بهینه سازی کلونی مورچه برای پراکنده کردن روکش پانل های کامپوزیتی تحت بارگذاری دومحوری

The current study aims to show the benefits of dispersed laminates (laminates in which the orientation angles are not limited to the conventional, 0°, ±45° and 90°, orientations) over conventional ones, in terms of stiffness, buckling resistance and strength, in structural applications. The Ant Colony Optimization algorithm is used with strength constraints to find the best candidate to achieve this goal. A study is conducted to select the most suitable failure criterion among three common ones. The methodology is used for two loading cases: biaxial compression and biaxial tension. In the case of biaxial compression, the problem is formulated to maximize the critical buckling load whereas with the biaxial tension, the formulation is to minimize the failure index. For both loading cases, the methodology succeeds in improving the response of dispersed laminates with respect to the conventional ones. These results support the movement of the composite industry toward using dispersed laminates

The evolution of manufacturing and tooling technologies of laminated composite materials in aeronautical applications has led to the development of fiber placement machines capable of building laminates with a varied number of ply orientations. Only by allowing plies to adopt any orientation within the −90°:90° range, can straight-fiber composite laminates exploit their full potential to replace the so-called ‘black aluminum’ (quasi-isotropic laminates with 0°, ±45° and 90° orientation angles). Although there has been a huge number of studies conducted and still conducted on the optimization of laminate stacking sequence, the industry has not benefited from the huge potential of the current manufacturing technology until recently. Some of this research [1], [2] and [3] found that tailoring the stacking sequence, without limiting orientations to conventional ones, can improve the laminate response. The ability to tailoring stiffness and strength to meet a certain application requirement is directly related to stacking sequence optimization. Ghiasi et al. [4] and [5] reviewed the optimization techniques used for laminated composites and the characteristics of each algorithm. In that work, it was concluded that gradient direct optimization methods are not suitable for the problem of optimizing the stacking sequence of composite laminates. The reasons are the discrete nature of the problem variables and the huge number of local optima where the gradient methods can converge without reaching the global optimal [6] and [7]. On the other hand, the enumeration technique can be used only for laminates with small numbers of layers and combinations of possible fiber orientations [8]. Metaheuristic search algorithms are the most suitable to solve the problems in which the objective function can be discontinuous, nondifferentiable, stochastic, or highly non-linear [9]. Among the metaheuristic methods, Genetic Algorithms (GA) represent the most commonly used technique in the optimization of laminated composites [10], [11], [12], [13], [14] and [15]. Other metaheuristic techniques were introduced in the literature during the last decade such as the Scatter Search algorithm (SS) [6], Simulated Annealing algorithm (SA) [16], Generalized Pattern algorithm (GP) [9], Fractal Branch and Bound algorithm (FB& B) [17] and [18], Tabu Search algorithm (TS) [19] and Particle Swarm algorithm (PS) [20]. The Ant Colony (AC) algorithm is one of the metaheuristic algorithms that was introduced in the early 1990s by Dorigo et al. [21]. The first use of the AC in the optimization of composite laminates was in 2008 by Aymerich and Serra [22]. The comparison between the Ant Colony algorithm and other metaheuristic algorithms was introduced by several authors; Aymerich and Serra [22] compared AC with GA, Bloomfield et al. [8] compared the AC, the PS and the GA and Hudson et al. [23] compared AC, SA and PS algorithms. The results of all these comparisons showed a good response of the AC algorithm in terms of both the solution quality and the computational costs. The usage of dispersed laminates in stacking sequence optimization studies can be divided into two categories. The first category includes research that modeled the orientation angle as a continuous variable (for example Adali et al. [3]). This approach may lead to a non-optimal or out of feasible region stacking sequence during the manufacturing. The second category includes studies that modeled the orientation angle as a discrete variable (for example Irisarri et al. [2] and Edral and Sonmez [16]). The current paper adopts the discrete modeling of the orientation angles. From the aeronautical manufacturing point of view, using the dispersed laminates helps to improve the damage resistance but its effect on the damage tolerance is not clear [24]. The damage tolerance is characterized by the buckling capacity of the sublaminates which adds an extra-motivation to the current study. The current paper describes the effect of using stacking sequences not limited to the conventional orientations. The AC algorithm is selected for this purpose due to its capabilities and the results of the comparisons presented in [8], [22] and [23]. The fiber orientations are modeled as a discrete variable ranging from 0° to 90° with a 5° jump. To achieve symmetry, only one half of the laminate is designed and the other half is defined by mirroring the stacking sequence. To achieve balance, each layer with a θ° orientation angle is followed by one of −θ°. The content of this paper is structured as follows. Firstly, the theoretical background of a laminated composite panel under biaxial loading is introduced. Secondly, the Ant Colony algorithm is summarized. Then, a convenient failure criteria is chosen. After that, a flat laminated panel subjected to biaxial loading is analyzed under compression and tension. With respect to the biaxial compression loading case, the problem is formulated so as to maximize the critical buckling load by dispersing the stacking sequence under strength constraints. For the biaxial tension case, the problem is formulated to minimize the failure index (the matrix cracking and the fiber tensile failure indices).

The Ant Colony Optimization algorithm is used to optimize laminated panels subjected to biaxial loading (compression and tensile). The algorithm is implemented and validated using data available in the literature [7]. A study is conducted to check the validity of using a simple failure criteria (for example the maximum strain criterion or the Tsai-Wu criterion) instead of the physically-based failure criteria that usually require higher computational time. The results showed that the use of the maximum strain criterion usually leads to local optima while the Tsai-Wu leads to out-of-feasible region solutions as compared to the physically-base LaRC03 failure criteria. The result of that study was the decision to use the LaRC03 failure criteria in spite of its associated computational time given to the trustworthiness of the results. With respect to the biaxial compression loading condition, the problem is formulated to maximize the critical buckling load under strength constraints (LaRC03 failure criteria). For the biaxial tensile loading case, the problem is modeled in two ways: as a single-objective optimization to minimize the matrix cracking failure index, and as a multi-objective optimization to minimize both the matrix cracking and the fiber tensile failure indices. The results showed that, by using the dispersed laminates, the improvement in the buckling load ranged from 2.5% to 8% with respect to the loading ratio. For the tension case, the failure index for matrix cracking can be reduced by up to 100%. These improvements are obtained due to the higher freedom given to the algorithm when selecting the stacking sequences.