Parametric, reduced and multi-scale model for interactive optimization of composite structures.

Summary Designing a composite structure is a major challenge: while an engineer designing a mechanical product based on metallic material is mainly focused on developing a shape that will guarantee a specific behavior, the engineer for whom the design problem is that of a product based on composite materials must find the best shape - material structure combination. Thus, he must also simultaneously design a material and the product topology. The combinatorics are complex and the solution spaces are very large. CAD and finite element simulation tools do not provide the designer with an approach to explore the search spaces interactively and quickly. The thesis work leads to a new numerical approach to manipulate each design parameter characterizing a composite structure, regardless of the scale at which it is relevant.First, the Parametric and Reduced Behavior Model (PRBM) is a so-called separate model. It allows:1- a multi-scale approach: the mechanical parameters of the structure are explicitly described as coming from the material quality of each fiber, the matrix, each layer and the topology of the laminate itself,2- a multi-physics approach: independently the mechanical behavior of each layer and each interface is processed to give rise to the behavior of the laminate. Static and dynamic behavior situations are studied. In the case of dynamic behavior, the viscoelastic character became a conceptual issue.Secondly, a method mixing non-integer derivatives and use of the PGD method allowed the realization of the PRBM. Integrated in a Parametric Knowledge Model (PKM) with expert knowledge models, it is the basis of an interactive design support method.The PKM is processed by an evolutionary optimization method. The PKM is processed by an evolutionary optimization method. As a result, the designer can interactively explore the design spaces. To qualify our models and our PRBM, we study 2 design problems of laminated structures. The determined solutions are qualified against finite element simulations or according to an empirical approach.