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Nonconvex Superpotentials and Hemivariational Inequalities. Quasidifferentiability in Mechanics

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Nonsmooth Mechanics and Applications

Part of the book series: International Centre for Mechanical Sciences ((CISM,volume 302))

Abstract

These lectures concern the study of mechanical problems involving non-convex and possibly nondifferentiable energy functions, the superpotentials. First superpotentials connected with the notion of generalized gradient are considered, then the V-superpotentials are defined and finally the quasidifferential. After the defintion and formulation of several classes of mechanical problems involving superpotentials we study the questions of existence and approximation of the solution of a variationalhemivariational inequality resulting in the delamination theory of von Kármán laminated plates. Then a general semicoercive hemivariational inequality is studied and necessary and sufficient conditions are derived. The last section is devoted to the new notion of quasidifferentiability and its application to the study of mechanical problems.

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Authors and Affiliations

  1. Aristotle University, Thessaloniki, Greece

    P. D. Panagiotopoulos

  2. R.W.T.H., Aachen, Germany

    P. D. Panagiotopoulos

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  1. University of Montpellier, France

    J. J. Moreau

  2. Aristotle University, Greece

    P. D. Panagiotopoulos

  3. R.W.T.H., Germany

    P. D. Panagiotopoulos

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Panagiotopoulos, P.D. (1988). Nonconvex Superpotentials and Hemivariational Inequalities. Quasidifferentiability in Mechanics. In: Moreau, J.J., Panagiotopoulos, P.D. (eds) Nonsmooth Mechanics and Applications. International Centre for Mechanical Sciences, vol 302. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2624-0_2

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  • DOI: https://doi.org/10.1007/978-3-7091-2624-0_2

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  • Online ISBN: 978-3-7091-2624-0

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