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

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 formulation, the structure domain is overlapped by a refined solid model which is needed to either get more accuracy or to capture highly nonlinear events. 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.