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Static stability of higher order functionally graded beam under variable axial load
- Source :
- Alexandria Engineering Journal, Vol 59, Iss 3, Pp 1661-1675 (2020)
- Publication Year :
- 2020
- Publisher :
- Elsevier, 2020.
-
Abstract
- This article investigates effects of axial load distribution on buckling loads and their modes of functionally graded (FG) beams including a shear effect for the first time, since all previous studies focused on constant axial load. The parabolic higher order shear theory of Reddy is proposed to consider the shear effect of both thick and thin beams. The gradation of the material is distributed continuously through thickness direction with generalized power-law function. The in-plane axial compressive load is simulated by continuous functions through the axial direction, which are constant, linear, and parabolic functions. The equilibrium equations are developed by Hamilton’s principles, which yields variable-coefficients differential equations. Modified differential quadrature method (DQM) is employed to discretize and mesh the spatial domain and covert the differential equations and boundary conditions to algebraic equations. Algebraic set of equations is formed as a generalized matrix eigenvalue problem, then solved to obtain buckling loads (eigenvalues) and mode-shapes (eigenvectors). Numerical results are presented to illustrate effects of gradation parameter, load types, slenderness ratio and boundary conditions on buckling loads and mode-shapes of functionally graded beams structures. This model can be applied in designing of space-shuttle, spacecraft, nuclear structure, and naval structure subjected to distributed in-plane axial load.
- Subjects :
- Physics
Discretization
FG beams
Differential equation
Buckling Stability, Variable In-Plane Load
020209 energy
Mathematical analysis
General Engineering
02 engineering and technology
Shear deformation theory
Engineering (General). Civil engineering (General)
01 natural sciences
010305 fluids & plasmas
Algebraic equation
Buckling
0103 physical sciences
0202 electrical engineering, electronic engineering, information engineering
Differential Quadrature Method (DQM)
Nyström method
Boundary value problem
TA1-2040
Eigenvalues and eigenvectors
Beam (structure)
Variable-coefficients differential equations
Subjects
Details
- Language :
- English
- ISSN :
- 11100168
- Volume :
- 59
- Issue :
- 3
- Database :
- OpenAIRE
- Journal :
- Alexandria Engineering Journal
- Accession number :
- edsair.doi.dedup.....04c48fdb43364288e5e99005e24d3cb5