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ÖgeA study on optimization of a wing with fuel sloshing effects(Graduate School, 2022-01-24) Vergün, Tolga ; Doğan, Vedat Ziya ; 511181206 ; Aeronautics and Astronautics Engineering ; Uçak ve Uzay MühendisliğiIn general, sloshing is defined as a phenomenon that corresponds to the free surface elevation in multiphase flows. It is a movement of liquid inside another object. Sloshing has been studied for centuries. The earliest work  was carried out in the literature by Euler in 1761 . Lamb  theoretically examined sloshing in 1879. Especially with the development of technology, it has become more important. It appears in many different fields such as aviation, automotive, naval, etc. In the aviation industry, it is considered in fuel tanks. Since outcomes of sloshing may cause instability or damage to the structure, it is one of the concerns about aircraft design. To prevent its adverse effect, one of the most popular solutions is adding baffles into the fuel tank. Still, this solution also comes with a disadvantage: an increase in weight. To minimize the effects of added weight, designers optimize the structure by changing its shape, thickness, material, etc. In this study, a NACA 4412 airfoil-shaped composite wing is used and optimized in terms of safety factor and weight. To do so, an initial composite layup is determined from current designs and advice from literature. When the design of the initial system is completed, the system is imported into a transient solver in the Ansys Workbench environment to perform numerical analysis on the time domain. To achieve more realistic cases, the wing with different fuel tank fill levels (25%, 50%, and 75%) is exposed to aerodynamic loads while the aircraft is rolling, yawing, and dutch rolling. The aircraft is assumed to fly with a constant speed of 60 m/s (~120 knots) to apply aerodynamic loads. Resultant force for 60 m/s airspeed is applied onto the wing surface by 1-Way Fluid-Structure Interaction (1-Way FSI) as a distributed pressure. Using this method, only fluid loads are transferred to the structural system, and the effect of wing deformation on the fluid flow field is neglected. Once gravity effects and aerodynamic loads are applied to the wing structure, displacement is defined as the wing is moving 20 deg/s for 3 seconds for all types of movements. On the other hand, fluid properties are described in the Ansys Fluent environment. Fluent defines the fuel level, fluid properties, computational fluid dynamics (CFD) solver, etc. Once both structural and fluid systems are ready, system coupling can perform 2-Way Fluid-Structure Interaction (2-Way FSI). Using this method, fluid loads and structural deformations are transferred simultaneously at each step. In this method, the structural system transfers displacement to the fluid system while the fluid system transfers pressure to the structural system. After nine analyses, the critical case is determined regarding the safety factor. Critical case, in which system has the lowest minimum safety factor, is found as 75% filled fuel tank while aircraft dutch rolling. After the determination of the critical case, the optimization process is started. During the optimization process, 1-Way FSI is used since the computational cost of the 2-Way FSI method is approximately 35 times that of 1-Way FSI. However, taking less time should not be enough to accept 1-Way FSI as a solution method; the deviation of two methods with each other is also investigated. After this investigation, it was found that the variation between the two methods is about 1% in terms of safety factors for our problem. In the light of this information, 1-Way FSI is preferred to apply both sloshing and aerodynamic loads onto the structure to reduce computational time. After method selection, thickness optimization is started. Ansys Workbench creates a design of experiments (DOE) to examine response surface points. Latin Hypercube Sampling Design (LHSD) is preferred as a DOE method since it generates non-collapsing and space-filling points to create a better response surface. After creating the initial response surface using Genetic Aggregation, the optimization process is started using the Multi-Objective Genetic Algorithm (MOGA). Then, optimum values are verified by analyzing the optimum results in Ansys Workbench. When the optimum results are verified, it is realized that there is a notable deviation in results between optimized and verified results. To minimize the variation, refinement points are added to the response surface. This process is kept going until variation comes under 1%. After finding the optimum results, it is noticed that its precision is too high to maintain manufacturability so that it is rounded into 1% of a millimeter. In the end, final thickness values are verified. As a result, optimum values are found. It is found that weight is decreased from 100.64 kg to 94.35 kg, which means a 6.3% gain in terms of weight, while the minimum safety factor of the system is only reduced from 1.56 to 1.54. At the end of the study, it is concluded that a 6.3% reduction in weight would reflect energy saving.
