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A general formulation of structural topology optimization for maximizing structural stiffness

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Abstract

This paper presents a general formulation of structural topology optimization for maximizing structure stiffness with mixed boundary conditions, i.e. with both external forces and prescribed non-zero displacement. In such formulation, the objective function is equal to work done by the given external forces minus work done by the reaction forces on prescribed non-zero displacement. When only one type of boundary condition is specified, it degenerates to the formulation of minimum structural compliance design (with external force) and maximum structural strain energy design (with prescribed non-zero displacement). However, regardless of boundary condition types, the sensitivity of such objective function with respect to artificial element density is always proportional to the negative of average strain energy density. We show that this formulation provides optimum design for both discrete and continuum structures.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (90816025, 10421202). The supports are gratefully acknowledged. We thank Prof. Pauli Pedersen and Prof. Niels L. Pedersen for the stimulating and invaluable discussions, we thank Doc. Jiangs comments and suggestions for improvement of an earlier version of this manuscript.

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Authors and Affiliations

  1. State Key Laboratory of Structural Analysis for Industrial Equipments, Department of Engineering Mechanics, Dalian University of Technology, Dalian, People’s Republic of China

    Fei Niu & Gengdong Cheng

  2. School of Energy and Power Engineering, Dalian University of Technology, Dalian, People’s Republic of China

    Shengli Xu

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  1. Fei Niu
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  2. Shengli Xu
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  3. Gengdong Cheng
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Correspondence to Fei Niu.

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Niu, F., Xu, S. & Cheng, G. A general formulation of structural topology optimization for maximizing structural stiffness. Struct Multidisc Optim 43, 561–572 (2011). https://doi.org/10.1007/s00158-010-0585-8

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  • DOI: https://doi.org/10.1007/s00158-010-0585-8

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