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  Volume 5, Number 4, October 2020, pages 397-416
DOI: https://doi.org/10.12989/acd.2020.5.4.397
 


Buckling analysis of noncontinuous linear and quadratic axially graded Euler beam subjected to axial span-load in the presence of shear layer
Abbas Heydari

 
Abstract
    Functionally graded material (FGM) illustrates a novel class of composites that consists of a graded pattern of material composition. FGM is engineered to have a continuously varying spatial composition profile. Current work focused on buckling analysis of beam made of stepwise linear and quadratic graded material in axial direction subjected to axial span-load with piecewise function and rested on shear layer based on classical beam theory. The various boundary and natural conditions including simply supported (S-S), pinned – clamped (P-C), axial hinge – pinned (AH-P), axial hinge – clamped (AH-C), pinned – shear hinge (P-SHH), pinned – shear force released (P-SHR), axial hinge – shear force released (AH-SHR) and axial hinge – shear hinge (AH-SHH) are considered. To the best of the author's knowledge, buckling behavior of this kind of Euler-Bernoulli beams has not been studied yet. The equilibrium differential equation is derived by minimizing total potential energy via variational calculus and solved analytically. The boundary conditions, natural conditions and deformation continuity at concentrated load insertion point are expressed in matrix form and nontrivial solution is employed to calculate first buckling loads and corresponding mode shapes. By increasing truncation order, the relative error reduction and convergence of solution are observed. Fast convergence and good compatibility with various conditions are advantages of the proposed method. A MATLAB code is provided in appendix to employ the numerical procedure based on proposed method.
 
Key Words
    buckling; stepwise axially graded beam; linear and quadratic material gradation; piecewise load function; shear layer
 
Address
Abbas Heydari:Department of civil engineering, Faculty of Razi, Ardabil branch,Technical and Vocational University (TVU), Ardabil, Iran
 

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