CC BY
14
Том 26, № 02, 2023
Научный Вестник МГТУ ГА
Vol. 26, No. 02, 2023
Civil Aviation High Technologies
МАШИНО СТРОЕНИЕ
2.5.12 - Аэродинамика и процессы теплообмена летательных аппаратов; 2.5.13 - Проектирование конструкция и производство летательных аппаратов;
2.5.14 - Прочность и тепловые режимы летательных аппаратов;
2.5.15 - Тепловые электроракетные двигатели и энергоустановки
летательных аппаратов; 2.5.16 - Динамика, баллистика, управление движением летательных аппаратов
УДК 629.7.025
DOI: 10.26467/2079-0619-2023-26-2-37-48
Optimization of the fin structure from polymer composite materials
using bioinspired structural layouts
Abstract: To comply with efficiency in terms of strength, stability and weight of the aircraft, a complex problem for designing a structural layout should be solved. At the same time, it is essential to take into consideration optimization of the shape, quantity, component layout. Now, the main variant of a structural layout is a combination of longitudinal and transverse elements, optimization of which has virtually exhausted itself. The use of polymer composite materials based on glass and carbon fibers, possessing high specific performance compared to metals, makes it possible to improve the performance of a product and additionally optimize a frame structure due to anisotropy of material properties. However, fundamentally innovative structural layouts are needed for further improving properties. It has become practical to create new promising structural layouts due to the development of technologies for manufacturing products from composite materials, including additive manufacturing and 3D printing as well as developing methods of mathematical modeling and computer-assisted design. Bioinspired structures based on natural analogues such as insect wings are attributed to them. The paper is devoted to a highly topical problem of searching and selecting innovative structural layouts. The purpose of the article is to reduce aircraft fin mass while providing structural strength. The paper considers five variants of structural layouts inclusive of the conventional original structure. Aerodynamic loads on the structure were determined by modeling the flow-around process at an assigned flight mode. Stress-and-strain behavior of the structural layout was determined, and the optimal variant of the considered was chosen. The advantage of polymer composite bioinspired structures over conventional metal variants was established. The paper results will be taken into consideration and used in the subsequent optimization of structural layouts and the development of methods for choosing structural layouts.
Key words: fin, structural layout, spar, rib, bioinspired structure, carbon fiber.
For citation: Baranovski, S.V., Lin, Zay Yar (2023). Optimization of the fin structure from polymer composite materials using bioinspired structural layouts. Civil Aviation High Technologies, vol. 26, no. 2, pp. 37-48. DOI: 10.26467/2079-0619-202326-2-37-48
Оптимизация конструкции киля из полимерных композиционных материалов за счет применения биоподобных конструктивно-силовых схем
Аннотация: Для удовлетворения потребности в эффективности по прочности, устойчивости, массе летательного аппарата необходимо решить комплексную сложную задачу проектирования силового каркаса. При этом необходимо
1
S.V. Baranovski1, Zay Yar Lin1
Bauman Moscow State Technical University (BMSTU), Moscow, Russia
1
С.В. Барановски1, Зай Я Лин1
1 Московский государственный технический университет имени Н.Э. Баумана, г. Москва, Россия
1
Научный Вестник МГТУ ГА
Civil Aviation High Technologies
Том 26, № 02, 2023
Vol. 26, No. 02, 2023
принимать во внимание оптимизацию формы, количество, места расположения элементов. В настоящий момент основным вариантом конструктивно-силовой схемы является набор продольных из поперечных элементов, оптимизация которых уже практически исчерпала себя. Применение полимерных композиционных материалов на основе стеклянных и углеродных волокон, обладающих высокими удельными характеристиками по сравнению с металлами, позволяет повысить характеристики изделия и дополнительно оптимизировать структуру каркаса за счет анизотропии свойств материала. Однако для дальнейшего улучшения свойств необходимы принципиально новые силовые схемы. Благодаря развитию технологий изготовления изделий из композиционных материалов, в том числе аддитивному производству и трехмерной печати, а также развивающимся методам математического моделирования и автоматизированного проектирования и стало возможным создание новых перспективных силовых схем. К ним относятся биоподобные конструкции, основанные на природных аналогах, таких как крылья насекомых. Работа посвящена актуальной задаче поиска и выбора новых конструктивно-силовых схем. Целью работы является снижение массы киля самолета при обеспечении прочности конструкции. В работе рассмотрено пять вариантов конструктивно-силовых схем, включая классическую исходную конструкцию. Аэродинамические нагрузки на конструкцию определены с помощью моделирования процесса обтекания на заданном режиме полета. Определено напряженно-деформированное состояние силовой конструкции и выбран оптимальный из рассмотренных вариант. Установлено преимущество биоподобных конструкций из полимерных композиционных материалов над металлическими классическими вариантами. Результаты работы будут учтены и использованы в дальнейшей оптимизации силовых схем и разработке методик выбора силовых конструкций.
