Değişken açılı elyaf kompozitlerin uygulanabilirlik açısından yeni bir tasarım yaklaşımı ve diferansiyel evrim ile burkulma yükü optimizasyonu
A novel approach to optimize buckling load for variable angle fiber composites in terms of viability using differential evolution
Yazar: UMUT BEYAZGÜL
Danışman: DR. ÖĞR. ÜYESİ DEMET BALKAN ; PROF. DR. ZAHİT MECİTOĞLU
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Uçak ve Uzay Mühendisliği Ana Bilim Dalı / Uçak ve Uzay Mühendisliği Bilim Dalı
Derece: Yüksek Lisans, 2022
Konu: Mühendislik Bilimleri = Engineering Sciences ; Uçak Mühendisliği = Aeronautical Engineering
Dizin: Burkulma (fen) = Buckling ; Değişkenlik = Variability ; Lifli kompozitler = Fiber composites

Özet:
Hava-uzay araçları başta olmak üzere bir çok sektörde kullanılan elyaf kompozitlerin başlıca tercih edilme nedenleri önceden kullanılan muadillerine göre daha yüksek spesifik dayanım ve daha düşük ağırlık ile birlikte büyük bir maliyet tasarrufu sağlamasıdır.
Bir yapının maruz kaldığı yük isterleri göz önüne alınarak yöne bağlı mekanik özellikleri sayesinde her katmanda uygun bir oryantasyon açısı ile istifleme dizisi tasarlanarak geleneksel elyaf kompozitlerin performansı artırılmaktadır.
Bu tezdeki değişken oryantasyon açısıyla ifade edilen ise elyaf kompozitlerin değişken direngenliğini, elyaf açısını aynı katman içerisinde değiştirerek serim güzergahını değiştirmektir. Böylece, elyaf kompozit malzemenin yöne bağlı mekanik özelliklerini kullanarak optimizasyon kapsamını genişletmekte ve potansiyeline ulaşmasını sağlamaktadır.
Düzlem içinde daha avantajlı bir yük dağılımı oluşturmaya imkan vermektedir. Bu tasarıma sahip kompozitlerin üretimi, uzun yıllardır geleneksel kompozit üretiminde de kullanılan, yüksek hassasiyet ve hızlı serim sağlayan otomatik elyaf serim cihazı (AFP) ve otomatik bant serim cihazı (ATL) ile planlanmaktadır.
Bu çalışmada, mevcut laminasyon teorilerinde sabit sayı olarak geçen her bir katman açısı yerine konuma bağlı, lineer değişen bir oryantasyon açısı tanımı yapılmıştır ve tek eksende yükleme altında burkulma incelenmiştir.
Yüksek dereceden doğrusal olmayan, türevlenebilirlik açısından klasik-gradyan bazlı yöntemlerde uygulaması zor olan amaç fonksiyonlarının optimizasyonunda buluşsal aramaya bağlı stokastik özelliği olan yöntemler arasından göreceli olarak daha hızlı ve yüksek doğruluğu olan evrimsel algoritma kullanılmıştır.
Tasarım modellemesi ve optimizasyon kodu python programlama dilinde yazılarak Abaqus doğrusal burkulma analizi amaç fonksiyonu olarak entegre edilmiştir. Üretim sonrası kusurlardan kaçınmak için simetrik elyaf kompozit ve dengelenmiş katman açıları dizilimi tasarımın sınırlarını oluşturmuştur. Ayrıca, açı parametrelerinin alt ve üst limitlerinin yanı sıra, üretim cihazları ve filament demetlerinden kaynaklı eğrilik yarıçapı kısıtlaması da kullanılmıştır ve eğrilik yarıçap kısıtlama denklemi türetilmiştir.
Optimizasyon ve sayısal analizler sonucunda, farklı katman sayılarında ve farklı boy-en oranlarında değişken açılı elyaf kompozitlerin kritik burkulma yükü bakımından avantajlı olduğu gösterilmiştir ve boy-en oranına ve katman sayısına göre yük kazanım oranları arasındaki korelasyon analiz edilmiştir.

Abstract:
The primary reasons of using fiber composites mainly in aerospace vehicles and many other industries are their higher specific strength and lighter weight or namely high strength to weight ratio over their predecessors that, in turn, enables a large cost reduction including fuel saving that the industry has been benefiting for well over half a century.
