PGD and Separated Space Variables Representation for Linear Elasticity in Plate Domains

Brice Bognet (1) , Adrien Leygue (1) , Francisco Chinesta (1) , Arnaud Poitou (1)

1 GeM - Institut de Recherche en Génie Civil et Mécanique

In this paper, we focus on the simulation of linear elastic behaviour of plates using a 3D approach which numerical cost only scales like a 2D one. In the case of plates, the kinematic hypothesis introduced in plate theories to go from 3D to 2D is usually unsatisfactory where one cannot rely on St Venant’s principle (usually close to the plate edges). We propose to apply the PGD (Proper Generalized Decomposition) method [1] to the simulation of the linear elastic behavior of plates. This method allows us to separately search for the in‐plane and the out‐of plane contributions to the 3D solution, yielding significant savings in computational cost. The method is validated on a simple case and its full potential is then presented for the simulation of the behavior of laminated composite plates.

Mots clés: Linear elasticity; Model reduction; PGD; Plate domains

Domaines: Mécanique [physics.med-ph]; Matériaux

Brice Bognet, Adrien Leygue, Francisco Chinesta, Arnaud Poitou. PGD and Separated Space Variables Representation for Linear Elasticity in Plate Domains. AMPT (Advances in Material Processing Technologies) 2010, 2010, Paris, France. ⟨10.1063/1.3552441⟩. ⟨hal-01008654⟩