Structural and Multidisciplinary Optimization

, Volume 56, Issue 4, pp 755–765 | Cite as

Topology optimization of continuum structures subjected to the variance constraint of reaction forces



In this paper, the attainment of uniform reaction forces at the specific fixed boundary is investigated for topology optimization of continuum structures. The variance of the reaction forces at the boundary between the elastic solid and its foundation is firstly introduced as the evaluation criterion of the uniformity of the reaction forces. Then, the standard formulation of optimal topology design is improved by introducing the variance constraint of the reaction forces. Sensitivity analysis of the latter is carried out based on the adjoint method. Numerical examples are dealt with to reveal the effect of the variance constraint in comparison with solutions of standard topology optimization.


Topology optimization Reaction force Variance constraint Sensitivity analysis 



This work is supported by the National Key Research and Development Program of China (2017YFB1102800), the National Natural Science Foundation of China (11672239, 11432011, 11620101002), the Natural Science Basic Research Plan in Shaanxi Province of China (2017JM1002) and the Key Research and Development Program of Shaanxi (S2017-ZDYF-ZDXM-GY-0035)


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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 UniversityXi’anChina
  2. 2.Institute of Intelligence Material and Structure, Unmanned System TechnologiesNorthwestern Polytechnical UniversityXi’anChina

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