Optimization and Engineering

, Volume 20, Issue 1, pp 251–275 | Cite as

On the approximate reanalysis technique in topology optimization

  • Thadeu A. SenneEmail author
  • Francisco A. M. Gomes
  • Sandra A. Santos
Research Article


A classical problem in topology optimization concerns the minimization of the compliance of a static structure, subject to a volume constraint upon the available material. Assuming that the structure is under small displacements and it is composed of a linear elastic material, the evaluation of the objective function demands the solution of a linear system. Hence, within the computational optimization process of addressing topology optimization problems, the cost of evaluating the objective function may be an issue, especially as the discretized mesh is refined. This work pursues the approximate reanalysis technique in combination with the Sequential Piecewise Linear Programming method for obtaining optimized structures. Numerical evidences are presented to corroborate the usage of this blend in a study composed by three distinct strategies in three benchmark test problems. A further analysis has been performed concerning the impact of the computation of the gradient vector of the objective function, pointing out room for additional savings.


Topology optimization Linear systems Linear solvers Approximate reanalysis Nonlinear Programming 

Mathematics Subject Classification

90C30 65K05 49M37 65F05 15A23 



This work was supported by Fundação de Amparo à Pesquisa do Estado de São Paulo (Grants 2013/05475-7, 2013/07375-0); and Conselho Nacional de Desenvolvimento Científico e Tecnológico (Grants 302915/2016-8, 430678/2016-9). The authors are thankful to the anonymous reviewers, whose comments and suggestions have generated improvements upon the original version of the manuscript.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Thadeu A. Senne
    • 1
    Email author
  • Francisco A. M. Gomes
    • 2
  • Sandra A. Santos
    • 2
  1. 1.Institute of Science and TechnologyFederal University of São PauloSão José dos CamposBrazil
  2. 2.Institute of Mathematics, Statistics and Scientific ComputingState University of CampinasCampinasBrazil

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