A three-dimensional or penalty finite element method for plate bending

Abstract

This paper, a sequel to an earlier paper by the same authors, uses a three dimensional or penalty function approach to obtain finite element solutions for plate bending problems. The advantage in using this approach is that the finite element subspaces need only be continuous; the disadvantages are that more functions are needed. In our previous paper, we used piecewise quadratic and linear functions, in the present paper we use piecewise cubic and quadratic functions with a resultant reduction of the discretization error. We also suggest an interpolation method or an a priori choice of the thickness to length ratio which are appropriate for thin or moderately thick plates. Numerical results are given for clamped and simply supported plates with point and distributed loads. © 1976.