A three-dimensional finite element method for plate bending

Abstract

A three-dimensional finite element method is proposed for plate bending. The displacement function is assumed to have a particular form with respect to the thickness variable. The assumed displacement function is substituted into the three-dimensional potential energy functional and a two-dimensional variational problem emerges. The two-dimensional problem is treated by the finite element method and it is seen that for conforming solutions the only requirement is continuity of the basis functions. The method includes transverse shear and thickness effects and may be used for both thin and moderately thick shells. To illustrate the method and to compare it with other results, the problems of a square plate under point and distributed loads and with simply supported and clamped boundary are treated numerically. © 1974.