In this study, the single Fourier sine integral transform method was used to solve the elastic buckling problem of Kirchhoff rectangular plates simply supported at two opposite edges x = 0, and x = a and clamped at the other two edges y = 0, and y = b. The problem considered was that for uniaxial uniform compressive load in the x coordinate direction. The single finite Fourier sine integral transformation was applied to the governing fourth order partial differential equation of Kirchhoff plates under uniaxial uniform in-plane compressive loads to convert the problem to a fourth order ordinary differential equation in terms of the finite Fourier sine transform space variables. Solution of the ordinary differential equations yielded the buckling modal shape functions in the Fourier sine transform variables. Enforcement of boundary conditions along the y direction at y = 0, and y = b yielded an algebraic eigenvalue eigenvector problem which was solved to obtain non-trivial solutions. The characteristic buckling equation was obtained by requiring the vanishing of the matrix of coefficients as the transcendental equation involving the buckling load. The buckling load was obtained by solving the transcendental equation for various assumed values of the plate aspect ratios. Critical buckling loads for various values of the plate aspect ratio were found to be identical with classical solutions obtained in the technical literature. The present study thus yielded exact solution for the buckling loads and buckling modes of uniaxially compressed Kirchhoff plates; illustrating the effectiveness of the analytical tool.
elastic buckling equation, critical buckling load, characteristic buckling equation, Kirchhoff plate, eigenvalue problem
 Bouazza M, Quinas D, Yazid A, Hamouine A. (2012). Buckling of thin plates under uniaxial and biaxial compression. Journal of Material Science and Engineering 32(8): 487-492.
 Chattopadhyay AP. (2011). Elastic buckling behaviour of plate and tubular structures. MSc Thesis Dept of Mechanical and Nuclear Engineering. Kansas State University, Manhattan Kansas.
 Dima I. (2015). Buckling of flat thin plates under combined loading. Incas Bulletin 7(1): 83-96. https//doi.org/10.13111/2066-8201.2015.7.1.8
 Ibearugbulem OM, Ezeh JC. (2013). Instability of axially compressed CCCC thin rectangular plate using Taylor – Maclaurin’s series shape function on Ritz method. Academic Research International 4(1): 346-351.
 Ezeh JC, Owus IM, Opara HE, Oguaghamba OA. (2014). Galerkin’s indirect variational method in elastic stability analysis of all edges clamped thin rectangular plates. International Journal of Research in Engineering (IJRET) 3(4): 674-679.
 Ibearugbulem OM, Osadebe NN, Ezeh JC, Onwuka DO. (2011). Buckling analysis of axially compressed SSSS thin rectangular plate using Taylor – Maclaurin shape function. International Journal of Civil and Structural Engineering 2(2): 667–672.
 Nwoji CU., Onah HN, Mama BO, Ike CC, Ikwueze EU. (2017). Elastic buckling analysis of simply supported thin plates using the double finite Fourier sine integral transform method. Explorematics Journal of Innovative Engineering and Technology 1(1): 37-47.
 Timoshenko S, Lessells JM. (1925). Applied Elasticity. Westinghouse Technical Night School Press East Pittsburg, Pa, p. 544.
 Bridget FJ, Jerome CC, Vosseller AB. (1934). Some new experiments on buckling of thin wall construction. Trans. ASME Aero Eng. 56: 569-578.