ABSTRACT
Topology optimization of continuous structures can be divided into two fields departing from two different settings. The first field can be viewed as numerical modeling of the multi-material optimization problems based upon the relaxed formulations in which the merit functions are constructed by the direct methods of calculus of variations. The method of relaxation by homogenization is the most important approach, linked with the theory of composite media. This approach was originated in mathematical papers in 70’s in the context of the scalar conductivity problem and then applied to the vectorial problems of 2D and 3D elasticity, see Cherkaev (2000) and Allaire (2002). The first results on Kirchhoff plates were already found by Gibiansky & Cherkaev in 1984. In the first field of topology optimization the design variables are associated with the underlying microstructure. In the most simple numerical approaches like SIMP the density of the one material is the only design variable. Penalization of intermediate density values leads to the practical designs that can be further manufactured. This field of topology optimization has been presented in Chapters 1, 2 and 5 of Bendsøe (1995).
