Structural and Multidisciplinary Optimization

, Volume 55, Issue 6, pp 2259–2283 | Cite as

Sensitivity of structural response in context of linear and non-linear buckling analysis with solid shell finite elements

  • Lukas RadauEmail author
  • Nikolai Gerzen
  • Franz-Joseph Barthold


The paper is concerned with the sensitivity analysis of structural responses in context of linear and non-linear stability phenomena like buckling and snapping. The structural analysis covering these stability phenomena is summarised. Design sensitivity information for a solid shell finite element is derived. The mixed formulation is based on the Hu-Washizu variational functional. Geometrical non-linearities are taken into account with linear elastic material behaviour. Sensitivities are derived analytically for responses of linear and non-linear buckling analysis with discrete finite element matrices. Numerical examples demonstrate the shape optimisation maximising the smallest eigenvalue of the linear buckling analysis and the directly computed critical load scales at bifurcation and limit points of non-linear buckling analysis, respectively. Analytically derived gradients are verified using the finite difference approach.


Sensitivity analysis Solid shell Structural stability Buckling and snapping Eigenvalue buckling Direct computation of critical points 



We gratefully acknowledge the support of the German Research Foundation (DFG) under grant no. BA 1828/5-1.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Lukas Radau
    • 1
    Email author
  • Nikolai Gerzen
    • 1
  • Franz-Joseph Barthold
    • 1
  1. 1.Numerical Methods and Information ProcessingFaculty of Architecture and Civil EngineeringDortmundGermany

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