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soltani, masoumeh, asgarian, behrooz, Jafarzadeh, Firooz. (1398). Finite difference method for buckling analysis of tapered Timoshenko beam made of functionally graded material. نشریه مهندسی عمران امیرکبیر, 4(1), 91-102. doi: 10.22060/ajce.2019.15195.5525
masoumeh soltani; behrooz asgarian; Firooz Jafarzadeh. "Finite difference method for buckling analysis of tapered Timoshenko beam made of functionally graded material". نشریه مهندسی عمران امیرکبیر, 4, 1, 1398, 91-102. doi: 10.22060/ajce.2019.15195.5525
soltani, masoumeh, asgarian, behrooz, Jafarzadeh, Firooz. (1398). 'Finite difference method for buckling analysis of tapered Timoshenko beam made of functionally graded material', نشریه مهندسی عمران امیرکبیر, 4(1), pp. 91-102. doi: 10.22060/ajce.2019.15195.5525
soltani, masoumeh, asgarian, behrooz, Jafarzadeh, Firooz. Finite difference method for buckling analysis of tapered Timoshenko beam made of functionally graded material. نشریه مهندسی عمران امیرکبیر, 1398; 4(1): 91-102. doi: 10.22060/ajce.2019.15195.5525

Finite difference method for buckling analysis of tapered Timoshenko beam made of functionally graded material

AUT Journal of Civil Engineering
مقاله 8، دوره 4، شماره 1، خرداد 2020، صفحه 91-102    اصل مقاله (1.87 M)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22060/ajce.2019.15195.5525
نویسندگان
masoumeh soltani* 1؛ behrooz asgarian2؛ Firooz Jafarzadeh3
1Department of civil engineering, faculty of engineering, University of Kashan, kashan, Iran
2Department of Civil Engineering, University of Khajeh Nasireddin Tousi
3Department of Civil Engineering, Faculty of Engineering, Shahr-e-Qods Branch, Islamic Azad University
چکیده
This paper addresses the linear buckling behavior of tapered Timoshenko beams made of axially functionally graded material (AFGM). Material properties of the non-prismatic Timoshenko beam vary continuously along the length of the member according to power law as well as exponential law. Based on Timoshenko beam assumption and using small displacements theory, the linear equilibrium equations are adopted from the energy principle for functionally graded non-uniform Timoshenko beams related to constant compressive axial load. The resulting system of stability equations are strongly coupled due to the presence of transverse deflection and angle of rotation. The differential equations are then uncoupled and lead to a single homogeneous differential equation where only bending rotation is present. The finite difference method (FDM) is then selected to numerically solve the resulting second-order differential equation with variable coefficients and determine the critical buckling loads. Two numerical examples are finally conducted to demonstrate the performance and efficiency of this mathematical procedure. The obtained results are contrasted with accessible numerical and analytical benchmarks.
کلیدواژه‌ها
Critical Buckling Load؛ Functionally Graded Material؛ Tapered Timoshenko Beam؛ Finite Difference Method
مراجع
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