Design of architectured sandwich core materials using topological optimization methods
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1188-LL05-02
Design of architectured sandwich core materials using topological optimization methods Laurent Laszczyk1, Rémy Dendievel1, Olivier Bouaziz2, Yves Bréchet1 and Guillaume Parry1 1 SIMAP, Grenoble INP, CNRS, UJF, 101 rue de la physique BP46, 38402 St-Martin-d'Hères Cedex, France 2 ArcelorMittal Research. Voie Romaine BP30320, 57283 Maizières-lès-Metz Cedex, France ABSTRACT Sandwich structures are especially interesting when multiple functionalities (such as stiffness and thermal insulation) are required. Properties of these structures are strongly dependent on the general geometry of the sandwich, but also on the detailed patterns of matter partitioning within the core. Therefore it seems possible to tailor the core pattern in order to obtain the desired properties. But multi-functional specifications and the infinite number of possible shapes, leads to non-trivial selection and/or optimization problems. In this context of "material by design", we propose a numerical approach, based on structural optimization techniques, to find the core pattern that leads to the best performances for a given set of conflicting specifications. The distribution of matter is defined thanks to a level-set function, and the convergence toward the optimized pattern is performed through the evolution of this function on a fixed grid. It is shown that the solutions of optimization are strongly dependent on the formulation of the problem, which have to be chosen with respect to the physics. A first application of this approach is presented for the design of sandwich core materials, in order to obtain the best compromise between flexural stiffness and relative density. The influence of both the initialization (starting geometry) and the formulation of the optimization problem are detailed. INTRODUCTION Specifications in automotive industries are more and more complex in the way that multi-functional performances (such as stiffness, thermal and acoustic insulation) are required while keeping the weight as low as possible. Composite and architectured materials often give efficient solutions. Recently, numerous techniques have been developed for manufacturing lightweight structures like graded metal foams [1], hollow spheres and trusses [2,3], corrugated structures, honeycombs and other cellular solids [4]. In a "material by design" approach [5], finding the cellular architecture that combines in the most efficient way a given set of conflicting properties is the key issue. In this regard, shape optimization techniques can enlarge the degrees of freedom on the geometry. In this paper, topological optimization is applied to periodically architectured flexural panels. Before any comparison or optimization, it is necessary to define a way to measure the performances of those panels. In a first part, a determination method of the effective properties is presented on three test architectures. Then, a validation of these effective properties is numerically done on a four-point bending test. The bending stiffness of the homogeneous effectiv
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