Vol. 4, No. 6, 2009

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 refined sine-based finite element with transverse normal deformation for the analysis of laminated beams under thermomechanical loads

Philippe Vidal and Olivier Polit

Vol. 4 (2009), No. 6, 1127–1155
Abstract

In the framework of a sine model family, two new three-node beam finite elements including the transverse normal effect are designed for the analysis of laminated beams. They are based on a sine distribution with layer refinement and a second-order expansion for the deflection. The transverse shear strain is obtained using a cosine function, avoiding the use of shear correction factors. This kinematics accounts for the interlaminar continuity conditions on the interfaces between layers, and the boundary conditions on the upper and lower surfaces of the beam. A conforming FE approach is carried out using Lagrange and Hermite interpolations. It is important to notice that the number of unknowns is independent of the number of layers.

Both mechanical and thermomechanical tests for thin and thick beams are presented in order to evaluate the capability of these new finite elements to give accurate results with respect to elasticity or finite element reference solutions. Both convergence velocity and accuracy are discussed and this new finite element yields very satisfactory results at a low computational cost. In particular, the transverse stress computed from the constitutive relation is well estimated with regards to classical equivalent single layer models. This work focuses on the necessity to take into account the transverse normal stress, especially for thick beam and coupled analysis.

Keywords
finite element methods, composites, refined sine-based, layer refinement, transverse normal stress, thermal effects
Milestones
Received: 16 December 2008
Revised: 26 March 2009
Accepted: 27 May 2009
Published: 14 September 2009
Authors
Philippe Vidal
LMpX
Université Paris Ouest
50 rue de Sèvres
92410 Ville d’Avray
France
Olivier Polit
LMpX
Université Paris Ouest
50 rue de Sèvres
92410 Ville d’Avray
France