# Optimization of Composite Structures with Thin Rigid Fibers Using Bioinspired Algorithms
## 1 Introduction
In this paper, the layered structures of composites were considered and damage along and perpendicular to the notch was assumed in the study. Interesting methods of modeling composites and dealing with certain problems are also described in the following works. In Ref. [32], in order to overcome the many local minima issue that arises with fiber orientation optimization methods that take the fiber angle into account as the design variable, the authors presented a novel method based on the optimum selection of discrete angles. Based on various load path definitions, a number of load path-guided techniques for fiber trajectory optimization are presented in the study [31]. As an alternative to finite-element analysis (FEA), Ref. [33] suggests a machine learning (ML)-based method for optimizing the fiber orientations of variable stiffness carbon fiber-reinforced plastic (CFRP) structures. The topics described above can still be developed and supplemented with new approaches to composite design. Therefore, it was decided to optimize thin rigid fibers using bioinspired algorithms such as AIS and PSO. One of the ways to increase the strength and stiffness of composites is to use fibers as reinforcement [34; 35]. If the stiffness of the fibers is much higher than the surrounding matrix, the fibers can be treated as perfectly stiff. This approach significantly simplifies composite modeling [36]. In composite materials reinforced by fibers, there is a strong concentration of stresses on the ends of the fibers. This type of material can be modeled simply and, at the same time, precisely by BEM. The method requires division into the boundary elements of the external surfaces of the body and the surfaces of fibers in the composites. The other possibility is using the fast multipole boundary element method to analyze composites reinforced by nanotubes [37]. In this paper, BEM is applied in strength analysis of statically loaded, two-dimensional, and linear-elastic composites with rigid and straight-line fibers. A perfect connection between rigid reinforcements and a flexible matrix is assumed. In order to analyze the problem using BEM, the edges of the plate and fibers are divided into boundary elements. Boundary integral equations are used for nodes on the boundary of the plate and fibers. The unknown quantities in the presented method are the displacements and tractions along boundaries, the displacements of rigid fibers, and interaction traction [38]. The number of nodes and equations is much smaller than in methods that require discretization of the domain and the results are more accurate [39]. The method allows for easy modification of the reinforcement in composites. Based on the literature review, it can be concluded that the proposed method of optimization of composites with thin rigid fibers using bioinspired methods is a new approach to complement many works dealing with design composites. The combination of BEM and bioinspired optimization algorithms such as AIS and PSO is an innovative approach that provides fast and reliable solutions. In summary of the literature review, bioinspired methods are used during optimization for a variety of engineering problems, but the method is not applied to the materials themselves, as discussed in this paper. All programs used during the optimization of composite structures with thin rigid fibers were developed by the authors of this publication (including the program for analyzing composites using BEM, as well as both optimization algorithms). One of the primary goals defined in creating software based on AIS and PSO was its universality and simplicity in applying it with any programs to solve problems resulting from changing design variables. Therefore, a Procedure for the Exchange of Data (PED) is created between an optimization algorithm (AIS or PSO) and any program that solves the problem used to calculate the objective function [20]. This procedure allows us to quickly and easily combine the optimization program with any engineering calculation program.