Topology and Shape Optimization Procedures Using Hole Positioning Criteria

Theory and Applications
  • H. A. Eschenauer
  • A. Schumacher
Part of the International Centre for Mechanical Sciences book series (CISM, volume 374)


The topology of any constructions, i.e., the position and arrangement of structural elements in a given design space, has strong influence on its structural behaviour. Currently, the topology is still chosen intuitively or by referring to existing constructions (“Current Design World State”), or it is selected from a number of different variants. The topology optimization aims at the use of mathematical-mechanical strategies in a design process.

The present paper addresses a simultaneous method of topology and shape optimization, called Bubble-Method. Its basic idea is the iterative positioning of new holes into a given design domain. The essential task of this method is a problem-dependent finding of an optimal position vector for a hole that is to be inserted into a body. The criteria required for this purpose are derived from a general optimization problem. The positioning criteria are determined from so-called characteristic functions described by stresses, strains, and displacements. The characteristic functions depend on special optimization functionals and the shape of the hole.

In the final sub-chapter a number of application examples are shown, among others a panel truss structure for a radio telescope, a casing of a handsaw grip, and a wing rib of an airplane.


Design Variable Topology Optimization Load Case Circular Hole Elliptical Hole 
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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© Springer-Verlag Wien 1997

Authors and Affiliations

  • H. A. Eschenauer
    • 1
  • A. Schumacher
    • 1
  1. 1.University of SiegenSiegenGermany

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