Finite element formulation of spatially curved and twisted rods
type: Item
instance of: scholarly article
title: Finite element formulation of spatially curved and twisted rods
zbMATH Open document ID: 0635.73077
DOI: 10.1016/0045-7825(88)90021-7
author: B. George
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1988-01-01T00:00:00Z
review text: For spatially curved and twisted rods a set of governing equations consisting of equilibrium equations and strain displacement and constitutive relations are derived in terms of three translational and three rotational degrees of freedom. By solving the strain displacement relations for constant and zero states of strain the rigid body and constant strain modes of the rod are obtained. These displacement modes are then used as basis functions for development of a finite element model. To verify the formulation and the elemental matrices, three examples are analyzed and in each case the computed results are compared with those obtained from a discrete model representation, using prismatic Timoshenko rod elements. It is found that the curved element, which is geometrically exact, yields more accurate results and it eliminates the jumps in some force quantities, caused by the indeterminacy of the normal (and or tangent, binormal), at the nodes.
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74S30
zbMATH DE Number: 4035328
zbMATH Keywords: twisted rods
zbMATH Keywords: governing equations
zbMATH Keywords: equilibrium equations
zbMATH Keywords: constitutive relations
zbMATH Keywords: three translational and three rotational degrees of freedom
zbMATH Keywords: strain displacement relations
zbMATH Keywords: zero states of strain
zbMATH Keywords: constant strain modes
zbMATH Keywords: curved element
MaRDI profile type: Publication
full work available at URL: 0045-7825(88)90021-7
OpenAlex ID: W1980213461
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description: scientific article; zbMATH DE number 4035328