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Nonsmooth Mechanics I

Nonsmooth Modelling in Mechanics

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Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 10))

Abstract

In this Chapter the basic building elements of Nonsmooth Mechanics are explained. To this end the notions of convex, nonconvex and quasidifferentiable superpotential are introduced. Boundary conditions and material laws resulting from convex or nonconvex, nonsmooth energy functions are defined by using the concept of subdifferential or of qua-sidifferential. Additional information on these subjects can be found in Duvaut and Lions [13], Panagiotopoulos [51], Hlavaček et al. [29], Moreau, Panagiotopoulos, Strang [42], [43], Antes, Panagiotopoulos [1], Panagiotopoulos [54], Moreau [39], [41], [44] and [22], Naniewicz, Panagiotopoulos [47].

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Authors and Affiliations

  1. Department of Mathematics, St. Petersburg State University, St. Petersburg, Russia

    Vladimir F. Dem’yanov & Ludmila N. Polyakova

  2. Lehr- und Forschungsgebiet für Mechanik; Lehrstuhl C für Mathematik, RWTH, Aachen, Germany

    Georgios E. Stavroulakis

  3. Department of Civil Engineering, Aristotle University, Thessaloniki, Greece

    Panagiotis D. Panagiotopoulos

  4. Faculty of Mathematics and Physics, RWTH, Aachen, Germany

    Panagiotis D. Panagiotopoulos

Authors
  1. Vladimir F. Dem’yanov
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  2. Georgios E. Stavroulakis
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  3. Ludmila N. Polyakova
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  4. Panagiotis D. Panagiotopoulos
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Dem’yanov, V.F., Stavroulakis, G.E., Polyakova, L.N., Panagiotopoulos, P.D. (1996). Nonsmooth Mechanics I. In: Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics. Nonconvex Optimization and Its Applications, vol 10. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4113-4_3

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  • DOI: https://doi.org/10.1007/978-1-4615-4113-4_3

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