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Efficient Variational Design Sensitivity Analysis

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Mathematical Modeling and Optimization of Complex Structures

Part of the book series: Computational Methods in Applied Sciences ((COMPUTMETHODS,volume 40))

Abstract

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.

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Author information

Authors and Affiliations

  1. Numerische Methoden und Informationsverarbeitung, TU Dortmund, August-Schmidt-Str. 8, D-44227, Dortmund, Germany

    Franz-Joseph Barthold, Nikolai Gerzen & Wojciech Kijanski

  2. Department of Civil Engineering, Ostwestfalen-Lippe University of Applied Sciences, Emilienstrasse 45, D-32756, Detmold, Germany

    Daniel Materna

Authors
  1. Franz-Joseph Barthold
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  2. Nikolai Gerzen
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  3. Wojciech Kijanski
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  4. Daniel Materna
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Corresponding author

Correspondence to Franz-Joseph Barthold .

Editor information

Editors and Affiliations

  1. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Pekka Neittaanmäki

  2. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Sergey Repin

  3. Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland

    Tero Tuovinen

Appendix: MATLAB Source Code

Appendix: MATLAB Source Code

The appended Matlab source code contains two functions, i.e. plane_nl for the computation of the element matrices and Bmat for the B-matrices needed in structural analysis and sensitivity analysis, see Sect. 5 for detailed explanations.

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Barthold, FJ., Gerzen, N., Kijanski, W., Materna, D. (2016). Efficient Variational Design Sensitivity Analysis. In: Neittaanmäki, P., Repin, S., Tuovinen, T. (eds) Mathematical Modeling and Optimization of Complex Structures. Computational Methods in Applied Sciences, vol 40. Springer, Cham. https://doi.org/10.1007/978-3-319-23564-6_14

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  • DOI: https://doi.org/10.1007/978-3-319-23564-6_14

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-23563-9

  • Online ISBN: 978-3-319-23564-6

  • eBook Packages: EngineeringEngineering (R0)

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