Static and dynamic applications of a high- precision triangular plate bending element

Abstract

A fully conforming plate bending element of arbitrary triangular shape is developed and applied to the solution of several static and dynamic plate problems. The element incorporates 18 generalized coordinates, namely the transverse displacement and its first and second derivatives at each vertex. Example applications presented include static and dynamic analyses of a square plate with edges either simply supported or clamped, statics of an equilateral triangular simply supported plate, and vibrations of cantilevered triangular plates. Rates of convergence of the finite element approximations are investigated both theoretically and numerically. Excellent accuracy is achieved in all cases, and the rates of error convergence agree closely \vith predicted asymptotic values.