Solutions of Elastic Plates by Invariant Imbedding

A new method for the numerical solution of elastic plates is presented. The method is based in a relatively new theory called invariant imbedding and consists of the reduction of boundary-value problems to initial-value formulations. In this paper the equations of equilibrium of an elastic plate, conveniently approximated by a system of ordinary differential equations, are reduced to an initial value formulation by means of invariant imbedding techniques. Riccati differential equations subject to initial conditions are found for the flexibility and the stiffness matrices of plates of variable lengths subject to arbitrary forces or displacements on the boundary. Two different examples involving buckling problems, and the solution of clamped-simply supported plates are presented to show the feasibility and accuracy of the method.