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Steel and Composite Structures
  Volume 35, Number 5, June10 2020, pages 671-685
DOI: http://dx.doi.org/10.12989/scs.2020.35.5.671
 


Static stability and of symmetric and sigmoid functionally graded beam under variable axial load
Ammar Melaibari, Ahmed B. Khoshaim, Salwa A. Mohamed and Mohamed A. Eltaher

 
Abstract
    This manuscript presents impacts of gradation of material functions and axial load functions on critical buckling loads and mode shapes of functionally graded (FG) thin and thick beams by using higher order shear deformation theory, for the first time. Volume fractions of metal and ceramic materials are assumed to be distributed through a beam thickness by both sigmoid law and symmetric power functions. Ceramic–metal–ceramic (CMC) and metal–ceramic–metal (MCM) symmetric distributions are proposed relative to mid-plane of the beam structure. The axial compressive load is depicted by constant, linear, and parabolic continuous functions through the axial direction. The equilibrium governing equations are derived by using Hamilton\'s principles. Numerical differential quadrature method (DQM) is developed to discretize the spatial domain and covert the governing variable coefficients differential equations and boundary conditions to system of algebraic equations. Algebraic equations are formed as a generalized matrix eigenvalue problem, that will be solved to get eigenvalues (buckling loads) and eigenvectors (mode shapes). The proposed model is verified with respectable published work. Numerical results depict influences of gradation function, gradation parameter, axial load function, slenderness ratio and boundary conditions on critical buckling loads and mode-shapes of FG beam structure. It is found that gradation types have different effects on the critical buckling. The proposed model can be effective in analysis and design of structure beam element subject to distributed axial compressive load, such as, spacecraft, nuclear structure, and naval structure.
 
Key Words
    buckling stability; variable axial load; FG sigmoid distribution; higher beam theory; variable-coefficients differential equations; Differential Quadrature Method (DQM)
 
Address
Ammar Melaibari: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia;
Centre of Nanotechnology, King Abdulaziz University, Jeddah, Saudi Arabia
Ahmed B. Khoshaim: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia
Salwa A. Mohamed: Department of Engineering Mathematics, Faculty of Engineering, Zagazig University,P.O. Box 44519, Zagazig, Egypt
Mohamed A. Eltaher: Mechanical Engineering Department, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, Jeddah, Saudi Arabia;
Mechanical Design & Production Department, Faculty of Engineering, Zagazig University,P.O. Box 44519, Zagazig, Egypt
 

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