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.

This study explores a global–local non-intrusive computational strategy to address problems in computational mechanics, specifically applied to a double cantilever beam (DCB) with cohesive interfaces. The method aims to reduce computational requirements while maintaining accuracy. The DCB, representing two plates connected by a cohesive zone simulating delamination, was modeled with a 3D representation using the cohesive zone method for crack propagation. Different mesh configurations were tested to evaluate the strategy’s effectiveness. The results showed that the global–local strategy successfully provided solutions that were comparable to monolithic models. Mesh size had a significant impact on the results, but even with a simplified local model that did not fully represent the plate thickness, the structural deformation and crack displacement were accurately captured. The interface near the study area influenced the stress distribution. Although effective, the strategy requires careful mesh selection due to its sensitivity to mesh size. Future research could optimize mesh configurations, expand the strategy to other structures, and explore the use of orthotropic materials. This research introduces a computational approach that reduces costs while simulating delamination and crack propagation, highlighting the importance of mesh configuration for real-world applications.

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.

Unsupervised feature selection (UFS) has received great interest in various areas of research that require dimensionality reduction, including machine learning, data mining, and statistical analysis. However, UFS algorithms are known to perform poorly on datasets with missing data, exhibiting a significant computational load and learning bias. In this work, we propose a novel and robust UFS method, designated PFA-Nipals, that works with missing data without the need for deletion or imputation. This is achieved by considering an iterative nonlinear estimation of principal components by partial least squares, while the relevant features are selected through minibatch K-means clustering. The proposed method is successfully applied to select the relevant features of a robust health dataset with missing data, outperforming other UFS methods in terms of computational load and learning bias. Furthermore, the proposed method is capable of finding a consistent set of relevant features without biasing the explained variability, even under increasing missing data. Finally, it is expected that the proposed method could be used in several areas, such as machine learning and big data with applications in different areas of the medical and engineering sciences.