Multi-phase structural optimization of multi-layered composites and viscoelastic materials

Abstract : This work is devoted to the application of the level-set method for topology optimization to multi-phase design of multi-layered composites and viscoelastic structures. In the case of composite laminates, we study their optimal design by allowing a variable stacking sequence and in-plane shape of each ply. In order to optimize both variables we rely on a decomposition technique which aggregates the constraints into one unique constraint margin function. Thanks to this approach, a rigorous equivalent bi-level optimization problem is established. On the other hand, we consider the optimal design of viscoelastic vibration damping treatments. We prove a general result describing the complex frequencies of the underlying non-linear eigenvalue problem. In both cases every layer of the structure is represented as a bi-material structure where a level set method is used to characterize the interfaces meanwhile the shape evolution is driven by a Hadamard method for boundary variations using the shape gradient. Two numerical test-cases are exhibited: In the case of multi-layered laminates, we minimize the weight of the structure subjected to a compliance and a first buckling load constraint, meanwhile for viscoelastic treatments, we maximize the the structure capacity to dissipate energy measured via the loss factor.
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G Delgado, G. Allaire, M Hamdaoui. Multi-phase structural optimization of multi-layered composites and viscoelastic materials. XXV Congreso de Ecuaciones Diferenciales y Aplicaciones (CEDYA) + XV Congreso de Matemática Aplicada (CMA), Jun 2017, Carthagène, Spain. ⟨hal-01616471⟩

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