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TECHNICAL BRIEFS

First-Order Numerical Analysis of Linear Thin Layers

[+] Author and Article Information
F. Lebon1

Laboratoire de Mécanique et d’Acoustique, Université Aix-Marseille 1, 31 Chemin Joseph-Aiguier, 13402 Marseille Cedex 20, Francelebon@lma.cnrs-mrs.fr

S. Ronel

Laboratoire de Biomécanique et de Modélisation Humaine, Université Lyon 1, IUT B, 17 rue de France, 69100 Villeurbanne, Francesylvie.ronel@iutb.univ-lyon1.fr

1

Corresponding author.

J. Appl. Mech 74(4), 824-828 (Jun 27, 2006) (5 pages) doi:10.1115/1.2424716 History: Received January 18, 2006; Revised June 27, 2006

This paper deals with the first-order numerical analysis of thin layers. Theoretical results are recalled and compared with numerical data obtained on two classical examples. The effects of concentrated forces are discussed.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

The mechanical problem

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Figure 2

First example: square bar bonded with a rigid body (dimensions in mm)

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Figure 3

First example: three lines of nodes

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Figure 4

Square bar: numerical results on the contact zone: (a)u1 displacements; (b)u2 displacements; (c)σ22 stresses; (d)σ12 stresses (-) lower zone on the adhesive, (…) upper zone on the adhesive, (-.) lower zone on the elastic body)

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Figure 5

Square bar: numerical results on the contact zone: (a)[u1] displacements; (b)[u2] displacements; (c)[σ12] stresses; (d)[σ22] stresses ((…) jump in the stress, (-) derivative)

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Figure 6

Second example: two bonded bars (dimensions in mm)

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Figure 7

Two bars: numerical results on the contact zone: (a)[u1] displacements; (b)[u2] displacements; (c)[σ22] stresses; and (d)[σ12] stresses

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Figure 8

Two bars: numerical data on the contact zone (a)[u1] displacements; (b)[u2] displacements (… displacements, - stress); (c)[σ22] stresses; (d)[σ12] stresses ((…) jump in the stress, (-) derivative)

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Figure 9

Concentrated forces

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Figure 10

Application of the concentrated forces

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Figure 11

Numerical solution on the edge (a) limit problem with concentrated forces; (b) limit problem without concentrated forces; and (c) initial problem with two layers

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