Takviyeli panellerde burkulma sonrası perçin mukavemetinin incelenmesi
Investigation post-buckling strength of rivets in stiffened panels
Yazar: MUSTAFA İNCE
Danışman: PROF. DR. MESUT KIRCA
İstanbul Teknik Üniversitesi / Lisansüstü Eğitim Enstitüsü / Makine Mühendisliği Ana Bilim Dalı / Malzeme ve İmalat Bilim Dalı
Derece: Yüksek Lisans, 2024
Konu: Makine Mühendisliği = Mechanical Engineering

Özet:
Havacılık endüstrisi, uçakların performansını artırmak ve işletme maliyetlerini düşürmek için sürekli olarak daha hafif ve dayanıklı yapılar arayışındadır. Bu amaca yönelik çalışmalar, teknolojideki ilerlemelerle birlikte havacılık sektöründe kullanılan malzemelerin ve üretim tekniklerinin gelişmesine önemli ölçüde katkı sağlamaktadır. Geleneksel olarak uçak yapıları farklı parçaların, sac metal veya kompozit malzemeler kullanılarak üretilip ardından bir bağlayıcı yardımıyla birleştirilmesiyle oluşturulmaktadır. Bu yapılarda takviye elemanları ve ince cidarlı paneller sıklıkla kullanılmaktadır.  Panel ile takviye elemanlarının bağlantısında sürtünme kaynağı gibi yeni yöntemler ortaya çıksa da sayısız avantajları nedeniyle perçinli bağlantılar yeni uçak yapılarında bile hala yaygın olarak kullanılmaktadır. Panel ve takviye elemanları arasında yükleri aktaran perçinler, panellerin burkulma davranışında ve yapının genel performansında çok önemli bir rol oynamaktadır. 

Bu çalışmada, perçin bağlantı elemanları kullanılarak tasarımı yapılmış takviyeli panellerde burkulma ve burkulma sonrası perçinlere gelen yüklerin incelenmesi ve dayanımlarının kontrol edilmesi amaçlanmıştır. Daha öne yapılan çalışmalarda genellikle yapının taşıyabileceği yükler ve burkulma sonrasın davranışlarının incelenmesi bizi perçinler üzerinde detaylı bir çalışma yapmaya motive etmiştir.  

Çalışmada ilk olarak  perçin ile bağlantısı yapılmış takviyeli panellerdeki burkulma ve burkulma sonrası davranışlarını anlamak için literatürde mevcut bir deney çalışmasının sonlu elemanlar analiziyle doğrulanması gerçekleştirmiştir. Analiz modelinde takviyeli panel kabuk elemanlarla ve perçinler ise kiriş (beam) elemanlarla modellenmiştir. Ardından, burkulma modlarını elde etmek ve buna bağlı geometrik kusurları oluşturmak için ilk olarak doğrusal özdeğer analizi gerçekleştirilmiştir. Daha sonra panelin kritik burkulma yükünü ve burkulma sonrasını davranışını elde etmek için geometrik olarak doğrusal olmayan bir sonlu eleman modeli gerçekleştirilmiştir. Analiz modeline hem geometrik hem de malzeme açısından doğrusal olmayan özellikler dahil edilmiş, daha sonra panelin nihai yükünü ve hasar modlarını elde etmek için genel statik adımlar kullanılarak doğrusal olmayan bir analiz gerçekleştirilmiştir. Gerçekleştirilen analiz sonrasında, burkulma yüklemesi altında bu kiriş elemanlarına gelen eksenel ve kesme kuvvetleri elde edilerek, burkulma ve burkulma sonrasında perçinlerin mukavemeti incelenmiştir. 

Kabuk eleman analiz modeli ile gerçekleştirilen doğrusal olmayan burkulma analizleri sonucunda, kiriş elemanlara gelen kuvvetler incelendiğinde perçinli bağlantıların aynı anda hem kesme hem de çekme kuvvetlerine maruz kalabileceği görülmüştür. Bu durumda yapının emniyetli olması için perçinlerin dayanımının sadece kesme yüklerine göre değil,  aynı zamanda çekme kuvvetlerinin hesaplamaya dâhil edildiği bir mukavemet kontrolünün yapılmasının önemli olduğu görülmüştür. 

Sonuç olarak bu çalışma, burkulma koşulları altında perçinlere gelen yüklerin belirlenmesi ve perçin davranışlarının detaylı bir şekilde ele alınmasıyla perçinlerin yapısal bütünlük ve performans üzerindeki etkilerini anlamak için yapılmış bir çalışmadır. Perçin bağlantılarına aynı anda etki eden kesme ve çekme yüklerinin perçinlerin burkulma sonrasın takviyeli panellerdeki kritik rolünü ve bu bağlantıların panellerin genel davranışına nasıl etki ettiğini anlamak, havacılıkta mühendislik tasarımlarının geliştirilmesinde önemli bir adım olarak değerlendirilmektedir.

Abstract:
The aviation industry is constantly in search of lighter and more durable structures to improve the performance of aircraft and reduce operating costs. Efforts towards this goal, together with advances in technology, have contributed significantly to the development of materials and production techniques used in the aviation industry. Simple materials such as wood used in the early days of aviation have been replaced by integrated structures and composite materials. These developments have made it possible to produce lighter and more durable airplanes. 

Traditionally, airplane structures are constructed by manufacturing different parts using sheet metal or machining methods and then joining them together with the help of a fastener. In this context, stiffened thin panels are widely used and vital structural elements in aviation due to their light weight and high strength. These panels are formed by supporting thin-walled plates using stiffeners.

