Detection of Irregular Flaws in 2D Domains Using Extended Finite Element Method and Metaheuristics Algorithms, GA and GWO

Today, one of the important issues in the industry is the failure of parts due to the presence of holes or cracks. Among the numerical calculation tools, the classical and extended finite element method is known as the most useful numerical tools in solving engineering science problems. Identifying and investigating the types of cracks, flaws and cavities in structures is one of the most challenging issues in the field of engineering. In this article, the crack detection of two-dimensional (2D) structures using the extended finite element method (XFEM) along with genetic algorithm(GA) and grey wolf optimization method (GWO) to detect the existing crack and flaws by minimizing an error function which is also called as objective function that the evaluation of it, is based on difference between sensor measurements and suggested structure responses in each try of the algorithm.  Damage detecting in 2D domains, as a non-destructive evaluation problem, is investigated using the extended finite element method along with the optimization method of genetic algorithm and grey wolf. The extended finite element method has been used to model the structure containing cracks and holes in the abaqus program, and genetic optimization and grey wolf method have been used to determine the location of the damage in which the codes were in matlab program. The extended finite element method is a powerful tool for the analysis of structures containing cracks without remeshing and is therefore suitable for an iterative process in structural analysis. Also, in these problems, due to the wide range of parameters, it is not logical and rational to use mathematical methods. For this reason, meta heuristic methods have been developed, and grey wolf optimization methods and genetic algorithm are among these common non-gradient methods that are suitable for solving the inverse problem. This problem is set so that the optimizer algorithm finds the existing crack coordinates or holes coordinates by minimizing an objective function based on the values measured by the sensors installed on the structure. Among the limitations of the classical finite element method in the investigation of various problems in the field of fault and crack detection, we can point out the dependence of the crack or cavity on the finite element mesh, re-meshing and in other special cases the use of singular elements, which are completely removed by using The extended finite element. In this research, in order to identify the damage, the genetic optimization algorithm and the gray wolf have been used. These algorithms are designed in such a way to determine the characteristics of the damage by minimizing an error function. The defined error function is defined as the difference between the response obtained from the algorithm analysis and the response recorded in the main structure modeled in ABAQUS software, at the location of the sensors. Finally, three reference numerical examples have been solved to evaluate the capability and accuracy of the proposed method, and the result of the results shows a reduction in the cost of solving and an increase in the accuracy of the results.