Structural and Multidisciplinary Optimization

, Volume 46, Issue 3, pp 369–384 | Cite as

Topology optimization for minimum weight with compliance and stress constraints

  • Matteo BruggiEmail author
  • Pierre Duysinx
Research Paper


The paper deals with a formulation for the topology optimization of elastic structures that aims at minimizing the structural weight subject to compliance and local stress constraints. The global constraint provides the expected stiffness to the optimal design while a selected set of local enforcements require feasibility with respect to the assigned strength of material. The Drucker–Prager failure criterion is implemented to handle materials with either equal or unequal behavior in tension and compression. A suitable relaxation of the equivalent stress measure is implemented to overcome the difficulties related to the singularity problem. Numerical examples are presented to discuss the features of the achieved optimal designs along with performances of the adopted procedure. Comparisons with pure compliance–based or pure stress–based strategies are also provided to point out differences arising in the optimal design with respect to conventional approaches, depending on the assumed material behavior.


Topology optimization Stress constraints Compliance constraint Singularity problem Drucker–Prager failure criterion 



Part of the work has been supported by the “9th Executive Programme for Scientific Cooperation between the Francophone Belgian Community and Italy”, that is gratefully acknowledged.


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Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Structural EngineeringPolitecnico di MilanoMilanoItaly
  2. 2.Department of Aerospace and Mechanical EngineeringUniversity of LiègeLiègeBelgium

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