Structural and Multidisciplinary Optimization

, Volume 57, Issue 3, pp 1061–1078 | Cite as

Structural topology optimization under harmonic base acceleration excitations

  • Ji-Hong Zhu
  • Fei He
  • Tao Liu
  • Wei-Hong Zhang
  • Qinglin Liu
  • Chong Yang


This work is focused on the structural topology optimization methods related to dynamic responses under harmonic base acceleration excitations. The uniform acceleration input model is chosen to be the input form of base excitations. In the dynamic response analysis, we propose using the large mass method (LMM) in which artificial large mass values are attributed to each driven nodal degree of freedom (DOF), which can thus transform the base acceleration excitations into force excitations. Mode displacement method (MDM) and mode acceleration method (MAM) are then used to calculate the harmonic responses and the design sensitivities due to their balances between computing efficiency and accuracy especially when frequency bands are taken into account. A density based topology optimization method of minimizing dynamic responses is then formulated based on the integration of LMM and MDM or MAM. Moreover, some particular appearances such as the precision of response analysis using MDM or MAM, and the duplicated frequencies are briefly discussed. Numerical examples are finally tested to verify the accuracy of the proposed schemes in dynamic response analysis and the quality of the optimized design in improving dynamic performances.


Topology optimization Dynamic response Harmonic base acceleration excitations Large mass method Mode displacement method Mode acceleration method 



The authors would like to thank Prof Jianbin Du from Tsinghua University for valuable discussions. This work is supported by National Natural Science Foundation of China (11722219, 11432011, 11620101002), National Key Research and Development Program (2017YFB1102800), Key Research and Development Program of Shaanxi (2017KW-ZD-11 & 2017ZDXM-GY-059).


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.State IJR Center of Aerospace Design and Additive ManufacturingNorthwestern Polytechnical UniversityXianChina
  2. 2.MIIT Lab of Metal Additive Manufacturing and Innovative DesignNorthwestern Polytechnical UniversityXianChina
  3. 3.Institute of Intelligence Material and Structure, Unmanned System TechnologiesNorthwestern Polytechnical UniversityXianChina
  4. 4.Institute of Systems EngineeringChina Academy of Engineering PhysicsMianyangChina

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