Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous
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ORIGINAL ARTICLE
Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core M. A. Hamed1 · R. M. Abo‑bakr2 · S. A. Mohamed3 · M. A. Eltaher1,4 Received: 14 March 2020 / Accepted: 10 April 2020 © Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract 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 variablecoefficient 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. Keywords Critical buckling loads · Variable axial load · Sandwich FG-SWCNTs beam · Porous materials · Differential quadrature method (DQM) · Optimal axial load
1 Introduction
* M. A. Eltaher [email protected]; [email protected] M. A. Hamed [email protected] S. A. Mohamed [email protected] 1
Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia
2
Mathematical Department, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt
3
Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt
4
Mechanical Design & Production Department, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt
New innovative composite materials, known as functionally graded materials (FGMs), were proposed firstly in Sendai area for addressing heat-resistant problem by Japanese scientists in 1984 during the space-plane project [47, 48, 60]. FGMs are nonhomogeneous materials, whose properties are altered in a certain direction according to some laws, so that, their properties can better meet the needs of designers [84]. Sasaki et al. [67] exploited deposition process to manufacture SiC/C FG plate with 1 mm thickness. FGMs are commonly utilized in various engineering fields, such as v
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