Generalized Shape optimization based on the Level Set method
Abstract
This paper describes a first step work devoted to applying XFEM and Level Sets methods in opti-
mization of structures. This first step work is based on integrating an existing XFEM code within a
general open optimization tool, SAMCEF BOSS QUATTRO. Unlike most of the existing works, this
approach is more shape optimization oriented. A library of pre-formatted basic geometric entities (such
as ellipses, squares, triangles, etc.) described by Level Sets functions are used. These basic Level Set
features can be combined to represent many kinds of interfaces and holes. The construction parameters
of the basic Level Sets are considered as the design variables. In order to evaluate the sensitivities, a
finite difference scheme over the design variables is used in this first work. Different mechanical responses
(energy, weight, displacement, . . .) can be considered as objective functions or constraints in the problem
formulation. Several academic 2D test cases of shape and topology optimization are presented within
the XFEM and Level Set approach. In addition, a work by Missoum et al. [11], in which the shape and
topology optimization of the structure is carried out by an optimal selection of holes characteristics with
a genetic algorithm is presented.
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