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Topology Design of Elastic Structures for a Contact Model

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Optimization with PDE Constraints

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 101))

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Abstract

Contact problems are very important in the engineering design and the correct interpretation of the physical phenomena, and its influence in this process, is of paramount importance for the engineers. In this paper we employ the topological derivative concept for optimum design problems in contact solid mechanics. A nonlinear contact model governed by a variational inequality is considered. Beside the theoretical developments, some computational examples are included. The influence of the parameters of the contact model in the optimal results for the structures is studied. The numerical results show that the proposed method of optimum design can be applied to a broad class of engineering problems.

Mathematics Subject Classification (2010). Primary 49J40; Secondary 35J86, 74P15.

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Acknowledgements

This research is partially supported by LabEx CARMIN–CIMPA SMV programme (France), CONICET (National Council for Scientific and Technical Research, Argentina) and PID-UTN (Research and Development Program of the National Technological University, Argentina) under grant PID/UTN 1420. The work of J. Stebel was supported by the ESF grant Optimization with PDE Constraints, by the Czech Science Foundation (GAČR) grant no. 201/09/0917 and RVO 67985840. The supports of these agencies are gratefully acknowledged.

Jan Sokolowski is supported by the Brazilian Research Council (CNPq), through the Special Visitor Researcher Framework of the Science Without Borders.

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Authors and Affiliations

  1. Departamento de Ingeniería Civil, Facultad Regional Córdoba, Universidad Tecnológica Nacional (UTN/FRC - CONICET), Maestro M. López esq. Cruz Roja Argentina, X5016ZAA, Córdoba, Argentina

    S. M. Giusti

  2. Institut Élie Cartan, UMR7502 (Université Lorraine, CNRS, INRIA), Laboratoire de Mathématiques, Université de Lorraine, B.P.239, 54506, Vandoeuvre-lès-Nancy Cedex, France

    Jan Sokołowski

  3. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    Jan Stebel

Authors
  1. S. M. Giusti
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  2. Jan Sokołowski
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  3. Jan Stebel
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Correspondence to Jan Sokołowski .

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Editors and Affiliations

  1. Institut für Mathematik, Universität Augsburg, Augsburg, Germany

    Ronald Hoppe

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Giusti, S.M., Sokołowski, J., Stebel, J. (2014). Topology Design of Elastic Structures for a Contact Model. In: Hoppe, R. (eds) Optimization with PDE Constraints. Lecture Notes in Computational Science and Engineering, vol 101. Springer, Cham. https://doi.org/10.1007/978-3-319-08025-3_6

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