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A refined sine-based
finite element with transverse normal deformation for the
analysis of laminated beams under thermomechanical loads
Philippe Vidal and Olivier Polit |
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Vol. 4 (2009), No. 6, 1127–1155
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Abstract |
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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
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Milestones
Received: 16 December 2008
Revised: 26 March 2009
Accepted: 27 May 2009
Published: 14 September 2009
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Authors |
| Philippe Vidal | |
| LMpX Université Paris Ouest 50 rue de Sèvres 92410 Ville d’Avray France |
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| Olivier Polit | |
| LMpX Université Paris Ouest 50 rue de Sèvres 92410 Ville d’Avray France |
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