After such widespread use of composites in primary and secondary structures, there has been no significant new increase in performance and efficiency.
The performance of traditional fiber composites is enhanced by designing a stacking sequence with an appropriate orientation angle in each layer by means of its directional mechanical properties and by taking into account various load requirements that a structure undergoes. Typical fiber angles in these layers are 0, 90 and ±45, and traditionally it is preferred and even encouraged because of the easier production method.
The fact that conventional composites have been experimentally tested for numerous applications provides validation and abundance of test data. With this knowledge in the field, lamina design guides have been developed in which the design is tied to relevant standards of test methods, specifications, guides, and practices.
New production methods that have been used in the recent past have greatly expanded the design space, promising new possibilities for improved designs that needs to be explored. Since the rate of improvement in the buckling load that the proposed method will provide depends on the design geometry, many research studies are required on the subject as it was studied and well established for conventional fiber composites.
What is expressed by the variable orientation angle in this thesis is to serve as indication of changing the fiber angle throughout the same layer, hence the laying route of fiber tow or fiber tape. Therefore, variable stiffness of fiber composites are achieved layer-wise. Consequently, it expands the scope of optimization and enables to reach its potential by using the directional mechanical properties of the fiber composite material. It allows to create a more advantageous in-plane load distribution that serves to given task.
The production of composites with the design in question is planned to carry out with automated fiber placement device (AFP) and automated tape laying device (ATL), which have been used in traditional composite production for many years, providing high precision and fast laying.
The number one design challenge of thin-walled structures, especially in the fuel tank, wing and fuselage of aerospace vehicles, is buckling. Optimization of orientation angle, which is dependent on in-plane location, to increase the maximum buckling load in curvilinear fiber composites will yield remarkable results. In these optimizations, gains at maximum strength, maximum buckling load, and minimum weight levels are aimed to achieve by redistributing the load to provide variable stiffness distribution and alternative stress distribution. A significant weight saving is aimed with this method.
Modeling with the assumption of continuity between the elements indicating discontinuity in terms of orientation angle and not defining contact between these elements by using resin properties stands out as a common flaw in the modeling that are put forward in some previous studies. It is seen that gaps between tows or tapes are inevitable in designs of this type as many tows in each route are cut in different places, causing discontinuity, and resin-rich regions will form in these places.
Even though previous studies have shown improvements in structural response parameters such as natural frequency, critical buckling load, strain energy, displacement, etc., their enhancement levels are not certain because of both lack of experiments and theoretical reasons.
Although it is used in different ways and some successfully in some studies, a parameter that is missing in the design is the curvature of the fiber path or the radius of curvature. For all the reasons mentioned above, those proposed designs have not been manufactured. It is predicted that even if they were produced and tested, they would not represent their models, and some designs would not approach the performance revealed in numerical solutions.
In this study, a position-dependent linearly varying orientation angle is defined instead of singular angle for each layer, which is a constant number in current lamination theories, and buckling and critical buckling load under uni-axial loading is investigated.
In the optimization of the objective functions that are highly nonlinear and difficult to implement in classical-gradient based methods in terms of differentiability, an evolutionary algorithm with relatively faster and higher accuracy among the methods with stochastic features based on heuristic search was used.
Both conventional fixed-angle fiber composite designs and variable-angle fiber composite designs were obtained by using the differential evolution optimization method by making use of past studies and eliminating the shortcomings in terms of applicability.
Modeling of the design and optimization code is written in python programming language and Abaqus linear buckling analysis integrated as the objective function using the program's libraries.
Following design considerations are assumed to avoid post-production defects and set the limits of the design. Symmetrical fiber composite lay-up is adopted to avoid warp and balanced layer angles are arranged to avoid twist and delamination.
Furthermore, besides the lower and upper limits of the orientation angle parameters, the radius of curvature as a constraint due to automated fiber placement devices and tows (continuous fiber bundles) is also used and the radius of curvature is derived as constraint equation using curvature and arc-length definitions.
As a result of optimization and numerical analysis, it has been shown that variable angle fiber composites with different layer numbers and different aspect ratios have considerably well improved performance in terms of critical buckling load, and the correlation between buckling load improvement rates with respect to aspect ratio and number of layers is analyzed, and outlines for future experimental studies are laid out.