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Shape optimization and homogenization based approach in material optimization. (English) Zbl 0895.73048
Cioranescu, Doina (ed.) et al., Homogenization and applications to material sciences. Proceedings of the international conference, Nice, France, June 6–10, 1995. Tokyo: Gakkotosho. GAKUTO Int. Ser., Math. Sci. Appl. 9, 171-180 (1995).
Summary: This contribution is concerned with the approximation of problems that arise from relaxation of optimum material layout problems. The approach presented uses inner approximations of the $$G_\theta$$ closure sets both spatially (piecewise constant coefficients) and in the range of eigenvalues (due to a restriction of admissible microstructures). A numerical example with a non-compliance functional is presented.
For the entire collection see [Zbl 0873.00028].
##### MSC:
 74P99 Optimization problems in solid mechanics 74E05 Inhomogeneity in solid mechanics 35B27 Homogenization in context of PDEs; PDEs in media with periodic structure