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Nonconvex Optimization in Mechanics pp 119–158Cite as

Nonconvex Superpotential Problems. Variational and Hemivariational Inequalities

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Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 21))

Abstract

Linearity of the kinematics and of the constitutive relations combined with fairly general material stability assumptions guarantee the convexity of a structural analysis problem in either a potential energy or in a complementary energy formulation, as it has been discussed in details in the previous Chapter. In real life applications some of these assumptions may be violated: kinematic nonlinearity which is indispensable for the description of buckling effects, decohesion, damage and fracture problems which introduce material or interface instabilities and softening behaviour in elastoplasticity are some of the applications which lead to nonconvex problems in mechanics. This is due to the fact that most of the materials used are composite, e.g., concrete with steel, fibre reinforced materials etc. Moreover, the composite nature of the materials may appear also at the micromechanical level, e.g., concrete itself is a composition of stone aggregates and cement paste, etc.

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Authors and Affiliations

  1. Institute of Steel Structures, Department of Civil Engineering, Aristotle University, Thessaloniki, Greece

    E. S. Mistakidis

  2. Institute of Applied Mechanics, Department of Civil Engineering, Carolo Wilhelmina Technical University, Braunschweig, Germany

    G. E. Stavroulakis

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Mistakidis, E.S., Stavroulakis, G.E. (1998). Nonconvex Superpotential Problems. Variational and Hemivariational Inequalities. In: Nonconvex Optimization in Mechanics. Nonconvex Optimization and Its Applications, vol 21. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5829-3_4

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