Reinforcement of elastic structures in the presence of imperfect bonding
Author:
Robert Lipton
Journal:
Quart. Appl. Math. 59 (2001), 353-364
MSC:
Primary 74R20; Secondary 35J50, 35Q72, 74E05
DOI:
https://doi.org/10.1090/qam/1828458
MathSciNet review:
MR1828458
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Abstract: The two-dimensional problem of plane strain is considered in the presence of imperfectly bonded elastic reinforcements. A geometric criterion on the shape and size of the elastic reinforcement is found that determines when the effects of imperfect bonding overcome the benefits of the reinforcement. The criterion is given in terms of an eigenvalue problem posed on the surface of the reinforcement.
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- Robert Lipton, Optimal fiber configurations for maximum torsional rigidity, Arch. Rational Mech. Anal. 144 (1998), no. 1, 79–106. MR 1657324, DOI https://doi.org/10.1007/s002050050113
- Robert Lipton, Variational methods, bounds and size effects for two-phase composites with coupled heat and mass transport processes at the two-phase interface, J. Mech. Phys. Solids 47 (1999), no. 8, 1699–1736. MR 1686649, DOI https://doi.org/10.1016/S0022-5096%2898%2900118-5
J. Aboudi, Mechanics of Composite Materials: A Unified Micromechanical Approach, Studies in Applied Mechanics 29, Elsevier, New York, 1991
P. G. Ciarlet, Mathematical Elasticity. Volume II: Theory of Plates, Studies in Mathematics and its Applications 27, Elsevier, New York, 1997
V. Girault and P. A. Raviart, Finite Element Methods for Navier-Stokes Equations, Springer Series in Computational Mathematics, No. 5, Springer-Verlag, Berlin, 1986
J. P. Joines and J. S. Whittier, Waves at a flexibly bonded interface, J. Appl. Mech. 34, 905–909 (1967)
F. Léné and D. Leguillon, Étude de l’influence d’un glissement entre les constituants d’un matériau composite sur ses coefficients de comportment effectifs, Journal de Mécanique 20, 509–536 (1981)
R. Lipton, The second Stekloff eigenvalue and energy dissipation inequalities for functionals with surface energy, SIAM J. Math. Anal. 29, 673–680 (1998)
R. Lipton, Influence of interfacial surface conduction on the DC electrical conductivity of particle reinforced composites, Proc. Roy. Soc. Lond. A. 454, 1371–1382 (1998)
R. Lipton, Optimal fiber configurations for maximum torsional rigidity, Arch. Rational Mech. Anal. 144, 79–106 (1998)
R. Lipton, Variational methods, bounds, and size effects for two-phase composites with coupled heat and mass transport processes at the two-phase interface, Journal of Mechanics and Physics of Solids 47, 1699–1736 (1999)
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Article copyright:
© Copyright 2001
American Mathematical Society
