Revisited mixed-value method via symmetric BEM in the substructuring approach

Within the Symmetric Boundary Element Method, the mixed-value analysis is re-formulated. This analysis method contemplates the subdivision of the body into substructures having interface kinematical and mechanical quantities. For each substructure an elasticity equation, connecting weighted displacements and tractions to nodal displacements and forces of the same interface boundary and to external action vector, is introduced. The assembly of the substructures is performed through both the strong and weak regularity conditions of the displacements and tractions. We obtain the solving equations where the compatibility and the equilibrium are guaranteed in the domain Ω for the use of the fundamental solution and at the interface nodes for the strong regularity conditions imposed, whereas the previous quantities are respected in weighted form along the interface boundaries. The mixed-value method leads to a better solution than those obtained through the displacement method of the Symmetric Boundary Element Method, if compared with the analytical solution. By using the Karnak.sGbem program, developed with other researchers and updated through the implementation of the present method, some examples are made which show the advantages related to the computational aspects and to the convergence of the numerical response.