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Limit States of Materials and Structures pp 253–270Cite as

Shakedown Analysis of Composite Materials Based on Non-linear Mathematical Programming

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Abstract

Using a Representative Volume Element (rve) to represent the microstructure of periodic composite materials, a non-linear numerical technique is developed to calculate the macroscopic shakedown domains of composites subjected to cyclic loads. With the aid of homogenization theory, the classical kinematic shakedown theorem is generalized to incorporate the microstructure of composites. Using an associated flow rule, the plastic dissipation power for an ellipsoid yield criterion is expressed in terms of the kinematically admissible velocity. By means of non-linear mathematical programming techniques, a finite element formulation of kinematic shakedown analysis is then developed leading to a non-linear mathematical programming problem subject to only a small number of equality constraints. An effective, direct iterative algorithm is proposed to solve the non-linear programming problem. This can serve as a useful numerical tool for developing engineering design methods involving composite materials.

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Authors and Affiliations

  1. Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK

    H.X. Li

  2. School of Civil Engineering, University of Nottingham, Nottingham NG7 2RD, UK

    H.S. Yu

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  1. H.X. Li
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  2. H.S. Yu
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Editors and Affiliations

  1. Inst. Allgemeine Mechanik, RWTH Aachen, Templergraben 64, 52062 Aachen, Germany

    Weichert Dieter

  2. Dept. Engineering, University of Leicester, University Road, Leicester, United Kingdom LE1 7RH

    Ponter Alan

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Li, H., Yu, H. (2009). Shakedown Analysis of Composite Materials Based on Non-linear Mathematical Programming. In: Dieter, W., Alan, P. (eds) Limit States of Materials and Structures. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9634-1_13

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  • DOI: https://doi.org/10.1007/978-1-4020-9634-1_13

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-9633-4

  • Online ISBN: 978-1-4020-9634-1

  • eBook Packages: EngineeringEngineering (R0)

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