Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A variational-hemivariational inequality approach to the laminated plate theory under subdifferential boundary conditions

Authors: P. D. Panagiotopoulos and G. E. Stavroulakis
Journal: Quart. Appl. Math. 46 (1988), 409-430
MSC: Primary 73K20; Secondary 49A29, 73C60, 73K10
DOI: https://doi.org/10.1090/qam/963579
MathSciNet review: 963579
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Abstract: In this paper the delamination problem for laminated plates is studied. A nonmonotone multivalued law is introduced in order to describe the interlaminar bonding forces. This law is written as the generalized gradient in the sense of F. H. Clarke of an appropriately defined nonconvex superpotential. Moreover, monotone boundary conditions of the subdifferential type are assumed to hold. The problem is formulated as a variational-hemivariational inequality expressing the principle of virtual work in inequality form. By using compactness and monotonicity arguments, the existence and the approximation of the solution of this inequality are investigated.

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  • [1] P. D. Panagiotopoulos, Nonconvex superpotentials in the sense of F. H. Clarke and applications, Mech. Res. Comm. 8, 335-340 (1981) MR 639382
  • [2] P. D. Panagiotopoulos, Nonconvex energy functions. Hemivariational inequalities and substationarity principles, Acta Mech. 48, 160-183 (1983) MR 715806
  • [3] P. D. Panagiotopoulos, Inequality problems in mechanics and applications. Convex and non-convex energy functions, Birkhäuser Verlag, Basel, Boston, Stuttgard, 1985 MR 896909
  • [4] J. J. Moreau, La notion de sur-potentiel et les liaisons unilatérales en élastostatique, C. R. Acad. Sci. Paris Ser. A 267, 954-957 (1968) MR 0241038
  • [5] P. D. Panagiotopoulos, Ioffe fans and unilateral problems: a new conjecture, Proc. 3rd CISM Meeting on Unilateral Problems in Structural Analysis, Prescudin Udine, June 1985, CISM Courses and Lectures, Vol. 304, Springer-Verlag, Wien, New York, pp. 239-257, 1987
  • [6] G. Duvaut and J. L. Lions, Les inéquations en méchanique et en physique, Dunod, Paris, 1972 (English translation: Inequalities in mechanics and physics, Springer-Verlag, Berlin, Heidelberg, New York, 1976) MR 0464857
  • [7] F. H. Clarke, Nonsmooth analysis and optimization, Wiley, New York, 1984
  • [8] P. D. Panagiotopoulos, Une généralisation non-convexe de la notion du sur-potentiel et ses applications, C. R. Acad. Sci. Paris Sér. B 296, 580-584 (1983) MR 720434
  • [9] P. D. Panagiotopoulos, Hemivariational inequalities and substationarity in the static theory of v. Kármán plates, Z. Angew. Math. Mech. 65, 219-229 (1985) MR 801713
  • [10] R. Jones, Mechanics of composite materials, McGraw-Hill-Scripta, New York, Washington, D. C., 1975
  • [11] K. C. Chang, Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl. 80, 102-129 (1981) MR 614246
  • [12] H. Brezis, Problèmes unilatéraux, J. Math. Pures Appl. 51, 1-168 (1972) MR 0317123
  • [13] J. J. Moreau, Fonctionnelles convexes, Séminaire au Collége de France, 1966-1967
  • [14] J. Ekeland and R. Temam, Convex analysis and variational problems, North-Holland, Amsterdam, and American Elsevier, New York, 1976 MR 0463994
  • [15] J. Rauch, Discontinuous semilinear differential equations and multiple valued maps, Proc. Amer. Math. Soc. 64, 277-282 (1977) MR 0442453
  • [16] R. T. Rockafellar, Convex analysis, Princeton University Press, Princeton, N. J., 1970 MR 0274683
  • [17] J. P. Aubin and F. H. Clarke, Shadow prices and duality for a class of optimal control problems, SIAM J. Control Optim. 17, 567-586 (1979) MR 540838

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DOI: https://doi.org/10.1090/qam/963579
Article copyright: © Copyright 1988 American Mathematical Society

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