Trapezoidal Plate Bending Element with Double Set Parameters

Abstract

Using double set parameter method, a 12-parameter trapezoidal plate bending element is presented. The first set of degrees of freedom, which make the element convergent, are the values at the four vertices and the middle points of the four sides together with the mean values of the outer normal derivatives along four sides. The second set of degrees of freedom, which make the number of unknowns in the resulting discrete system small and computation convenient are values and the first derivatives at the four vertices of the element. The convergence of the element is proved.