Ключевые слова: киль, конструктивно-силовая схема, лонжерон, нервюра, биоподобная конструкция, углепластик.
Для цитирования: Барановски С.В., Лин Зай Я. Оптимизация конструкции киля из полимерных композиционных материалов за счет применения биоподобных конструктивно-силовых схем // Научный Вестник МГТУ ГА. 2023. Т. 26, № 2. С. 37-48. DOI: 10.26467/2079-0619-2023-26-2-37-48
Introduction
The design of the aircraft structural layout has always been a challenge taking into consideration a variety of different factors and aspects of a domain of science [1]. Strength, stability, aerodynamics, temperature effect is merely a part of a design envelope [2]. It is frequently necessary to consider simultaneous optimization of variable parameters, describing an external shape, an internal structure as well as special aspects of materials and internal mechanisms [3]. The task becomes complicated when polymer composite materials (PCM) are used [4, 5], which allows for specific performance of a component and the whole structure to be enhanced. Concurrently, it is feasible to gain a maximum effect from applying PCM when patterns of reinforcement, considering anisotropy of material properties and adaptation to acting loads, are chosen properly [6].
Now, the issues of upgrading aircraft performance are addressed in a greater degree by optimizing aerodynamics and an exterior. Improving the framework properties is conducted in the context of conventional structural layouts (SL) with rectilinear structural elements - selection of their number, position, shape, and material [7],
using the methods of parametric optimization [8]. However, the present progress in the methods of manufacture, especially using PCM [9], and the arrival of innovative technologies such as additive manufacture [10], on the whole, and 3D printing, in particular [11], allowed researchers to consider and design more cutting-edge configurations of aircraft units [12]. For example, composite panels of the aircraft airframe maintained not using the conventional stringer set but the anisogrid or net structure formed by the system of intercrossing transversal and diagonal ribs, which in the aggregate with PCM allows us to significantly increase weight efficiency of the structure [13]. Moreover, developing methods of design and mathematical modeling such as the topological optimization [14], making it possible to take advantage of mass without reducing strength properties [15], also enable us to design impractical - before structures. Bioin-spired SL [16], based on natural analogues, i. e., the installation direction, shape, number, similar orientation of structural elements in space as with bioinspired objects-analogues, for example, insect wings [17], are referred to such structures.
Conducted studies and computations by means of the hybrid optimization based on the particle swarm method and the gradient method to choose a shape and element layout, demon-
strate the essential positive effect of curvature on the general structure performance [18]. Curved elements show the best properties compared to the rectilinear ones in terms of achieving greater structural efficiency of the wing under the impact of operating loads at various flight modes [19]. SL with curved bioinspired spar-ribs, making it possible to reduce structure mass including aeroelastic constraints [20], are developed. Optimization of such elements engages an array of parameters, and the direction of these elements can be modeled on the plane using the third-order curves with constraints of the reference, passing and finite points with the subsequent generation of the finite-element unit model by means of algorithms which do not depend on nodal coordinates and the element distribution sequence and can be used for a wide specter of objects such as wings, vertical and horizontal stabilizers [21]. In the combination with curved installations, which allow us to implement a comprehensive specter of PMC performance and consider their anisotropy of properties, bioin-spired elements are the most preferable in terms of mass when providing strength, stability and aeroelasticity [22]. For this purpose, various methods of computation and determination of these structures are developed [23].
