The coupling of solids and shells by conjugate approximations


  • Mika Malinen CSC – IT Center for Science
  • Peter Råback CSC – IT Center for Science


mixed-dimensional coupling, shell, finite element, biorthogonal basis, tight coupling


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 solids
with 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 work
and does not depend on additional computational parameters, an augmentation of a potential-energy functional by introducing new unknowns, or computations over auxiliary meshes.

Suomen mekaniikkapäivien 2022 erikoisnumero




Malinen, M., & Råback, P. (2023). The coupling of solids and shells by conjugate approximations. Rakenteiden Mekaniikka, 55(4), 95–115.