Journal of Emerging Trends in Engineering and Applied Sciences: Research Areas

Article Title: Bending Analysis of Isotropic Rectangular Plate with All Edges Clamped: Variational Symbolic Solution
by Osadebe N. N and Aginam C. H

Abstract:
An alternative variational approach is developed for the bending analysis of thin isotropic clamped plate. The method by-passes the tedious and rigorous solution of plate's differential equation of equilibrium involved in the classical and numerical methods. The method is a modification of Ritz variational approach. It is based on total potetial energy. By the fomulation, the deformation surface of the clamped plate with uniformly distributed load is approximated to be the sum of products of constructed polynomals in the x and y axes. The constructed polynomials satisfy the plate's geometrical boundary conditions in addition to being interdependent and continuous. The sum of product of the constructed polynomial is substituted into plate's differential equations and then solved through minimization principle. Consequently, the deflections and the bending of the thin isotropic clamped plate are obtained in analytical form thus enabling the evaluation of these quantities at any arbitrary point on the plate with uniformly distributed load at various plate aspect ratios of 1.0 to 2.0. The solution is done for first, second, third and four terms- polynomials representing 1st, 2nd, 3rd and 4th approximations respectively. The variational procedure elucidates the ease and convergence of the results.

Keywords: clamped rectangular plate, deflections, moments, uniform load, variational method

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