Thus, it is relevant to ascertain that the utilization of revolutionary SL to comply with the increasing requirements for PCM structures is a crucial task.
Source data
The paper deals with the fin SL of the following parameters:
• Height - 5.2 m;
• Length of the root cross section - 4 m;
• Length of the tip section - 1.7 m;
• Sweep angle - 400;
• Surface area - 14.82;
• Aerodynamic airfoil - symmetrical.
For the given fin parameters, a theoretical surface was developed, which was used to model air-flow conditions and compute stress-and-strain behavior.
The different loading scenarios in conformity with the flight-landing airworthiness regulations1 as well as cases occurring during aircraft ground operation were considered.
The fin structure computation was carried out under the impact of forces resulting from:
• own distributed weight of framework elements;
• aerodynamic pressure as a result of ram air effect;
• concentrated weight of the rudder control elements (of three actuators by mass 4 kg considering hydraulic liquid in the system including the pipelines);
• response to the rudder and actuator actions while maneuvering.
The article presents the results for the aircraft maneuvers at an air speed of 218 km per hour for an arc turn of 180 m, at an altitude of 6 km.
The aerodynamic load computation was completed in the software package Ansys, in the module CFX. The medium was modeled with the parallelepipedon of the dimensions 46x15x15 m (LxWxH). The symmetric property problem was taken into consideration: half a fin (and respectively airflow media), split along the plane of symmetry with overlapping the respective boundary conditions, was considered. Only the right fin half was modeled. The input and output parameters of mid-air2, appropriate to the altitude, air speed, and maneuver direction, were overlapped on the parallelepipedon boundaries. The condition of the flow slipping (velocity equals zero) lack was established on the surface of flow body, the condition of free flow was established regarding the rest of surfaces. The k-s turbulence model was used. The irregular grid of finite volumes from tetrahedrons with digitali-zation at the fin surface and the introduction of prismatic cells boundary layers was built (fig. 1). The total amount of elements came to approximately 1.5 mil. The computations were completed in the stationary mode providing solution accuracy 10"4 The computations were completed using the Bauman Moscow State Technical University high-performance computer machinery.
The paper considers three structural materials: anisotropic glass fiber and carbon fiber
Научный Вестник МГТУ ГА
Civil Aviation High Technologies
Том 26, № 02, 2023
Vol. 26, No. 02, 2023
Fig. 1. View of the computational finite-volume mesh
Table 1
Physical and mechanical performance of the used materials
Parameter Glass fiber Carbon fiber Aluminum
Density, kg/m3 2000 1550 2700
Elasticity modulus, GPa Along the fiber 37.2 50.6 70
Elasticity modulus, GPa Along the fiber 37.2 50.6 70
Across the fiber 26.0 35,4
Shear elasticity, GPa 21.7 29.7 27
Tensile strength, MPa Along the fiber 352.6 483 390
Across the fiber 49.0 67.0
Compressive strength, MPa Along the fiber 202 297 390
Across the fiber 78 107
Shear strength, MPa 191 262 233
composites as basic materials, isotropic aluminum alloy was considered for the comparison of conventional aviation PCM metals. The material performance is provided in Table 1.
Structural layouts under consideration
The conventional layout with 2 spars and 12 ribs, arranged perpendicularly to the forward spar, is the first SL type which is considered in the article (fig. 2). The forward spar width is 3 mm, the rear one is 4 mm. The rib width is 2 mm, the skin one is 3 mm. The paper specifies structural elements of invariable width along the entire fin span. The given tolerance simplifies and accelerates computation, increases the margin of safety,
and it will be additionally optimized while working with the chosen SL. Furthermore, for all the layouts, the SL elevator remained the same - conventional with 12 ribs of 1.5 mm wide and 1 spar up to 2.5 mm wide. The elevator skin width was 1.5 mm. Variant 1 of the conventional SL is adopted as the original structural layout of the fin which will be compared to bioinspired analogues.
The second and basic SL type, which is considered in this article, is a bioinspired layout. The element layout was selected based on insect wings [24] and load-strain distribution in the structure determined as a result of preliminary computations.
