A 27-node hybrid brick and a 21-node hybrid wedge element for structural analysis

This paper presents a 27-node hybrid hexahedral and a 21-node hybrid wedge element for structural analysis. The motivation behind developing these elements is that, in many situations, it is convenient to use elements that involve only displacement degrees of freedom as in a standard displacement-based brick element, but, in order that computational costs are not prohibitively high, such elements should perform well irrespective of whether they are used to model three-dimensional or plate/shell geometries, whether the material is compressible or almost incompressible and so on. In other words, it is desirable to develop elements that are simple to use, but at the same time extremely versatile in modeling a wide range of geometries, material behavior, etc. The formulation of the proposed elements is based on a two-field mixed variational principle. The higher-order terms in the stress interpolation are identified based on the zero-energy modes that can occur in cubical and wedge-shaped elements, respectively. The resulting elements are “optimal” in the sense that they have the minimum number of assumed stress terms to ensure correct stiffness rank. Numerical examples are presented to show the excellent performance of the proposed elements under demanding situations such as when the elements are used to model plate/shell geometries, when the material is almost incompressible, the meshes are distorted, etc.

[1]  K. Y. Sze,et al.  An eight‐node hybrid‐stress solid‐shell element for geometric non‐linear analysis of elastic shells , 2002 .

[2]  J. J. Rhiu,et al.  A new efficient mixed formulation for thin shell finite element models , 1987 .

[3]  Y. K. Cheung,et al.  Three-dimensional 8-node and 20-node refined hybrid isoparametric elements , 1992 .

[4]  F. Bussamra,et al.  Three-dimensional hybrid-Trefftz stress elements , 2000 .

[5]  K. Y. Sze,et al.  A novel approach for devising higher‐order hybrid elements , 1993 .

[6]  S. Atluri,et al.  Development and testing of stable, invariant, isoparametric curvilinear 2- and 3-D hybrid-stress elements , 1984 .

[7]  Robert L. Spilker,et al.  Three‐dimensional hybrid‐stress isoparametric quadratic displacement elements , 1982 .

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

[9]  W. Soedel.  Vibrations of shells and plates , 1981 .

[10]  C. Jog.  Higher-order shell elements based on a Cosserat model, and their use in the topology design of structures , 2004 .

[11]  S. W. Lee,et al.  A new efficient approach to the formulation of mixed finite element models for structural analysis , 1986 .

[12]  K. Y. Sze,et al.  Stabilization schemes for 12-node to 21-node brick elements based on orthogonal and consistently assumed stress modes , 1994 .

[13]  Robert L. Spilker,et al.  Hybrid-stress eight-node elements for thin and thick multilayer laminated plates , 1982 .

[14]  Theodore H. H. Pian,et al.  Relations between incompatible displacement model and hybrid stress model , 1986 .

[15]  Robert L. Spilker,et al.  Hybrid-stress isoparametric elements for moderately thick and thin multilayer plates , 1986 .

[16]  K. Y. Sze,et al.  Hybrid‐stress six‐node prismatic elements , 2004 .

[17]  T. Pian,et al.  On the suppression of zero energy deformation modes , 1983 .