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 Steel and Composite Structures   Volume 45, Number 5, December10 2022 , pages 729-747 DOI: https://doi.org/10.12989/scs.2022.45.5.729 Buckling of 2D FG Porous unified shear plates resting on elastic foundation based on neutral axis Rabab Shanab, Salwa Mohamed, Mohammed Y. Tharwan, Amr E. Assie and Mohamed A. Eltaher Abstract The critical buckling loads and buckling modes of bi-directional functionally graded porous unified higher order shear plate with elastic foundation are investigated. A mathematical model based on neutral axis rather than midplane is developed in comprehensive way for the first time in this article. The material constituents form ceramic and metal are graded through thickness and axial direction by the power function distribution. The voids and cavities inside the material are proposed by three different porosity models through the thickness of plate. The constitutive parameters and force resultants are evaluated relative to the neutral axis. Unified higher order shear plate theories are used to satisfy the zero-shear strain/stress at the top and bottom surfaces. The governing equilibrium equations of bi-directional functionally graded porous unified plate (BDFGPUP) are derived by Hamilton's principle. The equilibrium equations in the form of coupled variable coefficients partial differential equations is solved by using numerical differential integral quadrature method (DIQM). The validation of the present model is presented and compared with previous works for bucking. Deviation in buckling loads for both mid-plane and neutral plane are developed and discussed. The numerical results prove that the shear functions, distribution indices, boundary conditions, elastic foundation and porosity type have significant influence on buckling stability of BDFGPUP. The current mathematical model may be used in design and analysis of BDFGPU used in nuclear, mechanical, aerospace, and naval application. Key Words bi-directional FGM; buckling stability; differential integral quadrature method; neutral plane; porous material; unified plate theories Address Rabab Shanab: Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt Salwa Mohamed:Department of Engineering Mathematics, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt Mohammed Y. Tharwan:Mechanical Engineering Department, Faculty of Engineering, Jazan University, P. O. Box 45142, Jazan, Kingdom of Saudi Arabia Amr E. Assie:1)Mechanical Engineering Department, Faculty of Engineering, Jazan University, P. O. Box 45142, Jazan, Kingdom of Saudi Arabia 2)Department of Mechanical Design and Production, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt Mohamed A. Eltaher:1)Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia 2)Department of Mechanical Design and Production, Faculty of Engineering, Zagazig University, P.O. Box 44519, Zagazig, Egypt

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