The coupling of solids and shells by conjugate approximations

In order to get detailed information about deformations of structures efficiently, it may be necessary to use finite element models which combine three-dimensional discretizations of solidswith approximations of two-dimensional models for shells. Here we show how the idea of conjugate approximations can be used as a means to obtain a formulation of mixed-dimensional coupling between shells and solids. Our method is consistent with respect to the principle of virtual workand does not depend on additional computational parameters, an augmentation of a potential-energy functional by introducing new unknowns, or computations over auxiliary meshes.