The homogenization method for topology and shape optimization. Single and multiple loads case

Abstract

ABSTRACT This paper is devoted to an elementary introduction to the homogenization methods applied to topology and shape optimization of elastic structures under single and multiple external loads. The single load case, in the context of minimum compliance and weight design of elastic structures, has been fully described in its theoretical as well as its numerical aspects in [4]. It is here briefly recalled. In the more realistic context of “multiple loads”, i.e. when the structure is optimized with respect to more than one set of external forces, most of the obtained theoretical results remain true. However, the parameters that define optimal composite materials cannot be computed explicity. In this paper, a method to treat numerically the multiple loads case is proposed.