Variant 2 (fig. 3) was developed based on the Odonata wings. Curved elements are arranged all over the fin area with different-size structural
Том 26. № 02. 2023
Vol. 26. No. 02. 2023
Научный Вестник МГТУ ГА
Civil Aviation High Technologies
Fig. 2. Conventional fin SL, Variant 1
cells. The elements are curved as in the direction of a flight path as vice versa. The basic structural elements stretch along the entire length of the fin and have the width of 3 mm. They can be a spar analogue. The elements of smaller length as well as bent by the empennage (conditional rib analogue) have the width ranging from 2 to 3 mm depending on the size and reinforced area. Additionally, thin joining webs of 1 mm wide peculiar to dragonfly wings were introduced into the
Fig. 4. Bioinspired fin SL based on the Hymenoptera wings, Variant 3
Fig. 3. Bioinspired fin SL based on the Odonata wing, Variant 2
structures. It is worth noting that the conditional division into spars and ribs or longitudinal and transverse elements for bioinspired structures is used only to simplify the description, as curved elements execute their functions simultaneously in the structure.
Variant 3 (fig. 4) was developed based on the Hymenoptera wings, specifically, of Apis (An-thophila). The given layout is distinguished with a smaller number of transverse elements, the width of which varies from 2 mm up to 2.5 mm, and longitudinal elements with the length along the entire fin are more. At the same time, their width is 2 mm and 3 mm. Structural cell sizes in the structure are bigger. As in the previous bioinspired variant, the structural elements of the fin are superposed with the rudder elements for possible hinging of the latter.
Variant 4 (fig. 5) was developed based on the wings of Coleoptera, and Melolonthina in particular. Taking into consideration a big radius of curvature, the elements were modeled rectilinear. The structural elements are equally arranged all over the entire area. The main mounting direction is diagonals from the lower forward-root section towards the upper rear-tip one. The element width, depending on the size and length, varies from 1 mm to 3 mm including thin joining webs.
Variant 5 (fig. 6) was developed based on honeycomb not as 3-layer structures which have
Fig. 5. Bioinspired fin SL based on the Coleoptera wings, Variant 4
been successfully utilized for a long time in aviation but scaled on the whole unit. Cells have the elongated shape in the direction of aircraft motion. In the diagram, the structure looks as if 2 juxtaposed on each other honeycomb rows with cell half-pitch offset. The element width is 2.5 mm. Long-size elements, passing throughout the entire fin, are not available in the structure. In terms of the periodicity of the layout, for this variant, the structural fin and rudder elements were not juxtaposed which reduces the potential structure advantages due to the required layout adaptation or the transitional elements addition.
Computation results and discussion of obtained data
Stress-and-strain behavior under load was determined for 5 variants of structural layouts. Hence, mass, yielding, stress was compared and analyzed in the structure. The computation results were presented in Table 2.
