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Robust topology optimization for dynamic compliance minimization under uncertain harmonic excitations with inhomogeneous eigenvalue analysis

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Abstract

Variability of load magnitude/direction is a most significant source of uncertainties in practical engineering. This paper investigates robust topology optimization of structures subjected to uncertain dynamic excitations. The unknown-but-bounded dynamic loads/accelerations are described with the non-probabilistic ellipsoid convex model. The aim of the optimization problem is to minimize the absolute dynamic compliance for the worst-case loading condition. For this purpose, a generalized compliance matrix is defined to construct the objective function. To find the optimal structural layout under uncertain dynamic excitations, we first formulate the robust topology optimization problem into a nested double-loop one. Here, the inner-loop aims to seek the worst-case combination of the excitations (which depends on the current design, and is usually to be found by a global optimization algorithm), and the outer-loop optimizes the structural topology under the found worst-case excitation. To tackle the inherent difficulties associated with such an originally nested formulation, we convert the inner-loop into an inhomogeneous eigenvalue problem using the optimality condition. Thus the double-loop problem is reformulated into an equivalent single-loop one. This formulation ensures that the strict-sense worst-case combination of the uncertain excitations for each intermediate design be located without resorting to a time-consuming global search algorithm. The sensitivity analysis of the worst-case objective function value is derived with the adjoint variable method, and then the optimization problem is solved by a gradient-based mathematical programming method. Numerical examples are presented to illustrate the effectiveness and efficiency of the proposed framework.

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Acknowledgments

The authors would like to thank Prof. Krister Svanberg for providing the source code of the GCMMA algorithm. The authors also gratefully acknowledge the support of the Natural Science Foundation of China (11425207, U1508209 and 91530110), China Postdoctoral Science Foundation (2015M581328), and Research Project of State Key Laboratory of Mechanical System and Vibration (MSV201603).

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Xiaopeng Zhang, Zhan Kang & Wenbo Zhang

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  1. Xiaopeng Zhang
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  2. Zhan Kang
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  3. Wenbo Zhang
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Correspondence to Zhan Kang.

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Zhang, X., Kang, Z. & Zhang, W. Robust topology optimization for dynamic compliance minimization under uncertain harmonic excitations with inhomogeneous eigenvalue analysis. Struct Multidisc Optim 54, 1469–1484 (2016). https://doi.org/10.1007/s00158-016-1607-y

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  • DOI: https://doi.org/10.1007/s00158-016-1607-y

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