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A large deformation solid‐shell concept based on reduced integration with hourglass stabilization
Author(s) -
Reese Stefanie
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1827
Subject(s) - hourglass , shell (structure) , quadrilateral , degrees of freedom (physics and chemistry) , finite element method , displacement field , jacobian matrix and determinant , geometry , mathematical analysis , mathematics , displacement (psychology) , structural engineering , physics , engineering , mechanical engineering , psychology , quantum mechanics , astronomy , psychotherapist
Abstract In this paper a new eight‐node (brick) solid‐shell finite element formulation based on the concept of reduced integration with hourglass stabilization is presented. The work focuses on static problems. The starting point of the derivation is the three‐field variational functional upon which meanwhile established 3D enhanced strain concepts are based. Important additional assumptions are made to transfer the approach into a powerful solid‐shell. First of all, a Taylor expansion of the first Piola–Kirchhoff stress tensor with respect to the normal through the centre of the element is carried out. In this way the stress becomes a linear function of the shell surface co‐ordinates whereas the dependence on the thickness co‐ordinate remains non‐linear. Secondly, the Jacobian matrix is replaced by its value in the centre of the element. These two assumptions lead to a computationally efficient shell element which requires only two Gauss points in the thickness direction (and one Gauss point in the plane of the shell element). Additionally three internal element degrees‐of‐freedom have to be determined to avoid thickness locking. One important advantage of the element is the fact that a fully three‐dimensional stress state can be modelled without any modification of the constitutive law. The formulation has only displacement degrees‐of‐freedom and the geometry in the thickness direction is correctly displayed. Copyright © 2006 John Wiley & Sons, Ltd.