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A two-step optimization scheme based on equivalent stiffness parameters for forcing convexity of fiber winding angle in composite frames

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Abstract

For stiffness design optimization of composite frame structures, one of the major problems when using fiber winding angles as design variables directly is the lack of convexity of the objective function, which may lead to different local optima depending on initial designs when a traditional gradient-based optimization algorithm is applied. Therefore, the present paper adopts a gradient-based two-step optimization scheme to cope with the difficulty and search for a better optimal design of composite frames in which the fiber winding angles are taken as design variables. To realize the two-step optimization scheme, the equivalent stiffness parameters of a composite beam with circular cross-section are derived in explicit expressions and used to force the convexity of the design optimization of the composite frame. The stiffness matrices are linearly expressed in terms of the stiffness parameters, which guarantee the convexity of the design variable feasible region in the stiffness parameter space. The equivalent stiffness parameters are adopted to keep invariance of physical quantities between fiber winding angle and equivalent stiffness parameter spaces. In the two-step optimization scheme, the minimum identification problem with the constraint that the objective function at the new starting point is less than or equal to the previous objective function at the optimum point in fiber winding angle space is established. Then, the two-step optimization scheme can be implemented in the fiber winding angle and structural equivalent stiffness parameter spaces, respectively, until the minimum identification problem is not possible to identify a new starting point. The proposed two-step optimization scheme for composite frames fully takes advantage of the stiffness parameters in convexity and fiber winding angles as practically physical quantities, respectively. The sensitivity information of the objective function with respect to fiber winding angles and equivalent stiffness parameters is derived by the analytical sensitivity analysis method. Numerical examples show that the two-step optimization scheme can effectively force convexity of the optimization model and help to eliminate the initial design dependency. The effectiveness of the proposed two-step scheme is further verified through the particle swarm optimization (PSO) algorithm which is an evolutionary algorithm with global optimization capability.

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Acknowledgments

The authors thank Prof. Bin Niu for checking the correctness of the formula derivation.

Funding

Financial supports for this research were provided by the National Natural Science Foundation of China (Nos. 11672057,11711530018 and 11732004), the National Key R&D Program of China (2017YFC0307203), Program (LR2017001) for Innovative Talents at Colleges and Universities in Liaoning Province, the 111 project (B14013), the Korea Institute of Energy Technology Evaluation and Planning, and the Ministry of Trade Industry & Energy of the Republic of Korea (No. 20172010000830).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, International Research Center for Computational Mechanics, Dalian University of Technology, Dalian, 116024, Liaoning, China

    Zunyi Duan, Jun Yan & Jingyuan Wang

  2. Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejeon, 34141, Republic of Korea

    Zunyi Duan & Ikjin Lee

  3. Harbin Electric Power Equipment Company Limited, Harbin Electric Corporation, Harbin, 150028, China

    Zunyi Duan

  4. Department of Materials and Production, Aalborg University, 9220, Aalborg, Denmark

    Erik Lund

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  1. Zunyi Duan
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  2. Jun Yan
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  4. Erik Lund
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  5. Jingyuan Wang
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Correspondence to Jun Yan or Ikjin Lee.

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This work has been presented on 21st International Conference on Composite Materials Xi’an, 20-25th August 2017

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Duan, Z., Yan, J., Lee, I. et al. A two-step optimization scheme based on equivalent stiffness parameters for forcing convexity of fiber winding angle in composite frames. Struct Multidisc Optim 59, 2111–2129 (2019). https://doi.org/10.1007/s00158-018-2179-9

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  • DOI: https://doi.org/10.1007/s00158-018-2179-9

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