In all the structures under consideration, the ultimate stress limit is not exceeded. Safety margins - minimal 1.03 (variant 1.5), maximal 1.12 (variant 1.2) for aluminum variants (index 1) are given. Aluminum variants do not require additional optimization, and vice versa, variants with a low coefficient of safety margin can be addi-
Fig. 6. Bioinspired fin SL based on honeycomb, Variant 5
tionally reinforced. The similar pattern is observed for glass fiber: a coefficient of safety margin is close to a unit for variant 2.5, a maximum one is 1.23 for variant 2.3. In case of carbon fiber, a minimum coefficient of safety margin is 1.18 (variant 3.5), a maximum one is 1.98 (variant 3.3). In response to its performance, carbon fiber can withstand significant load. The difference in aluminum SL variants with a maximum coefficient of safety margin from glass fiber and carbon fiber is caused by anisotropy of properties of the latter, making it possible to enhance the performance capabilities of the layout. Alternatively, the SL performance can be additionally improved using anisotropy and reinforcement layouts which will be implemented in subsequent papers. The honeycomb-based SL possesses a minimum coefficient of safety margin. Moreover, the honeycomb layout demonstrated the worst results from the bioinspired, but in terms of deformation and mass, it surpasses the initial one. It is specified by the lack of single-piece structural elements arranged along the entire length of the fin. In these conditions, the structure mass is minimal for every type of material. The given layout was considered for an analysis of a possible application of similar layouts. Transition from the wing to the fuselage can be one of the possible locations of application for a flying wing layout which requires ad-
Том 26, № 02, 2023_Научный Вестник МГТУ ГА
Vol. 26, No. 02, 2023 Civil Aviation High Technologies
Table 2
Computation results
№ Variant Mass, kg Deformation, mm Maximal stress, MPa Material
1.1 312.2 12.1 350.4 Aluminum
1.2 295.7 11.7 347.1
1.3 284.2 13.7 350.2
1.4 292.9 14.0 356.4
1.5 279.6 17.4 376.5
2.1 231.3 11.1 314.4 Glass fiber
2.2 213.8 10.4 309.0
2.3 205.4 13.3 285.5
2.4 211.1 14.2 329.0
2.5 201.0 26.6 341.4
3.1 183.2 8.7 349.0 Carbon fiber
3.2 165.5 8.3 363.0
3.3 159.4 10.5 243.5
3.4 163.6 11.0 381.4
3.5 156.8 21.2 409.3
ditional research. This layout requires additional modification.
As all the types of SL provide the ultimate stress limit, a subsequent variant selection was
executed by mass and deformation in the structure. The variant distribution by these two parameters in relative values (regarding minimal of possible magnitudes) (fig. 7) was built up.
Fig. 7. SL variant distribution by mass and deformation in relative values from materials: ♦ - aluminum, ▲ - glass
fiber, • - carbon fiber
Three individual groups of variants, appropriate to the materials under consideration, which directly depends on density, can be emphasized in the Figure. The metallic SL are further located from the beginning of coordinates which is an ideal center (IC) - the variant with the best parameters. The carbon fiber SL are more proximate to it. Glass fiber - variant values are by 1.5 times more (in relative values). The distribution of SL variants has the same pattern and differs with merely values.
The selection was conducted by determining the distance to IC for equisignificant variants from the Pareto distribution - 3.3, 3.2 and 3.5. As it was stated before, variant 3.5 based on honeycomb is excluded from the consideration, even provided the least mass, due to the low safety margin and the required modification. In terms of variants 3.2 and 3.3, which are based on Anthophila and Odonata wings, the first one is more proximate to IC. Its mass is 165.5 kg which is twice less (53%) than a metal analogue and by 10% less than the carbon-fiber fin. Additional optimization on account for the element shape and arrangement as well as the utilization of the specified installation will allow us to improve structural capabilities of the SL unit and reduce the article mass. Notably, the considered bioinspired designs are similar regarding the performance and differ no more than by 10-15% which indicates a potentiality of subsequent search of an alike layout and the algorithm development for design.
Conclusion and findings
The paper considers the perspective bioin-spired variants of the fin SL allowing for the specific structure indices to be increased.
Based on modeling the SL stress-and-strain behavior under load effect, the values of stressstrain were determined, and the optimal internal layout of the fin by the criterion of mass minimum was chosen. It was established, that the carbon-fiber bioinspired layouts surpass the conventional metal SL up to 50% by mass and can be additionally optimized. The advantage by mass compared to the conventional SL from PCM amounts to approximately 10%.
SL data were obtained by the direct search and the modeling method, the results will serve as a foundation in the subsequent search of perspective structural layouts and be taken into consideration while generating an algorithm to choose a location for the arrangement and the direction of element mounting in the aggregate with PCM curved installations.
References
1. Balunov, K.A., Ishmuratov, F.Z., Tuktarov, S.A., Uskov, V.M., Chedrik, V.V.
(2017). Multidisciplinary aspects in research on the synthesis and optimization of structural layout of aircraft. Prochnost konstruktsiy letatel-nykh apparatov: sbornik statey nauchno-tekhni-cheskoy konferentsii, vol. 2764, pp. 29-36. (in Russian)
2. Mitrofanov, O., Osman, M. (2022). Designing of smooth composite panels providing stability and strength at postbuckling behavior. Mechanics of composite materials, vol. 58, pp. 15-30. DOI: http://dx.doi.org/10.1007/ s11029-022-10008-3
3. Molinari, G., Arrieta, A.F., Erman-ni, P. (2014). Aero-structural optimization of three-dimensional adaptive wings with embedded smart actuators. AIAA journal, vol. 52, no. 9, pp. 1940-1951. DOI: 10.2514/1.J052715 (accessed: 27.04.2022).
