Topology optimization by a neighbourhood search method based on efficient sensitivity calculations
Krister Svanberg and Mats Werme
Optimization and Systems Theory, Royal Institute of
Technology (KTH), Stockholm, Sweden
ABSTRACT:
This paper deals with topology optimization of discretized
load-carrying continuum structures, where the design of the structure
is represented by binary design variables indicating material or void
in the various finite elements. Efficient exact methods for discrete
sensitivity calculations are developed. They utilize the fact that if
just one or two binary variables are changed to their opposite binary
values then the new stiffness matrix is essentially just a low-rank
modification of the old stiffness matrix, even if some nodes in the
structure may disappear or re-enter. As an application of these
efficient sensitivity calculations, a new neighbourhood search method
is presented, implemented, and applied on some test problems, one of
them with 6912 nine-node finite elements where the von Mises stress in
each non-void element is considered.