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Signorini’s Problem

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Finite Element Approximation of Contact and Friction in Elasticity

Part of the book series: Advances in Mechanics and Mathematics ((ACM,volume 48))

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Abstract

In this chapter, we present the Signorini problem in small strain elasticity, as a first step before going into its numerical approximation and into more complex contact and friction problems. Indeed, Signorini conditions are the simplest conditions that allow to model appropriately frictionless contact between an elastic body and a rigid support, and they are formulated in terms of inequalities and a nonlinear complementarity condition. The Signorini problem can be recast weakly as a variational inequality of the first kind, for which well-posedness can be established thanks to Stampacchia’s theorem.

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Authors and Affiliations

  1. University of Burgundy, Dijon, France

    Franz Chouly

  2. Paul Sabatier University, Toulouse, France

    Patrick Hild

  3. National Institute of Applied Sciences of Lyon, Lyon, France

    Yves Renard

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  1. Franz Chouly
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  2. Patrick Hild
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  3. Yves Renard
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Chouly, F., Hild, P., Renard, Y. (2023). Signorini’s Problem. In: Finite Element Approximation of Contact and Friction in Elasticity. Advances in Mechanics and Mathematics(), vol 48. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-31423-0_3

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