Direct Method of Analysis of an Isotropic Rectangular Plate Using Characteristic Orthogonal Polynomials
This work evaluates the static analysis of an isotropic rectangular plate with various boundary conditions. The direct variation method according to Ritz is used to obtain the total potential energy of the plate by employing the static elastic theory of plate. The shape function of fourth order for the plate under uniformly distributed load for various boundary conditions were formulated using the characteristic orthogonal polynomials (COP), which is also known as product of orthogonal strips of the plate along the two axes. Analyses of results obtained were compared with exact results presented in the monograph of Timoshenko and Woinowsky – Krieger. The previous work adopted shape function in the form of trigonometric series to solve the fourth order governing differential equation of the plate. This work is helpful for obtaining the shape functions not only for simply supported plates but also for rectangular plates with various kinds of support conditions, where the exact method presents intricate and complex solution. Finally, comparison has been done for the coefficients of deflection and moments at various aspect ratios of the plate for different support conditions. The results obtained by the use of the COP in the classical Ritz method are in close agreement with the results obtained from exact solutions from classical method.