Solutions To Plate Problem With Constant Rigidity Using Singularity Functions

Abstract

A new and novel method of solving problems of rectangular plates of constant stiffness using singularity functions is proposed. The working methods and manifestations of the use of singularity functions in plate analysis are presented.

Use of singularity functions, to represent the loading and reactive forces and moments at the boundary, along with the finite difference equations for plates of constant stiffness, is the new direction of plate analysis proposed.

Here for some problems of plates of constant stiffness, the method is to find mathematical solution to the basic partial differential equations (namely,) along with the representation of the load q in terms of singularity function to get a closed form solution is presented.

The advantage of the proposed method over finite elements lies in the fact, that the solution can be found without the help of computers, In contrast, the need for a computer for even a simple problem in the finite element method is required.

The solution of certain types of problems of plates with constant and variable stiffness for certain types of loading and boundary conditions is included to exemplify the technique of use of singularity functions.