Elastic Strip Analysis of The Biharmonic Equation for Moments and Deflections of Simply Supported Rectangular Plates Developed from Finite Series Expression for A Suggested Valid Displacement Function

Abstract

The infinite series method has been used to solve plate problems and the results justified by applying same to beam problems with striking results. The opinion of the author that successful application of the infinite series method to beams when improved upon can be extended to plate problems after considering a plate to comprise four(4) beam strips as indicated by the plate biharmonic equation. The trigonometric function was expressed as the fundamental i.e for the first harmonic alone. Load sharing among the strips was done by the consideration that every strip carried a fraction of the total load of the area obtained by its length multiplied by the length of the perpendicular reaching the plate boundary and such that the sum of all these fractions will equal the total load on the plate. This is quite phenomenal. The application of this shared load to the beams with its substitution into the biharmonic expressions for strips of plates, produced striking results compared to classical methods. A table design tool for plates both with corners held down and corners allowed to lift is evolving.