Topology optimization of fluidic pressure-loaded structures and compliant mechanisms using the Darcy method

Prabhat Kumar, Jan Frouws, Matthijs Langelaar

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
15 Downloads (Pure)


In various applications, design problems involving structures and compliant mechanisms experience fluidic pressure loads. During topology optimization of such design problems, these loads adapt their direction and location with the evolution of the design, which poses various challenges. A new density-based topology optimization approach using Darcy’s law in conjunction with a drainage term is presented to provide a continuous and consistent treatment of design-dependent fluidic pressure loads. The porosity of each finite element and its drainage term are related to its density variable using a Heaviside function, yielding a smooth transition between the solid and void phases. A design-dependent pressure field is established using Darcy’s law and the associated PDE is solved using the finite element method. Further, the obtained pressure field is used to determine the consistent nodal loads. The approach provides a computationally inexpensive evaluation of load sensitivities using the adjoint-variable method. To show the efficacy and robustness of the proposed method, numerical examples related to fluidic pressure-loaded stiff structures and small-deformation compliant mechanisms are solved. For the structures, compliance is minimized, whereas for the mechanisms, a multi-criteria objective is minimized with given resource constraints.

Original languageEnglish
Pages (from-to)1637-1655
JournalStructural and Multidisciplinary Optimization
Issue number4
Publication statusPublished - 2020

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project

Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Compliant mechanisms
  • Darcy’s law
  • Pressure loads
  • Stiff structures
  • Topology optimization


Dive into the research topics of 'Topology optimization of fluidic pressure-loaded structures and compliant mechanisms using the Darcy method'. Together they form a unique fingerprint.

Cite this