A variational approach for coupling kinematically incompatible structural models

In this work an extended variational framework aimed at properly addressing the coupling of kinematically incompatible structural models is presented. The main goal is to variationally state the theoretical bases to deal with the coupling of structural models with different dimensionality. In this approach, the coupling conditions are naturally derived from the governing variational principle formulated at the continuous level. Furthermore, by means of a real parameter γγ we manage to build different continuous mechanical models that have different mechanical and mathematical features. In particular, the coupling of 3D solid models and 2D shell models, under Naghdi hypothesis, is treated by introducing the corresponding kinematical assumptions into the proposed extended variational principle. Also, the coupling between 3D solid and 1D beam models, under Bernoulli hypothesis, is presented. Moreover, for the continuous 3D–2D coupled problem a numerical approximation is addressed via the finite element method and some numerical results are given, comparing the responses of the system when the discrete model varies by changing the value of the parameter γγ. Finally, a discussion comprising the main conclusions of the work is given.