"The art of structure is where to put the holes" Robert Le Ricolais,
1894-1977 This is a completely revised, updated and expanded version of
the book titled "Optimization of Structural Topology, Shape and
Material" (Bends0e 1995). The field has since then developed rapidly
with many new contributions to theory, computational methods and
applications. This has that a simple editing of Bends0e (1995) had to be
superseded by what meant is to a large extent a completely new book, now
by two authors. This work is an attempt to provide a unified
presentation of methods for the optimal design of topology, shape and
material for continuum and discrete structures. The emphasis is on the
now matured techniques for the topology design of continuum structures
and its many applications that have seen the light of the day since the
first monograph appeared. The technology is now well established and
designs obtained with the use of topology optimization methods are in
production on a daily basis. The efficient use of materials is important
in many different settings. The aerospace industry and the automotive
industry, for example, apply sizing and shape optimization to the design
of structures and mechanical elements.