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Optimal fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach

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Abstract

A double stage sequential optimization algorithm for finding the optimal fiber content and its distribution in solid composites, considering uncertain design parameters, is presented. In the first stage, the optimal amount of fiber in a Fiber Reinforced Composite (FRC) structure with uniformly distributed fibers is conducted in the framework of a Reliability Based Design Optimization (RBDO) problem. In the second stage, the fiber distribution optimization having the aim to more increase in structural reliability is performed by defining a fiber distribution function through a Non-Uniform Rational B-Spline (NURBS) surface. The output of stage 1(optimal fiber content for homogeneously distributed fibers) is considered as the input of stage 2. The output of stage 2 is Reliability Index (RI) of the structure with optimal fiber content and optimal fiber distribution. First order reliability method in order to approximate the limit state function and a homogenization approach, based on the assumption of random orientation of fibers in the matrix, are implemented. The proposed combined model is able to capture the role of available uncertainties in FRC structures through a computationally efficient algorithm using all sequential, NURBS and sensitivity based techniques. Performed case studies show as an increase in model uncertainties yields to structural unreliability. Moreover, when system unreliability increases fiber distribution optimization becomes more influential.

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Acknowledgments

This work was supported partially by Marie Curie Actions under the grant IRSES-MULTIFRAC and German federal ministry of education and research under the grant BMBF SUA 10/042. Nachwuchsförderprogramm of Ernst Abbe foundation, the National Basic Research Program of China (973 Program: 2011CB013800), Program for Changjiang Scholars and Innovative Research Team in University (PCSIRT, IRT1029), Pujiang Program (12PJ1409100) and the research support provided by the Italian Ministry for University and Technological and Scientific Research (MIUR) are also acknowledged.

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Authors and Affiliations

  1. Institute of Structural Mechanics, Bauhaus University Weimar (BUW), Marienstraße 15, 99423, Weimar, Germany

    Hamid Ghasemi & Timon Rabczuk

  2. Department of Civil Engineering, Environment and Architecture, University of Parma, Parco Area delle Scienze, 181/A, 43100, Parma, Italy

    Roberto Brighenti

  3. Department of Geotechnical Engineering, College of Civil Engineering, Tongji University, 1239 Siping Road, Shanghai, 200092, China

    Xiaoying Zhuang

  4. School of Mechanical, Industrial and Aeronautical Engineering, University of the Witwatersrand, WITS, 2050, Johannesburg, South Africa

    Jacob Muthu

  5. Professor at BUW and School of Civil, Environmental and Architectural Engineering, Korea University, Seoul, South Korea

    Timon Rabczuk

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  1. Hamid Ghasemi
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  2. Roberto Brighenti
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  3. Xiaoying Zhuang
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  4. Jacob Muthu
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  5. Timon Rabczuk
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Correspondence to Hamid Ghasemi or Xiaoying Zhuang.

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Ghasemi, H., Brighenti, R., Zhuang, X. et al. Optimal fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach. Struct Multidisc Optim 51, 99–112 (2015). https://doi.org/10.1007/s00158-014-1114-y

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  • DOI: https://doi.org/10.1007/s00158-014-1114-y

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