On the essential mechanical boundary conditions in two-field finite element approximations

Abstract

Abstract In this paper relatively well-known two-field (mixed) finite element approximations in the mechanics of solids are studied. However, in the proposed approach a significant novelty (in the finite element area) is introduced — the treatment of the boundary traction constraints as essential boundary conditions. It should be noted that multifield approximations are in no way limited to the realm of classical elasticity. However, for convenience, the linear elastic domain will be considered, where the comparable analytical solutions are available.