4. Reznik, S.V., Esetbatyrovich, A.S. (2021). Composite air vehicle tail fins thermal and stress-strain state modeling. AIP Conference Proceedings, vol. 2318, issue 1, ID: 020012. DOI: 10.1063/5.0036561 (accessed: 27.04.2022).
5. Mitrofanov, O.V. (2021). Load-bearing composite panels design based on post-buckling state: review and relevant objectives. Natural and Technical Sciences, no. 11 (162), pp. 224-226. DOI: 10.25633/ETN.2021.11.17 (in Russian)
6. Mikhailovskiy, K.V., Baranovski, S.V.
(2018). The methods of designing a polymer composite wing using parametrical modeling. Part III. Selection and justification of optimal schemes for reinforcing load bearing elements. BMSTU Journal of Mechanical Engineering,
no. 5 (698), pp. 75-84. DOI: 10.18698/05361044-2018-5-75-84 (in Russian)
7. Tatarnikov, O.V., Phyo, W.A., Na-ing, L.A. (2021). Selection of the optimal structural design of a spar composite wing. BMSTU Journal of Mechanical Engineering, no. 12 (741), pp. 90-99. DOI: 10.18698/05361044-2021-12-90-99 (in Russian)
8. Bolshikh, A.A., Eremin, V.P. (2020). Method of parametric optimization in the problems of passenger airliner design. Engineering Journal: Science and Innovation, no. 10 (106), 14 p. DOI: 10.18698/2308-6033-2020-10-2022 (accessed: 27.04.2022). (in Russian)
9. Guzeva, T.A., Malysheva, G.V. (2022). Features of development of design-and-techno-logical solutions during design of parts made of polymers and composites. Tehnologia Metallov, no. 4, pp. 34-41. DOI: 10.31044/ 1684-24992022-0-4-35-41 (in Russian)
10. Martinez, D.W., Espino, M., Di-zon, J.R., Cascolan, H.M., Crisostomo, J.L. (2022). A comprehensive review on the application of 3D printing in the aerospace industry. Key engineering materials, vol. 913, pp. 27-34. DOI: 10.4028/p-94a9zb
11. Azarov, A.V., Kolesnikov, V.A., Kha-ziev, A.R. (2020). Development of equipment for composite 3D printing of structural elements for aerospace applications. IOP conference series: materials science and engineering, vol. 934, ID: 012049. DOI: 10.1088/1757-899X/934/1/012049 (accessed: 27.04.2022).
12. Song, L., Gao, T., Tang, L. et al. (2021). An all-movable rudder designed by thermo-elastic topology optimization and manufactured by additive manufacturing. Computers and structures, vol. 243, ID: 106405. DOI: 10.1016/j.compstruc.2020.106405 (accessed: 27.04.2022).
13. Azarov, A.V., Babichev, A.A., Razin, A.F. (2020). Optimal design of an airplane wing composite lattice panel under axial compression. Mekhanika kompozitsionnykh ma-terialov i konstruktsii, vol. 26, no. 4, pp. 490-500. DOI: 10.33113/mkmk.ras.2020. 26.04.490_500.04 (in Russian)
14. Zhu, J.H., Zhang, W.H., Xia, L. (2016). Topology optimization in aircraft and
aerospace structures design. Archives of computational methods in engineering, no. 23, pp. 595-622. DOI: 10.1007/s11831-015-9151-2
15. Yurgenson, S.A., Lomakin, E.V., Fedulov, B.N., Fedorenko, A.N. (2020). Structural elements based on the metamaterials. PNRPUMechanics Bulletin, no. 4, pp. 211-219. DOI: 10.15593/perm.mech/2020.4.18 (in Russian)
16. Dubois, A., Farhat, C., Abukhwe-jah, A.H. (2016). Parameterization framework for aeroelastic design optimization of bio-inspired wing structural layouts. 57th AIAA/ASCE/ AHS/ASC structures, structural dynamics, and materials conference, vol. 2016-0485, pp. 1-16. DOI: 10.2514/6.2016-0485
17. Soboyejo, W., Daniel, L. (Eds.). (2020). Bioinspired structures and design. Cambridge: Cambridge University Press, 360 p. DOI: 10.1017/9781139058995
18. Singh, K., Zhao, W., Jrad, M., Kapa-nia, R.K. (2019). Hybrid optimization of curvi-line-arly stiffened shells using parallel processing. Journal of Aircraft, vol. 56, no. 3, pp. 1068-1079. DOI: 10.2514/1.C035069 (accessed: 27.04.2022).
