Finite element approximation for optimal shape, material and topology design. (English) Zbl 0845.73001

Haslinger, J.; Neittaanmaki, P.

Chichester: Wiley. xiii, 423 p. (1996).

[See the review of the first ed. (1988; Zbl 0713.73062).]
In the second, revised and extended edition, chapters 11,12,13 are completely new. In chapter 11 we show how the tools of classical shape optimization combined with the homogenization approach can be used for the designing of new material properties. This approach also seems to be useful for the numerical study of the so-called \(G\)-closure of a system of elliptic operators.
Chapter 12 deals with the topology design of an elastic sheet unilaterally supported by a rigid foundation. Topology optimization is considered as a special case of sheet thickness optimization.
Finally, in chapter 13 a new technique for the numerical realization of a class of optimal shape design problems is developed. In contrast to the classical boundary variation technique, this new one, called the fictitious domain approach, enables us to perform all the computations in a fixed simple shape domain, without regriding the finite element mesh.

MSC:

74-02	Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74S05	Finite element methods applied to problems in solid mechanics
74P99	Optimization problems in solid mechanics

Keywords:

topology design of elastic sheet; homogenization; \(G\)-closure; system of elliptic operators; sheet thickness optimization; fictitious domain approach