DERIVATION OF STABILIZATION MATRICES FOR MINDLIN PLATES FROM THE COMBINED MIXED FUNCTIONAL AND THEIR MATHEMATICAL CHARACTERISTICS

Abstract

A new mixed functional is proposed for the analysis of Mindlin plates. The functional is constructed by combining the Hellinger-Reissner mixed functional and the total potential energy linearly. Existence and uniqueness of the solution of the proposed mixed model are proven and finite element equations are derived. The equivalence theorem for mixed elements and reduced/selective integration elements is applied and the stabilization matrix of Belytschko is obtained for the four-node plate element. Using the present method, stabilization matrices which have strong mathematical properties can be obtained for higher-order elements and triangular elements without any difficulty.