gradation index, load types and boundary conditions on buckling loads of sandwich FG SWCNTs beam with porous core. Particle swarm optimization algorithm is adopted to get optimal axial load function.

中文翻译：

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轴向荷载函数及优化对多孔芯夹层功能梯度梁静稳定性的影响

承受非均匀轴向压缩和剪切载荷的梁的静态稳定性在许多工业应用中至关重要，例如飞机、汽车、机械、民用和海军。因此，本文首次试图研究和优化具有多孔芯的薄/厚夹层功能梯度 (FG) 梁的临界屈曲载荷。所提出的模型是为了考虑三层夹心梁而开发的，其顶部和底部 FG 层由单壁碳纳米管 (SWCNT) 和具有各种孔隙率分布的核心多孔层增强。可变面内压缩载荷由不同的分布函数描述。采用Reddy抛物线高阶剪切变形理论描述运动位移场，兼顾薄结构和厚结构。用广义变分原理详细地得到了控制变系数微分方程的平衡点。采用微分求积法对平衡方程进行数值求解，得到临界屈曲载荷。数值结果说明了孔隙率函数、孔隙率百分比、分布级配指数、载荷类型和边界条件对多孔芯夹层 FG SWCNTs 梁屈曲载荷的影响。采用粒子群优化算法得到最优轴向载荷函数。多孔芯夹层 FG SWCNTs 梁屈曲载荷的分布级配指数、载荷类型和边界条件。采用粒子群优化算法得到最优轴向载荷函数。多孔芯夹层 FG SWCNTs 梁屈曲载荷的分布级配指数、载荷类型和边界条件。采用粒子群优化算法得到最优轴向载荷函数。