Kantorovich variational method for the flexural analysis of CSCS Kirchhoff-Love plates

Abstract

Abstract. The Kantorovich variational method was used in this study to solve the flexural problem of Kirchhoff-Love plates with two opposite edges = ± 2 ⁄ clamped and the other two edges = ± 2 ⁄ simply supported, for the case of uniformly distributed transverse load over the entire plate domain. The plate considered was assumed homogeneous, and isotropic. The total potential energy functional for the Kirchhoff-Love plate was found as the sum of the potential energy of the applied distributed load and the strain energy functional of the plate. The symmetrical nature of the plate and the load was used to choose the deflection function as a single series of infinite terms involving the cosine function of the y coordinate variable with the unknown function being dependent on the coordinate variable. Integration with respect to the coordinate variable simplified the total potential energy functional to be dependent on the unknown function of , and its derivatives. Euler-Lagrange differential equations were used to find the differential equations of equilibrium of the plate as a system of homogeneous fourth order ordinary differential equations (ODE) in the unknown function. The system of fourth order ODE was solved using the method of differential D operators, or the method of trial functions to obtain the general solution as the linear superposition of the homogeneous and particular solutions. The demands of symmetry of unknown function about the point = 0, and the boundary conditions at the clamped edges were used to obtain all the four integration constants; thus, completely determining the deflection. Bending moment distributions were determined using the bending moment deflection relations. The deflection was determined at the centre of the plate. The bending moment values were also determined at the centre of the plate, and at the middle of the clamped edges. Expressions obtained for the deflection at the centre, and bending moment values were found to be single series of infinite terms with highly converging properties. The solutions obtained converged to the exact solutions with the use of only four terms of the series.

Generalized Integral Transform Method for Bending and Buckling Analysis of Rectangular Thin Plate with Two Opposite Edges Simply Supported and Other Edges Clamped

“…In [27], the author presented two-dimensional Fourier cosine series technique to solve bending problems of rectangular thin plates supported by Winkler one-parameter foundations with the plate domain subject to transverse loading. Kantorovich-Vlasov method was used for the thin plate flexure problems by authors in [9], [28]- [31].…”

“…In [30], the authors used the Kantorovich-Vlasov methodology for solving the flexural problems of rectangular Kirchhoff plates with opposite sides fixed, and the other two sides simply supported; with the plate subject to distributed uniform loading. In [31], the authors used the Kantorovich method to solve flexural problems of Kirchhoff-Love plates having two sides fixed and the other sides on simple supports.…”

Single Finite Fourier Sine Integral Transform Method for the Flexural Analysis of Rectangular Kirchhoff Plate with Opposite Edges Simply Supported, Other Edges Clamped for the Case of Triangular Load Distribution

“…Kantorovich variational method has been used for plate problems by Ike [28], Ike and Nwoji [29], Nwoji et al [30], Onah et al [31], Ike and Mama [32], Ike et al [33].…”