Using finite strain 3D-material models in beam and shell elements

• Published in: Engineering computations Vol. 19; no. 8; pp. 902 - 921
• Main Authors: Klinkel, Sven, Govindjee, Sanjay
• Format: Journal Article
• Language: English
• Published: Bradford MCB UP Ltd 01.01.2002; Emerald Group Publishing Limited
• Subjects: Algorithms; Mechanical engineering; Studies; Finite elements; Beams; Plane stress analysis
• ISSN: 0264-4401; 1758-7077
• DOI: 10.1108/02644400210450341

In this paper an interface is derived for the use of arbitrary 3D-material laws in finite elements which include special stress conditions. The mechanical models of beams and shells are usually based upon zero-stress conditions. This requires a material law respecting the stress condition for each finite element formulation. Complicated materials, e.g. finite strain models are often described in the 3D-continuum. Considering the zero-stress condition requires a reformulation of these material laws, which is often complicated. The subject of this paper is to incorporate physically non-linear 3D-material laws in beam and shell elements. To this effect a local algorithm will be developed to condense an arbitrary 3D-material law with respect to the zero-stress condition. The algorithm satisfies the stress condition at each integration point on the element level. A comparison of the proposed algorithm to a prior algorithm is made to highlight the properties of the current proposal.