Extension of the variational theory of complex rays to orthotropic shallow shell structures

Alessandro Cattabiani (1) , Andrea Barbarulo (2) , Hervé Riou (1) , Pierre Ladevèze (1)

1 LMT - Laboratoire de Mécanique et Technologie
2 MSSMat - Laboratoire de mécanique des sols, structures et matériaux

Nowadays, the interest of aerospace and automotive industries on virtual testing of medium-frequency vibrational behavior of shallow shell structures is growing. The development of software capable of predicting the vibrational response in such frequency range is still an open question because classical methods (i.e., FEM, SEA) are not fully suitable for the medium-frequency bandwidth. In this context the Variational Theory of Complex Rays (VTCR) is taking place as an ad-hoc technique to address medium-frequency problems. It is a Trefftz method based on a weak variational formulation. It allows great flexibility because any shape function that satisfies the governing equations can be used. This work further develops such theory. In particular, orthotropic materials are introduced in the VTCR formulation for shallow shell structures. A significant numerical example is proposed to show the strategy.

Mots clés: VTCR; medium-frequency; orthotropic materials; shallow shells

Domaines: Mécanique des structures [physics.class-ph]; Analyse numérique [math.NA]

Alessandro Cattabiani, Andrea Barbarulo, Hervé Riou, Pierre Ladevèze. Extension of the variational theory of complex rays to orthotropic shallow shell structures. Advances in Aircraft and Spacecraft Science, 2016, 3 (3), pp.317-330. ⟨10.12989/aas.2016.3.3.317⟩. ⟨hal-01647841⟩