Mixed finite element formulation based on the discontinuous stress approximation

The paper is devoted to the development of the mixed form of finite element method for the calculation of constructions and structures. We consider the approach based on the approximation of discontinuous stress fields and the use of the penalty function method to satisfy the equilibrium equations. It is shown that the continuity of both normal and tangential stresses only on the adjacent sides of the finite elements contributes to the expansion of the class of statically admissible stress fields. At the same time, the consistent approximation is provided, both of the main part of the functional of additional energy, and its penalty part. Using the given approach, solutions of some problems were obtained and analyzed, in particular, the calculation of the cantilever beam-wall. The results obtained were compared with the decisions on the FEM in displacements and stresses, as well as with the exact solutions. It is shown that solutions based on the approximation of discontinuous stress fields in mixed form FEM converge to exact values from below and are more flexible in comparison with the solutions obtained by FEM in displacements. In addition, the accuracy of determining stresses is higher here.