Limit Analysis of Plates By a Finite Element Approach.

Abstract

A variational principle for plastic plate bending problems is formulated in accordance with the upper bound theorem. A finite element representation using non-conforming elements for the plate deflection field is imposed. The load carrying capacity of a plate is then sought by a minimization process in a finite dimensional space. An effective quadratic programming technique is used for the minimization process. The collapse loads for a square and a circular plate with simply supported and clamped boundary conditions under uniform pressure are solved. The results are consistant with the existing solutions which are based on different yield criteria. The optimal support problem of a square and a rectangular plates with four support points is solved by maximizing the sequence of minimal solutions. This finite element approach is economical, easily h and les arbitrary shape of plate, arbitrary lateral load and general boundary conditions, and thus applies to a wide class of applications in optimal design.