Hybrid‐stress solid elements for shell structures based upon a modified variational functional

In this paper, we start with a modified generalized laminate stiffness matrix that serves as a remedy to resolve the thickness locking and some abnormalities encountered by solid-shell elements in laminate analyses. A modified Hellinger–Reissner functional having displacement and a set of generalized stresses as independent fields is devised. Based upon the functional, eight-node and 18-node hybrid-stress solid-shell elements are proposed. A number of benchmark tests on homogenous and laminated plates/shells are conducted. The accuracy of the elements is promising. Copyright © 2002 John Wiley & Sons, Ltd.

[1]  S. Lee,et al.  An eighteen‐node solid element for thin shell analysis , 1988 .

[2]  Richard H. Macneal,et al.  A theorem regarding the locking of tapered four‐noded membrane elements , 1987 .

[3]  S. W. Lee,et al.  A nine-node assumed-strain finite element for composite plates and shells , 1987 .

[4]  K. Park,et al.  A Curved C0 Shell Element Based on Assumed Natural-Coordinate Strains , 1986 .

[5]  E. Stein,et al.  A 4-node finite shell element for the implementation of general hyperelastic 3D-elasticity at finite strains , 1996 .

[6]  K. Y. Sze,et al.  Admissible matrix formulation—from orthogonal approach to explicit hybrid stabilization , 1996 .

[7]  S. Lee,et al.  A solid element formulation for large deflection analysis of composite shell structures , 1988 .

[8]  Theodore H. H. Pian,et al.  Finite elements based on consistently assumed stresses and displacements , 1985 .

[9]  K. Y. Sze,et al.  On immunizing five‐beta hybrid‐stress element models from ‘trapezoidal locking’ in practical analyses , 2000 .

[10]  O. C. Zienkiewicz,et al.  The patch test—a condition for assessing FEM convergence , 1986 .

[11]  Chahngmin Cho,et al.  An efficient assumed strain element model with six DOF per node for geometrically non‐linear shells , 1995 .

[12]  Amin Ghali,et al.  Hybrid hexahedral element for solids, plates, shells and beams by selective scaling , 1993 .

[13]  K. Y. Sze,et al.  A hybrid stress ANS solid‐shell element and its generalization for smart structure modelling. Part I—solid‐shell element formulation , 2000 .

[14]  Ted Belytschko,et al.  Assumed strain stabilization procedure for the 9-node Lagrange shell element , 1989 .

[15]  K. Y. Sze,et al.  A stabilized hybrid-stress solid element for geometrically nonlinear homogeneous and laminated shell analyses , 2002 .

[16]  K. Y. Sze,et al.  A quadratic assumed natural strain curved triangular shell element , 1999 .

[17]  R. Hauptmann,et al.  A SYSTEMATIC DEVELOPMENT OF 'SOLID-SHELL' ELEMENT FORMULATIONS FOR LINEAR AND NON-LINEAR ANALYSES EMPLOYING ONLY DISPLACEMENT DEGREES OF FREEDOM , 1998 .

[18]  E. Ramm,et al.  Large elasto-plastic finite element analysis of solids and shells with the enhanced assumed strain concept , 1996 .

[19]  Eduardo N. Dvorkin,et al.  A formulation of general shell elements—the use of mixed interpolation of tensorial components† , 1986 .

[20]  R. L. Harder,et al.  A proposed standard set of problems to test finite element accuracy , 1985 .

[21]  K. Y. Sze,et al.  An Explicit Hybrid Stabilized Eighteen-Node Solid Element for Thin Shell Analysis , 1997 .