Efficient Variational Design Sensitivity Analysis

  • Franz-Joseph BartholdEmail author
  • Nikolai Gerzen
  • Wojciech Kijanski
  • Daniel Materna
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 40)


The authors’ variant of variational design sensitivity analysis in structural optimisation is highlighted in detail. A rigorous separation of physical quantities into geometry and displacement mappings based on an intrinsic presentation of continuum mechanics build up the first step. The variations with respect to design and displacements are easily available in a second step. The subsequent discrete matrix expressions are used to formulate the finite element equations in a third step. The fourth step elaborates the derived Matlab implementation while the fifth step shows the computational behaviour for an academic example. Both, the general case of nonlinear structural behaviour and the linearised approximation are outlined. The advocated scheme is compared with the well-known analytical differentiation approach of the discrete finite element equations.


Finite Element Approximation Design Sensitivity Analysis Finite Element Equation Reference Placement Design Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Franz-Joseph Barthold
    • 1
    Email author
  • Nikolai Gerzen
    • 1
  • Wojciech Kijanski
    • 1
  • Daniel Materna
    • 2
  1. 1.Numerische Methoden und InformationsverarbeitungTU DortmundDortmundGermany
  2. 2.Department of Civil EngineeringOstwestfalen-Lippe University of Applied SciencesDetmoldGermany

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