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Topology optimization of plate structures subject to initial excitations for minimum dynamic performance index

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Abstract

This paper studies optimal topology design of damped vibrating plate structures subject to initial excitations. The design objective is to minimize an integrated square performance measure. The artificial density of the plate element is the topology design variable and the material volume is given. The Lyapunov’s second method is applied to reduce the calculation of performance measure to the solution of the Lyapunov equation. An adjoint sensitivity analysis method is used, which only needs to solve the Lyapunov equation twice. However, when the problem has a large number of degrees of freedom, the solution process of Lyapunov equation is computational costly. Thus, the full model is transformed to a reduced space by mode reduction method. To further reduce the scale of reduced model, we propose a mode screen method to decrease the number of eigenmodes. Numerical examples of optimum topology design of bending plates are presented for illustrating validity and efficiency of our new algorithm.

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Acknowledgments

This work is supported by National Natural Science Foundation of China (91216201 and 11372062) and the 973 Program (No. 2014CB049000).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Faculty of Vehicle Engineering and Mechanics, Dalian University of Technology, Dalian, 116023, People’s Republic of China

    Kun Yan & Gengdong Cheng

  2. Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, P.O. Box 19023, Arlington, TX, 76019, USA

    Bo Ping Wang

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  1. Kun Yan
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  2. Gengdong Cheng
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  3. Bo Ping Wang
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Correspondence to Kun Yan.

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Yan, K., Cheng, G. & Wang, B.P. Topology optimization of plate structures subject to initial excitations for minimum dynamic performance index. Struct Multidisc Optim 53, 623–633 (2016). https://doi.org/10.1007/s00158-015-1350-9

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  • DOI: https://doi.org/10.1007/s00158-015-1350-9

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