Nitsche's method method for mixed dimensional analysis: conforming and non-conforming continuum-beam and continuum-plate coupling

Vinh Phu Nguyen (1) , Pierre Kerfriden (1) , Susanne Claus (2) , Stephane Pierre-Alain Bordas (3)

1 School of Engineering [Cardiff]
2 UCL Department of Mathematics
3 IMAM - Institute of Mechanics and Advanced Materials

A Nitche's method is presented to couple different mechanical models. They include coupling of a solid and a beam and of a solid and a plate. Both conforming and non-conforming formulations are presented. In a non-conforming for- mulation, the structure domain is overlapped by a refined solid model. Applications can be found in multi-dimensional analyses in which parts of a structure are modeled with solid elements and others are modeled using a coarser model with beam and/or plate elements. Discretisations are performed using both standard Lagrange elements and high order NURBS (Non Uniform Rational Bsplines) based isogeometric elements. We present various examples to demonstrate the performance of the method.

Mots clés: Nitsche; mixed dimensional analysis (MDA); isogeometric analysis (IGA); NURBS; beam; plate

Domaines: Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Vinh Phu Nguyen, Pierre Kerfriden, Susanne Claus, Stephane Pierre-Alain Bordas. Nitsche's method method for mixed dimensional analysis: conforming and non-conforming continuum-beam and continuum-plate coupling. 2013. ⟨hal-00857372⟩