Séminaire de Patrice Cartraud (Univ. Nantes)

Asymptotic analysis of heterogeneous beams
Patrice Cartraud, Nantes Université, Centrale Nantes, GeM - Institut de Recherche en Génie Civil et Mécanique, UMR CNRS 6183

Many engineering structures are slender and heterogeneous. Their analysis by 3D finite element models generates prohibitive computation times. It is therefore appealing to propose simplified 1D models, such as beams, taking into account that one dimension of the structure, its length, is large compared to the other two, which correspond to the dimensions of the cross-section. Many approaches have been proposed in the literature to derive a beam model. After reviewing them, we will focus on the asymptotic expansion method. With this method the solution is searched under the form of an expansion in increasing powers of a small parameter corresponding to the inverse of the slenderness ratio. General principles and numerical implementation of this method will be presented. The method will be illustrated through various examples, from an elastic sandwich beam to a non-linear elastic submarine power cable used for off-shore wind turbine.

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