2 HIGHER-ORDER SHELL FINITE-ELEMENTS WITH STABILIZATION MATRIX

A 32-node three-dimensional solid element and a 16-node degenerate solid element that are applicable to analysis of thin-shell structural problems are presented in this paper. Both elements are formulated by using the Hellinger-Reissner principle with independent strain. The assumed independent strain field is divided into higherand lower-order polynomial terms. The element stiffness matrix associated with the higher order assumed strain plays the role of the stabilization matrix. Various types of the higher-order assumed strain are tested for the present elements. The resulting finite-element models require much less time to compute the element stiffness matrix than the corresponding conventional mixed models or assumed displacement models with a full Gaussian quadrature rule. Numerical results demonstrate that, with a properly chosen set of higher-order assumed strain, the present elements produce reliable and very accurate solutions even for very thin plates and thin shells with deeply curved geometry. © 1990 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.