Some Concise Exact Analytical Solutions of Rectangular Plate Bending

Abstract

Analytical solutions have great value in both theory and numerical computation.Enlightened by the classical method of deriving analytical solutions of rectangular plate bending,new idea and method are proposed for deriving concise exact analytical solutions(without special functions and infinite series)of simple supported bending and rigid fixing bending.In such cases,the given function for bending has to be changed from the external loading function to the normal displacement function of the plate which satisfies the boundary conditions.Then,the external loading distribution and other parameters can be derived from the basic equations.For the simple supported bending,the normal displacement functions should have at least two roots in each coordinate, and there are two roots situated at the inflexion point of the normal displacement function.The examples of such functions are given as even polynomial,probability function and versiera function.In addition,the concise exact analytical solutions for the rigid fixing bending are derived similarly to the abovementioned approach;the normal displacement functions should also have at least two roots in each coordinate,but there are two roots situated at the maximum point of the normal displacement function.Two examples of such functions(odd-order polynomial and asteroid)and their concise normal displacement function are also given.The idea and method proposed can be developed further.For example,for a hybrid boundary condition problem.