Damage detection of 2D elastic continuum structures incorporating finite cell method and particle swarm optimization

There are many factors causing damages to a structure, including earthquakes, winds, environmental effects, etc. In order to repair a damaged structure, first its damage locations should be identified. Therefore, the damage identification of structures is considered as an important issue in civil engineering as well as mechanical engineering. Many methodologies have been devised for damage identification of structures, which are generally categorized to destructive and non-destructive cases. As a non-destructive damage identification approach, solving inverse problems for identifying the properties of a damaged structure is one of the popular methods which utilizes an optimization algorithm to minimize an error function in terms of measured strains or displacements. Since an iterative procedure with significant number of structural analyses should be carried out for the optimization process, an efficient numerical method should be employed to reduce the total computational cost. In this paper, the identification of hole in two-dimensional continuum structures is investigated with finite cell method and particle swarm optimization algorithm. The finite cell method is an efficient numerical method for solving the governing equations of continuum structures having geometrical complexity and/or discontinuities, which uses the concept of virtual domain method. The use of this concept makes the mesh generation easier such that the simple structured meshes can be utilized even for the curved boundaries of a structure, and hence mesh refinement is not necessary for the problems like damage detection. The finite cell method uses adaptive numerical integration for the cells including non-uniform material distribution. Accordingly, quadtree integration is utilized for the structural analysis using the finite cell method. Consequently, the computational time is significantly reduced. On the other hand, particle swarm optimization is a well-known meta-heuristic algorithm, and hence it does not require the gradient information of the problem. This population-based algorithm has been inspired by the social behaviour of animals such as fish schooling and birds flocking. The basis of this algorithm relies on the social influence and learning which enable individuals to preserve cognitive consistency. Thus, the exchange of ideas and interactions between individuals can lead them to solve optimization problems like damage detection. This study proposes the finite cell method and particle swarm optimization algorithm for damage detection of plate structures with single hole or multiple holes. As a non-gradient-based method, particle swarm optimization explores the search space to find the coordinates of the existing damage by minimizing an error function. This error function is evaluated by the strains or displacements calculated by the structural analysis utilizing the finite cell method. In order to evaluate the proposed methodology, numerical examples are provided to demonstrate the capability of finite cell method and particle swarm optimization algorithm in damage detection of two-dimensional structures. The first example considers the damage detection of a plate with a single hole, and it also considers the effects of mesh density. The second example employs a plate structure with three holes. The results demonstrate that the proposed methodology, with suitable computational efforts, can successfully be applied to damage detection of these structures.