Finite rotation analysis and consistent linearization using projectors

doi:10.1016/0045-7825(91)90248-5

Computer Methods in Applied Mechanics and Engineering

Volume 93, Issue 3, December 1991, Pages 353-384

https://doi.org/10.1016/0045-7825(91)90248-5 Get rights and content

Abstract

A systematic procedure is presented that may be used to extend the capabilities of an existing linear finite element to accomodate finite rotation analysis. This procedure is a generalization of the work presented in Computers and Structures, Volume 30, pp. 257–267. The basis of our approach is the element-independent co-rotational algorithm, where the element rigid body motion (translations and rotations) is separated from the deformational part of its total motion. The variation of this co-rotational relation results in a projector matrix, with the property that a consistent internal force vector is invariant under its action. The consistent tangent stiffness matrix is shown to depend on this invariance condition through the derivative of the projector. This results in an unsymmetric tangent matrix whose anti-symmetric part depends on the out-of-balance force vector. In this paper we prove that using the symmetric part of the tangent matrix, the Newton iteration retains its quadratic rate of convergence. This approach has been used to solve a number of large rotation test example problems. The results demonstrate that it is possible to analyze structures undergoing large rotations within a general co-rotational framework, using simple and economical finite elements. The resulting improvements in the performance of these simple elements are brought about through the use of convenient software utilities as pre- and post-processors to the element routines.

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Finite rotation analysis and consistent linearization using projectors

Abstract

Internat. J. Solids and Structures

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Internat. J. Engrg. Sci.

Comput. & Structures

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Comput. Methods Appl. Mech. Engrg.

Internat. J. Solids and Structures

Non-linear transient finite elements analysis with convected co-ordinates

Internat. J. Numer. Methods Engrg.

An element-independent co-rotational procedure for the treatment of large rotations

ASME J. Pressure Vessel Techn.