Material interpolation schemes in topology optimization

被引:2192
作者
Bendsoe, MP [1 ]
Sigmund, O
机构
[1] Tech Univ Denmark, Dept Math, DK-2800 Lyngby, Denmark
[2] Tech Univ Denmark, Dept Solid Mech, DK-2800 Lyngby, Denmark
关键词
topology optimization; multi-material designs; effective property; interpolation scheme; micro-mechanics;
D O I
10.1007/s004190050248
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
In topology optimization of structures, materials and mechanisms, parametrization of geometry is often performed by a grey-scale density-like interpolation function. In this paper we analyze and compare the various approaches to this concept in the light of variational bounds on effective properties of composite materials. This allows us to derive simple necessary conditions for the possible realization of grey-scale via composites, leading to a physical interpretation of all feasible designs as well as the optimal design. Thus it is shown that the so-called artificial interpolation model in many circumstances actually falls within the framework of microstructurally based models. Single material and multi-material structural design in elasticity as well as in multi-physics problems is discussed.
引用
收藏
页码:635 / 654
页数:20
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