Adaptive anisotropic integration scheme for high-order fictitious domain methods: Application to thin structures

Grégory Legrain (1, 2) , Nicolas Moes (2)

1 ECN - École Centrale de Nantes
2 GeM - Institut de Recherche en Génie Civil et Mécanique

A novel integration scheme is proposed for fictitious domain finite element methods. It relies on the use of a surface tracking strategy based on anisotropic mesh adaptation. Thanks to an error estimator, the method builds iteratively an adapted anisotropic mesh which is refined near the geometrical interface, and elongated in the direction of small curvature. This strategy allows to decrease the integration cost which can be problematic for high order fictitious domain methods. In addition, it opens the possibility for the creation of unfitted solid shell strategies that can be used for the treatment of thin structures. Numerical studies show that the method leads to promising results for both integration cost and behaviour with respect to locking.

Mots clés: X-FEM; high-order; fictitious domain; anisotropic meshing; solid-shell; shell; plates; beams

Domaines: Mécanique des structures [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]; Thermique [physics.class-ph]

Grégory Legrain, Nicolas Moes. Adaptive anisotropic integration scheme for high-order fictitious domain methods: Application to thin structures . International Journal for Numerical Methods in Engineering, 2018, 114 (8), pp.882-904. ⟨10.1002/nme.5769⟩. ⟨hal-01682264⟩