This article has been withdrawn as it was published elsewhere and accidentally duplicated. The original article can be seen here: 10.1108/02644400210423918. When citing the…
Abstract
This article has been withdrawn as it was published elsewhere and accidentally duplicated. The original article can be seen here: 10.1108/02644400210423918. When citing the article, please cite: Sven Klinkel, Sanjay Govindjee, (2002), “Using finite strain 3D-material models in beam and shell elements”, Engineering Computations, Vol. 19 Iss: 3, pp. 254 - 271.
Sven Klinkel and Sanjay Govindjee
In this paper an interface is derived between arbitrary three‐dimensional material laws and finite elements which include special stress conditions. The mechanical models of beams…
Abstract
In this paper an interface is derived between arbitrary three‐dimensional material laws and 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.
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Analyses several algorithms for the integration of the Jaumann stress rate. Places emphasis on accuracy and stability of standard algorithms available in commercial and government…
Abstract
Analyses several algorithms for the integration of the Jaumann stress rate. Places emphasis on accuracy and stability of standard algorithms available in commercial and government finite element codes in addition to several other proposals available in the literature. The analysis is primarily concerned with spinning bodies and reveals that a commonly used algorithm is unconditionally unstable and only first‐order objective in the presence of rotations. Other proposals are shown to have better accuracy and stability properties. Finally, shows by example that even a consistent and unconditionally stable integration of hypoelastic constitution does not necessarily yield globally stable finite element simulations.