### Optimization and Systems Theory Seminar

Friday, February 28, 2003, 11.00-12.00, Room 3721, Lindstedtsv. 25

**Mathias Stolpe**

Division of Optimization and Systems Theory

Department of Mathematics

KTH

E-mail: stolpe@math.kth.se

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Topology optimization of continuum structures

This talk gives an overview of the results presented in the last three
papers included in my thesis. To begin with, an introduction to
topology optimization of discretized continuum structures in linear
elasticity is given.
Thereafter, we study a common heuristic method for solving minimum
compliance (maximum stiffness) problems. These problems are usually
modeled as mixed or pure nonlinear 0-1 programs. Since the number of
binary variables needs to be large, solving these nonlinear 0-1
programs becomes a major challenge. A way to find feasible or almost
feasible solutions is to use material interpolation models. In this
approach the the binary constraints are relaxed and the material
behavior is modeled using a nonlinear function. The resulting
nonlinear program is then solved using standard optimization
techniques. The basic idea with this approach is that variables with
non-integer values will have little influence on the stiffness of the
structure compared to the volume which is occupied, thus steering the
variables to become either zero or one.

Finally, it is shown that a broad range of nonlinear 0-1 topology
optimization problems, including stress- and displacement-constrained
minimum weight problems, can equivalently be modeled as linear mixed
0-1 programs. This result implies that any of the standard methods
available for general linear integer programming can now be used on
topology optimization problems.

Calendar of seminars

*Last update: February 19, 2003 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*