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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 268
Comparison of Beam Theories with Finite Element Analysis in Three-Point Bending of Thick Composites F. Duchaine1, E.M. Baten2, H. Champliaud1 and H.E.N. Bersee2
1Mechanical Engineering Department, École de Technologie Supérieure, Montreal, Canada
Full Bibliographic Reference for this paper
F. Duchaine, E.M. Baten, H. Champliaud, H.E.N. Bersee, "Comparison of Beam Theories with Finite Element Analysis in Three-Point Bending of Thick Composites", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 268, 2006. doi:10.4203/ccp.83.268
Keywords: thick laminated composites, three-point bending, beam theory, classical laminate theory, first order, refined higher order, finite element analysis.
Summary
This paper investigates the thickness effect in composite laminates. In plate
structures that are loaded in the plane, the effect of the thickness is hard to evaluate.
To clearly present this effect, the deflection of a simply supported laminated beam
with different thicknesses is studied. Therefore, the results of a finite element
analysis (FEA) and three other analytical theories are compared together. The first
method is a beam theory based on the classical laminate theory (CLT) [1,2]; the
second is based on a first order shear theory [1], with two different shear correction
factor calculations [1,3]; and the third uses a refined higher order method [4].
The simply supported composite laminated beam is loaded in the middle with a
linear force Several analytical theories have been developed for laminated beams [1,2], and most of them reduce 3D problems to 2D ones. The first method considered is based on the CLT [1,2], and this theory uses the Kirchhoff assumption, which results in neglecting the transverse shear and the out-of-plane normal effects. The displacement in the z direction is given by the following equation [1]:
The second method is the Timoshenko first-order beam theory (TFBT) for a
simply supported beam. It extends the previous theory by including a transverse
shear deformation term. The shear correction factor K is often difficult to calculate
for composite laminated beams. Since a quasi-isotropic symmetric lay-up is used,
Through the years, several higher order theories have been developed in order to
avoid the calculation of the shear correction
The FEA model was built in ANSYSR [6] using a SOLID46 element type. The
element type is defined by eight nodes, each having three degrees of freedom (
By comparing the results, a clear thickness effect can be outlined. The CLT is not
available for thick laminated beams (
The results show that for a low thickness ratio, there is an obvious thickness effect, and there remains a need for extensive experiments of thick laminates in order to be able to better handle this effect. References
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