Finite rotation analysis and consistent linearization using projectors
type: Item
instance of: scholarly article
title: Finite rotation analysis and consistent linearization using projectors
zbMATH Open document ID: 0757.73034
DOI: 10.1016/0045-7825(91)90248-5
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1992-09-27T00:00:00Z
review text: A systematic procedure is presented for extending the capabilities of an existing linear finite element of accomodate finite rotation analysis. The approach is based on the element -- independent co-rational algorithm, where the element rigid body motion is separated from the deformational part of its total motion by attaching a local frame to the element, such that the motion of the element with respect to this local frame fully describes the deformation. The independence of the internal strain energy of an element on the rigid body part of the motion is used to obtain invariance conditions for the element internal force vector and the tangent stiffness matrix. The consistent linearization of the co- rotational formulation results in a projector matrix, whose action has no effect on consistent internal forces and moments. The anti-symmetric part of the tangent stiffness matrix is shown to depend on the out-of-balance force vector. It is proved that using the symmetric part of the tangent matrix, the Newton iteration retains its quadratic rate of convergence. Three large rotation test examples are solved. The results demonstrate that it is possible to analyze structures displaying highly nonlinear behaviour involving very large rotations within a general co-rotational framework, using simple and economical finite elements.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74S05
zbMATH DE Number: 63170
zbMATH Keywords: co-rational algorithm
zbMATH Keywords: internal strain energy
zbMATH Keywords: tangent stiffness matrix
zbMATH Keywords: projector matrix
zbMATH Keywords: Newton iteration
zbMATH Keywords: large rotations
author: Bahram Nour-Omid
author: Charles C. Rankin
reviewed by: L. Sperling
MaRDI profile type: Publication
full work available at URL: 0045-7825(91)90248-5
OpenAlex ID: W1986681597
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description: scientific article; zbMATH DE number 63170