Soft Computing

, Volume 21, Issue 5, pp 1157–1179

Topology optimization of compliant structures and mechanisms using constructive solid geometry for 2-d and 3-d applications

  • Anmol Pandey
  • Rituparna Datta
  • Bishakh Bhattacharya
Methodologies and Application

DOI: 10.1007/s00500-015-1845-8

Cite this article as:
Pandey, A., Datta, R. & Bhattacharya, B. Soft Comput (2017) 21: 1157. doi:10.1007/s00500-015-1845-8


This research focuses on the establishment of a constructive solid geometry-based topology optimization (CSG-TOM) technique for the design of compliant structure and mechanism. The novelty of the method lies in handling voids, non-design constraints, and irregular boundary shapes of the design domain, which are critical for any structural optimization. One of the most popular models of multi-objective genetic algorithm, non-dominated sorting genetic algorithm is used as the optimization tool due to its ample applicability in a wide variety of problems and flexibility in providing non-dominated solutions. The CSG-TOM technique has been successfully applied for 2-D topology optimization of compliant mechanisms and subsequently extended to 3-D cases. For handling these cases, a new software framework involving optimization routine for geometry and mesh generation with FEA solver has been developed. The efficacy of the approach has been demonstrated for 2-D and 3-D geometries and also compared with state of the art techniques.


Structural and topology optimization Finite element analysis (FEA) Multi-objective genetic algorithms Compliant structures 

Abbreviations and symbols


Constructive solid geometry-based topology optimization methods


Solid isotropic material with penalization


Evolutionary structural optimization


Multi-objective genetic algorithm


Simulated binary crossover


Topology optimization using python


Total nodes


Variable nodes


Fixed nodes


Special nodes


Symmetry nodes

\(\eta _i\)

Volume fraction of topology in ith generation

\(\varvec{\alpha }\)

Volume correction factor

\(\varvec{\varepsilon }\)

Ratio of required volume fraction to current volume fraction

\(W_{-}, W_{+}\)

Width selection operator

\(\lambda \)

Symmetry condition operator

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Anmol Pandey
    • 1
  • Rituparna Datta
    • 1
  • Bishakh Bhattacharya
    • 1
  1. 1.Department of Mechanical EngineeringIndian Institute of Technology KanpurKanpurIndia

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