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In the context of shape optimization, we seek minimizers of the sum of the elastic compliance and of the weight of a solid structure under specified loading. This problem is known not to be well-posed, and a relaxed formulation is introduced. Its effect is to allow for microperforated composites as admissible designs. In a two-dimensional setting the(More)
(Reçu le jour mois année, accepté après révision le jour mois année) Abstract. We study a level-set method for numerical shape optimization of elastic structures. Our approach combines the level-set algorithm of Osher and Sethian with the classical shape gradient. Although this method is not specifically designed for topology optimization, it can easily(More)
We extend the level-set method for shape and topology optimization to new objective functions such as eigenfrequencies and multiple loads. This method is based on a combination of the classical shape derivative and of the Osher-Sethian level-set algorithm for front propagation. In two and three space dimensions we maximize the first eigenfrequency or we(More)
This paper proposes a few steps to escape structured extensive representations for objects, in the context of evolutionary Topological Optimum Design (TOD) problems: early results have demonstrated the potential power of Evolutionary methods to find numerical solutions to yet unsolved TOD problems, but those approaches were limited because the complexity of(More)
We present a numerical implementation of the Francfort-Marigo model of damage evolution in brittle materials. This quasi-static model is based, at each time step, on the minimization of a total energy which is the sum of an elastic energy and a Griffith-type dissipated energy. Such a minimization is carried over all geometric mixtures of the two, healthy(More)
This paper is devoted to an elementary introduction to the homogenization method 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(More)
A numerical coupling of two recent methods in shape and topology optimization of structures is proposed. On the one hand, the level set method, based on the classical shape derivative, is known to easily handle boundary propagation with topological changes. However, in practice it does not allow for the nucleation of new holes (at least in 2-d). On the(More)
This paper is devoted to minimum stress design in structural optimization. The homogenization method is extended to such a framework and yields an efficient numerical algorithm for topology optimization. The main idea is to use a partial relaxation of the problem obtained by introducing special microstructures which are sequential laminated composites.(More)
The aim of this paper is to propose a new regularized optimal control formulation for recovering an extended inclusion from boundary measurements. Our approach provides an optimal representation of the shape of the inclusion. It guarantees local Lipschitz stability for the reconstruction problem. Some numerical experiments are performed to demonstrate the(More)