Discriminant Analysis Based on the Patch Length and Crack Depth to Determine the Convergence of Global–Local Non-Intrusive Analysis with 1D-to-3D Coupling

Abstract

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.