Topology Optimization of Discrete Structures

An Introduction in View of Computational and Nonsmooth Aspects
  • W. Achtziger
Part of the International Centre for Mechanical Sciences book series (CISM, volume 374)


We discuss standard problems of topology optimization of discrete structures. This paper is an attempt to provide an (almost) self-contained introduction and stresses the techniques of reformulating problems and mathematical tools needed for a successful numerical treatment.

First, relations between several classical formulations of single load problems are shown in order to illustrate the mathematical techniques used, such as minimax-Theorems, duality etc. Numerical approaches are discussed. The outlined concept is then generalized to the multiple load case where minimization of compliance in the sense of worst case design is considered. We end up with displacement based nonsmooth optimization formulations. In the fourth section the problem of simultaneous optimization of topology and geometry is considered. We illustrate its mathematical treatment as a bilevel problem which again uses nonsmooth optimization. In each section a few numerical examples show the applicability of the proposed approaches.

Since nonsmooth analysis is non-standard in structural optimization, we close with a short introduction to important terms up to the concept of an algorithm.


Topology Optimization Nodal Point Load Case Nonsmooth Optimization Bilevel Problem 


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Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • W. Achtziger
    • 1
  1. 1.University of Erlangen-NurembergErlangenGermany

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