Applications of Topology Optimization Techniques in Seismic Design of Structure - Structural Seismic Design Optimization and Earthquake Engineering - page 233

Figure 1. The three levels of structural optimization: top) sizing optimization; middle) shape optimiza-
tion; bottom) topology optimization

are known and it is desired to find the optimum
dimensions. On another level, one can choose
the design variables to control the shape of the
boundaries of the members. Such selection will
lead to shape optimization . If the overall layout
of the members is known and it is already decided
where to put each member, in order to find the
best shapes of the members, one can use shape
optimization. In order to optimize the topology,
connectivity, or layout of a system, topology
optimization techniques should be used. In topol-
ogy optimization the design variables control the
topology and connectivity of the design. Figure
1 schematically illustrates these three categories
of structural optimization.
Starting from topology optimization and feed-
ing the results to shape and sizing optimization
routines will generally result in far greater savings
than merely using shape and sizing optimization.
Topology optimization techniques can thus be
considered as important and powerful tools in
hand of design engineers.
In this chapter we review the application of to-
pology optimization techniques in seismic design
of structures. We start with a brief review of the

history of topology optimization. Then we focus
on two general optimization problems in seismic
design of structures, the eigenvalue optimization
problem and the problem of maximizing the en-
ergy absorption.

2. TOPOLOGY OPTIMIZATION

Initially addressed by Culmann (1866), the lay-
out optimization problem is not quite new. The
interesting work of Michell (1904) laid down the
principles of topology optimization of structures
more than a century ago. After that, the field re-
mained untouched for nearly seven decades until
Prager and Rozvany improved and generalized the
Michell's theory (e.g. refer to Prager 1969, 1974
and Rozvany 1972a,b). Yet the field didn't attract
much attention until Bendsøe and Kikuchi (1988)
proposed a finite element-based numerical method
for topology optimization of continuum structures.
Usually referred to as the homogenization method ,
this approach soon became a basis upon which
other topology optimization techniques have been
developed.