Vol. 3, No. 8, 2008

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12
Issue 3, 249–351
Issue 2, 147–247
Issue 1, 1–146

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
Cover
Editorial Board
Research Statement
Scientific Advantage
Submission Guidelines
Submission Form
Subscriptions
Author Index
To Appear
 
ISSN: 1559-3959
A generalized Cosserat point element (CPE) for isotropic nonlinear elastic materials including irregular 3-D brick and thin structures

M. Jabareen and M. B. Rubin

Vol. 3 (2008), No. 8, 1465–1498
Abstract

A generalized form for the strain energy of inhomogeneous deformations is developed for a 3-D brick Cosserat Point Element (CPE) which includes full coupling of bending and torsional modes of deformation. The constitutive coefficients, which depend on the reference geometry of the element, are determined by solving eighteen bending problems and six torsion problems on special elements that are parallelepipeds with two right angles. The resulting constitutive coefficients ensure that the strain energy for inhomogeneous deformations remains a positive definite function of the inhomogeneous strain measures for all reference element shapes. A number of example problems are considered which show that the generalized CPE produces results as accurate as enhanced strain and incompatible elements for thin structures and is free of hourglass instabilities typically predicted by these enhanced elements in regions experiencing combined high compression with bending.

Keywords
Cosserat point, element irregularity, finite element, nonlinear elasticity
Milestones
Received: 22 December 2007
Revised: 26 June 2008
Accepted: 29 June 2008
Published: 1 October 2008
Authors
M. Jabareen
Institute of Mechanical Systems
Department of Mechanical Engineering
ETH Zentrum
8092 Zürich
Switzerland
M. B. Rubin
Faculty of Mechanical Engineering
Technion – Israel Institute of Technology
32000 Haifa
Israel