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Free-form optimization method for frame structures aiming at controlling time-dependent responses

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Abstract

In this paper, a parameter-free optimization method for controlling the time-dependent response of frame structures is proposed. The proposing method deals with three optimization problems, including a vibration displacement minimization problem, a vibration displacement control problem, and a dynamic compliance minimization problem, which is the special case of the vibration minimization problems. These time-dependent optimum design problems are formulated as distributed-parameter optimization problems and the sensitivity functions for the shape variation to obtain the optimal shape are derived based on the material derivative method, Lagrange multiplier method, and the adjoint method. The derived sensitivity function is applied to the H1 gradient method for frames, which is a gradient method in the function space to determine the optimal shape variation. With the proposed method, the optimal shape for time-dependent response problems such as a forced vibration, a free vibration, or a transient response is obtained while minimizing the objective functional and maintaining the smoothness of a frame structure. Several numerical design examples including a continuous dynamic force or an impulse force as an input force are shown to verify and validate the effectiveness of the proposed method and the results are discussed.

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Funding

A part of this research was supported by a Grants-in-Aid for Scientific Research given by JKA (Grant Number 2019M1-141).

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Authors and Affiliations

  1. Department of Advanced Science and Technology, Toyota Technological Institute, 2-12-1 Hisakata, Tenpaku-ku, Nagoya, 468-8511, Japan

    Masatoshi Shimoda

  2. Department of Mechanical Engineering, Sojo University, 4-22-1, Ikeda, Nishi-Ku, Kumamoto, 860-0082, Japan

    Yang Liu

  3. Graduate School of Toyota Technological Institute, 2-12-1 Hisakata, Tenpaku-ku, Nagoya, 468-8511, Japan

    Mamoru Wakasa

Authors
  1. Masatoshi Shimoda
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  2. Yang Liu
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  3. Mamoru Wakasa
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Corresponding author

Correspondence to Yang Liu.

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The authors declare that there is no conflict of interest.

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Responsible Editor: Gengdong Cheng

Replication of results

The optimization system developed consists of in-house C programs and MSC NASTRAN for FE analyses. Their executions are controlled with “Batch program” on Windows OS until the convergence. For the benchmark calculation by readers, we will provide NASTRAN model data used in this paper.

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Shimoda, M., Liu, Y. & Wakasa, M. Free-form optimization method for frame structures aiming at controlling time-dependent responses. Struct Multidisc Optim 63, 479–497 (2021). https://doi.org/10.1007/s00158-020-02708-y

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  • DOI: https://doi.org/10.1007/s00158-020-02708-y

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