Although new methods such as friction welding have recently been introduced to the connection of the panel to the stiffeners, riveted connections are still widely used even in new aircraft structures due to their numerous advantages. The benefits of these joints consist of low manufacturing costs, ease of fabrication, the opportunity of repeated meeting and disassembly, the opportunity of automating the riveting process, ease of inspection connection.

Panels manufactured using rivet fasteners are structural components consisting of stiffened elements made of materials such as steel, aluminum, titanium or composites, which are fastened with rivets. These panels are especially preferred in the aerospace industry due to their light weight, high strength and cost effectiveness.

Rivets, which transfer loads between the panel and the stiffened elements, have a very important role in determining the overall performance and strength characteristics of the panels. Especially the residual stresses that may occur during the riveting process are also critical for the strength of the integrated structure. However, regardless of the material strength, reinforced integrated structures in the aerospace industry tend to buckle due to the thin-walled nature of the panels. The main cause of panel buckling is the compressive stresses in the reinforced thin panels. Due to the compressive stresses, thin panels can buckle long before the limit load of the panel. For this reason, local buckling is usually allowed in the design of aerospace structures. Once the critical buckling load is reached, the panel cannot support any further load and the stiffeners carry additional loads that the buckled panel cannot withstand. For this reason, in the aerospace industry, stiffeners are designed to support panels when panel buckling is encountered. Therefore, the determination of buckling load and post-buckling behavior of panels have become critical.

In this study, firstly, an experimental study available in the literature was validated by finite element analysis to understand the buckling and post-buckling behavior of the stiffened elements in riveted panels. Two different analysis models were then prepared. In the first analysis model, the stiffened panel is modeled with shell elements and the rivets are modeled with beam elements. Then, linear eigenvalue analysis was first performed to obtain the buckling modes and to generate the associated geometric imperfections. Then, a geometrically nonlinear finite element model was performed to obtain the critical buckling load and post-buckling behavior of the panel. Nonlinear properties, both geometrically and in terms of materials, were introduced into the analysis model, and then a nonlinear analysis was performed using general static steps to obtain the ultimate load and failure modes of the panel. After the analysis, the axial and shear forces on these beam members under buckling loading were obtained and the strength and behavior of the rivets were investigated during and after buckling. 

In the second analysis model, modeling was performed using solid elements. Here, it is aimed to include the residual stresses that occur during the assembly of rivets in the analysis model. In this section, two different analyses were performed for the stiffened panel modeled with solid elements. In the first analysis, similar to the finite element analysis performed for the shell elements, the analysis was performed for the analysis model prepared with solid elements with the same boundary conditions and loadings. In the second analysis, in addition to this analysis, residual stresses are included in the analysis model. The residual stress obtained after the riveting process was added to all rivets and the panel as initial stress in the linear buckling and nonlinear buckling analysis model. Linear buckling and nonlinear buckling analyses were performed according to the boundary conditions and loadings described previously.

As a result of the nonlinear buckling analyses performed with the shell element analysis model, it was seen that the riveted connections could be exposed to both shear and tensile forces at the same time when the forces on the beam members were analyzed. In this case, it was seen that in order to ensure the safety of the structure, it is important to check the strength of the rivets not only according to the shear loads, but also to perform a tensile strength check in which the combined shear and tensile forces are included in the calculation. In the rivet calculations, the first 5 rivets with the highest shear forces were taken as basis and the tensile forces on these rivets were taken into consideration. In this case, it is seen that one rivet was failed. When we look at the study we referenced in the literature, we see that there is a failed rivet, but we do not know how many of them since the number is not specified.  According to our calculations and strength checks, we see that one rivet was failed. We can say that this rivet and the rivet failed in the literature are not the same rivet.  The reason for this may be that the buckling modes of the panel tested and the panel in our analysis model are different or the test conditions and the analysis model are not exactly the same.

A new model was prepared to investigate how the post-buckling strength of the panel and rivets would change when the number of rivets was increased. The analyses were repeated by decreasing the distance between the rivets and increasing the number of rivets in each stiffener by three rivets. In the results of the analysis, rivet strength calculations were made again according to the forces on rivets. In addition, when compared in terms of critical buckling load, it was seen that the structure had approximately three percent better load carrying capacity in the analysis results with increased number of rivets.

Residual stresses resulting from the riveting process were included in the analysis. Then, when the results of the linear buckling analyses were compared with the results of the solid analysis model without residual stresses, it was observed that the first two buckling mode shapes changed. However, it is not possible to say whether this is a mode shifting or a coincidence without more detailed additional work on this subject. The reason for this change and the effect of residual stress on buckling modes can be investigated in future studies. In addition, when the force-displacement curves were examined as a result of nonlinear buckling analyses in which residual stress was included, it was observed that the buckling and post-buckling behavior did not change much. However, with the current study, we can say that it is too early to say whether the residual stress has an effect on buckling and post-buckling behavior. The effect of the stiffened panels with riveted connections on the behavior of the structure buckling and  post-buckling and the effect on the fatigue of the structure can be investigated in more detail in future studies.

The fact that the previous studies generally examined the post-buckling behavior of stiffened panels and did not examine the post-buckling behavior of rivets motivated us to investigate the rivets in a detailed study.  Consequently, this study is an attempt to understand the effects of rivets on structural strength and performance by investigating in detail the behavior of rivets and determining the loads on rivets under buckling conditions. Understanding the critical role of rivet joints and how they affect the overall behavior of panels is an important step in the development of aerospace and structural engineering designs.