On the Delamination Problem of Two-Layer Plates

• L. Ascione
• D. Bruno
Conference paper
Part of the International Centre for Mechanical Sciences book series (CISM, volume 288)

Summary

In this paper we analyze the delamination problem of a two-layer plate by means of a unilateral contact approach. The mathematical formulation of the problem is discussed and a finite element approximation is presented. Two numerical examples concerning one — dimensional and two-dimensional problems are examined. Some comparisons with analytical results are also given, which show the effectiveness of the unilateral approach.

Keywords

Variational Inequality Iterative Scheme Elastic Foundation Finite Element Mesh Finite Element Approximation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Sommario

In questo lavoro si esamina, mediante un approccio di tipo contatto unilaterale, il problema di delaminazione di pannelli compositi a due strati. Si discute la formulazione matematica del problema, di cui si presenta una approssimazione mediante elementi finiti.

I risultati numerici ottenuti riguardano un problema di delaminazione monodimensionale ed un altro bidimensionale.

Il confronto di questi risultati con soluzioni analitiche disponibili mostra l’efficienza del modello proposto.

References

1. 1.
Fichera, G. Boundary - Value Problems of Elasticity with Unilateral Constraints, Enc. of Physics, Vol. VIa/2, Springer-Verlag, (1972).Google Scholar
2. 2.
Duvaut, G. and Lions, J.L. Les Inéquations en Mécanique et en Physique, Dunod, Paris, (1972).
3. 3.
Glowinski, R., Lions, J.L. and Trémolieres, R. Analyse Numérique des Inéquations Variationnelles, Dunod, Paris, (1976).
4. 4.
Toscano, R. and Maceri, A., On the problem of the elastic plate on one-side foundation, Meccanica, Vol. 15, No. 2, 95–106, (1980).
5. 5.
Ascione, L., Grimaldi, A. and Maceri, F., Modeling and analysis of beams on tensionless foundations, Int. J. of Modelling and Simulation, Vol. 3, No. 2, (1983).Google Scholar
6. 6.
Ascione, L. and Grimaldi, A., Unilateral contact between a plate and an elastic foundation, Meccanica, to appear, (1983).Google Scholar
7. 7.
Panagiotopoulos, P.D. and Talaslidis, D., A linear analysis approach to the solution of certain classes of variational inequality problems in structural analysis, Int. J. Solids Structures, Vol. 16, 991–1005, (1980).
8. 8.
Frémond, A., Adhésion de solides élastiques, Lecture delivered at the First Symposium on Unilateral Problems in Mechanics, CISM - Udine, Italy, May 1982.Google Scholar
9. 9.
Mindlin, R.D. Influence of rotatory inertia and shear on flexural motions of isotropic elastic plates, J. AppL Mech., vol. 18, 31–88, (1951).
10. 10.
Reddy, J.N., A penalty plate-bending element for the analysis of laminated anisotropic composite plates, Int. J. Numer. Meth. Eng., Vol. 15, pp. 1187–1206, (1980).
11. 11.
Reddy, J.N., An Introduction to the Finite Element Method, Mc Graw-Hill, New York, (1983).Google Scholar
12. 12.
Oden, J.T. and Reddy, J.N., Variational Methods in Theoretical Mechanics, Springer-Verlag, (1976).Google Scholar
13. 13.
Bunidge, R. and Keller, J.B., Peeling, slipping, and cracking — some one dimensional free-boundary problems in mechanics, SIAM Review, Vol. 20, No. 1, (1978).Google Scholar
14. 14.
Grimaldi, A. and Reddy, J.N., On delamination in plates: a unilateral-contact approach, This Meeting, (1983).Google Scholar