3D global-local analysis using mesh superposition method

One of the main issue in a FEM analysis is to determine and minimizing discretization errors. This kind of errors assume a critical importance especially where the solution, in terms of displacement and stress, quickly changes inside the finite element. This issue can be overcame adopting a very refined element discretization in those regions. Hence, for this kind of simulations, it is common practice to use global-local methods rather than adopt a refined discretization over the entire domain. Indeed, global-local methods allow to define very refined elements distributions in some regions of interest, which can be coupled with coarser element distributions in the rest of the domain. A global-local approach based on the superposition technique is presented in this work. This approach allows the coupling of two different meshed domain by superimposing the refined local mesh on the global mesh for the region of interest. The coupling takes place without introducing multi-point constraints or transition regions; the mesh continuity and the well-conditioning of the stiffness matrix are satisfied by appropriate boundary conditions. This approach allows to obtain accurate solutions in the areas of interest while keeping the computational time within satisfactory limits. Several numerical applications are presented which allow to assess the effectiveness of the proposed approach for 3D linear static simulations.