Computational simulation is a highly reliable tool used to solve structural analysis problems. In recent times, several techniques have been developed in the field of computational mechanics in order to analyze non-linearities in less time, helping decision-making when structures suffer damage. The global–local analysis is a technique to increase the efficiency of computational simulations by using a global model to obtain boundary conditions in a coupling zone imposed on a local model. Coupling can be performed through the primal–dual method, which is used for crack propagation using 2D and 3D models with fine meshes, thus saving computational time. However, it has not been implemented at a commercial level to analyze large structures such as multi-story buildings with focused non-linearities. In this work, a global–local analysis with non-intrusive methodology and simplified models was implemented in a cracked framed structure, using a 1D (global) and 3D (local) coupling considering crack propagation with primal–dual interface conditions. Different lengths of the local model were analyzed, studying their influence on the convergence of the problem, and compared with a 3D monolithic model to check the reliability of the results. The results show that the proposed methodology solves the problem with an error less than 10%. Furthermore, it was determined that the dimensions of the local model affect the convergence of the problem. This work also provides an implementation of the method for large structures containing focused non-linearities and using commercial software, reducing computational time for the cracked structural analysis.

Reducing the time spent on computational simulations is an active area in solid mechanics, and efforts are being made to implement novel techniques and apply them to time-sensitive areas in the industry and research. One of these techniques is called global–local non-intrusive analysis, a methodology that enriches a local patch model using 3D elements with non-linear behavior (such as crack propagation), coupled with a linear, global 1D frame model that solves iteratively, thereby reducing overall times compared to a monolithic solution. However, engineers do not know the length of the local model (also known as the patch model) to be considered, which affects the convergence, computational time, and overall quality of the solution. Therefore, this study considered the use of categorical analyses for performing linear and quadratic discriminant solvers for a given set of simple cases with symmetric crack propagation within the local model and defining the convergence boundary with a certain probability of a successful convergence. In addition, a practical case was analyzed for different lengths of the local model, giving strong correlations to the results of the discriminant analysis. The solution of all the cases was also analyzed, considering the number of degrees of freedom, computational times, and the number of iterations for convergence. This aimed to establish a functional relation for engineering practice, enabling the determination of a suitable patch length for performing global–local non-intrusive analysis with crack propagation in doubly symmetric steel sections.

Global-local non-intrusive coupling is a well-established strategy for the analysis of structures with localised non-linear behaviour, but its practical applicability is limited by the requirement that the local patch coincides with a node of the global mesh. This work proposes a three-level non-intrusive global-local coupling strategy in which an intermediate 1D beam model is inserted between the global and the local domains, restoring full freedom in the placement of the local patch without modifying the global model. The formulation transfers displacements and reactions between two non-coincident interfaces through explicit projection operators, and the additional level introduces only three beam elements and four nodes per coupling region. The methodology is validated on a cantilever beam (linear, notched and crack-propagation variants) and on a three-storey framed structure with X-FEM crack propagation, against a monolithic 3D reference and against the standard matching-interface global-local method. For the framed structure, the non-matching scheme reduces the total degrees of freedom by 97.46% with respect to the monolithic solution and cuts the computation time by 68.19%, compared to 53.86% for the matching-interface version. Displacement errors remain below 10% and iteration counts drop by up to one third with respect to the matching scheme. The proposed formulation is therefore accurate, computationally efficient, and geometrically flexible in scenarios where the global model cannot be modified.