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Received: 22 September 2019 Accepted: 27 November 2019 This paper proposes a novel modified single finite Fourier cosine integral transform, which determines the elastic buckling loads of moderately-thick, fixed-end beams made of homogeneous, isotropic, linear elastic materials. First, such a beam was modelled with a fourth-order ordinary differential equation, according to the first-order shear deformation theory. Then, the single finite Fourier cosine integral transform was modified to satisfy all the boundary conditions at the fixed ends,using the apriori knowledge, and provide an exact buckling mode (shape) function for the beam. Through the modified transform, the boundary value problem was converted to an algebraic eigenvalue problem, which canbe described by a set of homogeneous algebraic equations. For nontrivial solutions, the characteristic buckling equation was drived from the vanishing of the determinant of the coefficient matrix. Solving the characteristic buckling equation, the authors obtained the eigenvalues and thus derived the buckling loads. The critical buckling load was found to correspond to the first buckling mode. The proposed modified transform gave exact expressions for the buckling loads and the critical buckling load of the fixed ends, because the integral kernel function satisfies all the boundary conditions, and the transform on the domain governing equation satisfies all the domain equations. The solutions of our method agree well with the previous studies.

revue des composites et des matériaux avancés

Modified Single Finite Fourier Cosine Integral Transform Method for Finding the Critical Elastic Buckling Loads of First Order Shear Deformable Beams with Fixed Ends