ÖgeA study on static and dynamic buckling analysis of thin walled composite cylindrical shells(Graduate School, 2022-01-24) Özgen, Cansu ; Doğan, Vedat Ziya ; 511171148 ; Aeronautics and Astronautics Engineering ; Uçak ve Uzay MühendisliğiThin-walled structures have many useage in many industries. Examples of these fields include: aircraft, spacecraft and rockets can be given. The reason for the use of thin-walled structures is that they have a high strength weight ratio. In order to define a cylinder as thin-walled, the ratio of radius to thickness must be more than 20, and one of the problems encountered in the use of such structures is the problem of buckling. It is possible to define the buckling as a state of instability in the structure under compressive loads. This state of instability can be seen in the load displacement graph as the curve follows two different paths. The possible behaviors; snap through or bifurcation behavior. Compressive loading that cause buckling; there may be an axial load, torsional load, bending load, external pressure. In addition to these loads, buckling may occur due to temperature change. Within the scope of this thesis, the buckling behavior of thin-walled cylinders under axial compression was examined. The cylinder under the axial load indicates some displacement. When the amount of load applied reaches critical level, the structure moves from one state of equilibrium to another. After some point, the structure shows high displacement behavior and loses stiffness. The amount of load that the structure will carry decreases considerably, but the structure continues to carry loads. The behavior of the structure after this point is called post-buckling behavior. The critical load level for the structure can be determined by using finite elements method. Linear eigenvalue analysis can be performed to determine the static buckling load. However, it should be noted here that eigenvalue-eigenvector analysis can only be used to make an approximate estimate of the buckling load and input the resulting buckling shape into nonlinear analyses as a form of imperfection. In addition, it can be preferred to change parameters and compare them, since they are cheaper than other types of analysis. Since the buckling load is highly affected by the imperfection, nonlinear methods with geometric imperfection should be used to estimate a more precise buckling load. It is not possible to identify geometric imperfection in linear eigenvalue analysis. Therefore, a different type of analysis should be selected in order to add imperfection. For example, an analysis model which includes imperfection can be established with the Riks method as a nonlinear static analysis type. Unlike the Newton-Rapson method, the Riks method is capable of backtracking in curves. Thus, it is suitable for use in buckling analysis. In Riks analysis, it is recommended to add imperfection in contrast to linear eigenvalue analysis. Because if the imperfection is added, the problem will be bifurcation problem instead of limit load problem and sharp turns in the graph can cause divergence in analysis. Another nonlinear method of static phenomena is called quasi-static analysis which is used dynamic solver. The important thing to note here is that the inertial effects should be too small to be neglected in the analysis. For this purpose, kinetic energy and internal energy should be compared at the end of the analysis and kinetic energy should be ensured to be negligible levels besides internal energy. Also, if the event is solved in the actual time length, this analysis will be quite expensive. Therefore, the time must be scaled. In order to scale the time correctly, frequency analysis can be performed first and the analysis time can be determined longer than the period corresponding to the first natural frequency. For three analysis methods mentioned within this study, validation studies were carried out with the examples in the literature. As a result of each type of analysis giving consistent results, the effect of parameters on static buckling load was examined, while linear eigenvalue analysis method was used because it was also sufficient for cheaper analysis method and comparison studies. While displacement-controlled analyses were carried out in the static buckling analyses mentioned, load-controlled analyses were performed in the analyses for the determination of dynamic buckling force. As a result of these analyses, they were evaluated according to different dynamic buckling criteria. There are some of the dynamic buckling criteria; Volmir criterion, Budiansky-Roth criterion, Hoff-Bruce criterion, etc. When Budiansky-Roth criterion is used, the first estimated buckling load is applied to the structure and displacement - time graph is drawn. If a major change in displacement is observed, it can be assumed that the structure is dynamically buckled. For Hoff-Bruce criterion, the speed - displacement graph should be drawn. If this graph is not focused in a single area and is drawn in a scattered way, it is considered that the structure has moved to the unstable area. As in static buckling analyses, dynamic buckling analyses were primarily validated with a sample study in the literature. After the analysis methods, the numerical studies were carried out on the effect of some parameters on the buckling load. First, the effect of the stacking sequence of composite layers on the buckling load was examined. In this context, a comprehensive study was carried out, both from which layer has the greatest effect of changing the angle and which angle has the highest buckling load. In addition, the some angle combinations are obtained in accordance with the angle stacking rules found in the literature. For those stacking sequences, buckling forces are calculated with both finite element analyses and analytically. In addition, comparisons were made with different materials. Here, the buckling load is calculated both for cylinders with different masses of the same thickness and for cylinders with different thicknesses with the same mass. Here, the highest force value for cylinders with the same mass is obtained for a uniform composite. In addition, although the highest buckling force was obtained for steel material in the analysis of cylinders of the same thickness, when we look at the ratio of buckling load to mass, the highest value was obtained for composite material. In addition, the ratio of length to diameter and the effect of thickness were also examined. Here, as the length to diameter ratio increases, the buckling load decreases. As the thickness increases, the buckling load increases with the square of the thickness. In addition to the effect of the length to diameter ratio and the effect of thickness, the loading time and the shape of the loading profile are also known in dynamic buckling analysis. In addition, the critical buckling force is affected by imperfections in the structure, which usually occur during the production of the structure. How sensitive the structures are to the imperfection may vary depending on the different parameters. The imperfection can be divided into three different groups as geometric, material and loading. Cylinders under axial load are particularly affected by geometric imperfection. The geometric imperfection can be defined as how far the structure is from a perfect cylindrical structure. It is possible to determine the specified amount of deviation by different measurement methods. Although it is not possible to measure the amount of imperfection for all structures, an idea can be gained about how much imperfection is expected from the studies found in the literature. Both the change in the buckling load on the measured cylinders and the imperfection effect of the buckling load can be measured by adding the measured amount of imperfection to the buckling load calculations. In cases where the amount of imperfection cannot be measured, the finite element can be included in the analysis model as an eigenvector imperfection obtained from linear buckling analysis and the critical buckling load can be calculated for the imperfect structure using nonlinear analysis methods. In this study, studies were carried out on how imperfection sensitivity changes under both static and dynamic loading with different parameters. These parameters are the the length-to-diameter ratio, the effect of the stacking sequence of the composite layers and the added imperfection shape. The most important result obtained in the study on imperfection sensitivity is that the effect of the imperfection on the buckling load is quite high. Even geometric imperfection equal to thickness can cause the buckling load to drop by up to half.