Engineering Analysis of Super Elliptic Plates on Nonlinear Elastic Foundation

A new combined numerical algorithm is introduced in this paper to analyze the structural behavior of super elliptic plates on nonlinear foundation. The objectives are two folds, one is to investigate the behavior of elliptic plates of different sizes residing on nonlinear foundation in terms of different power orders, and the other is to obtain approximate solutions by using genetic algorithms for comparison. Detailed description of nonlinear structural behaviors of elliptical plates of different geometric shapes are elaborated. Especially, as the power becomes large enough to have the shape turned into a rectangular one, or on the other hand, as the power equals to one, the shape of the ellipse goes to the other extremity of a circle. In either case, differential equations are derived based upon the maximum principle, and the residual solutions of monotony are presented with rigor validation. The problem solving of differential equations is further converted into a mathematical programming problem with practical constraints. By combining with optimization algorithms the solutions are obtained from bilateral sides and the solutions of minimal upper and maximal lower bounds are obtained. The weighted residual and collocation methods are also used to solve for the differential equations in combination with genetic algorithms (GA) to obtain satisfactory bounds that comply with specific optimization rules.