Computational Mechanics

, Volume 49, Issue 3, pp 379–396 | Cite as

The inner structure of sensitivities in nodal based shape optimisation

  • Nikolai GerzenEmail author
  • Daniel Materna
  • Franz-Joseph Barthold
Original Paper


The pseudo load matrix and the sensitivity matrix dominate design sensitivity analysis of shape optimisation problems. They describe how a structure reacts on an imposed design modification. We analyse these matrices for the model problem of nodal based shape optimisation by a singular value decomposition and show that they contain additional valuable information which is not yet used either in theory or computation of shape optimisation. The inner structure of the sensitivities is capable to formulate reduced quadratic sub-problems within the sequential quadratic programming approach. We also tackle the problem of indefinite Hessian matrices in nodal based shape optimisation. Furthermore, we avoid jagged boundaries and obtain mesh-independent optimised structures applying density filtering technique to shape optimisation. Overall, we emphasise an enhanced analysis of sensitivities and point to unused substantial capabilities.


Structural optimisation Sensitivity analysis Singular value decomposition (SVD) Model reduction Nodal based shape optimisation 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Nikolai Gerzen
    • 1
    Email author
  • Daniel Materna
    • 1
  • Franz-Joseph Barthold
    • 1
  1. 1.Numerical Methods and Information ProcessingTechnische Universität DortmundDortmundGermany

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