19. Baranovski, S.V., Mikhailovskiy, K.V. (2020). Structurally optimized polymer composite wing design. Part 1. Curvilinear load-bearing elements. TsAGI Science Journal, vol. 51, no. 2, pp. 79-86.
20. Zhao, W., Kapania, R.K. (2019). Bilevel programming weight minimization of composite flying-wing aircraft with curvilinear spars and ribs. AIAA Journal, vol. 57, no. 6, pp. 2594-2608. DOI: 10.2514/1.J057892 (accessed: 27.04.2022).
21. De, S., Jrad, M., Kapania, R.K. (2019). Structural optimization of internal structure of aircraft wings with curvilinear spars and ribs. Journal of Aircraft, vol. 56, no. 2, pp. 707-718. DOI: 10.2514/1.C034818 (accessed: 27.04.2022).
22. Stanford, B.K., Jutte, C.V. (2017). Comparison of curvilinear stiffeners and tow steered composites for aeroelastic tailoring of aircraft wings. Computers & Structures, vol. 183, no. 15, pp. 48-60. DOI: 10.1016/ j.compstruc.2017.01.010
23. Vescovini, R., Oliveri, V., Pizzi, D., Dozio, L., Weaver, P.M. (2020). A semi-analytical approach for the analysis of variable-stiffness panels with curvilinear stiffeners. International Journal of Solids and Structures, vol. 188-189, pp. 244-260. DOI: 10.1016/ j.ijsolstr.2019.10.011
24. Salcedo, M.K., Hoffmann, J., Do-noughe, S., Mahadevan, L. (2019). Computational analysis of size, shape and structure of insect wings. Biology Open, vol. 8, no. 10, ID: bio040774. DOI: 10.1242/bio.040774 (accessed: 27.04.2022).
Список литературы
1. Балунов К.А. Многодисциплинарные аспекты в исследованиях синтеза и оптимизации конструктивно-силовых схем летательных аппаратов / К.А. Балунов, Ф.З. Ишму-ратов, С.А. Туктаров, В.М. Уськов, В.В. Чед-рик // Прочность конструкций летательных аппаратов: сборник статей научно-технической конференции. Жуковский, 08-09 декабря 2016 г. Москва: ЦАГИ им. проф. Н.Е. Жуковского, 2017. Т. 2764. С. 29-36.
2. Mitrofanov O., Osman M. Designing of smooth composite panels providing stability and strength at postbuckling behavior // Mechanics of Composite Materials. 2022. Vol. 58. Pp. 15-30. DOI: http://dx.doi.org/10.1007/ s11029-022-10008-3
3. Molinari G., Arrieta A.F., Ermanni P.
Aero-structural optimization of three-dimensional adaptive wings with embedded smart actuators [Электронный ресурс] // AIAA Journal. 2014. Vol. 52, по. 9. Pp. 1940-1951. DOI: 10.2514/1.J052715 (дата обращения: 27.04.2022).
4. Reznik S.V., Esetbatyrovich A.S. Composite air vehicle tail fins thermal and stress-strain state modeling [Электронный ресурс] // AIP Conference Proceedings. 2021. Vol. 2318, iss. 1. ID: 020012. DOI: 10.1063/5.0036561 (дата обращения: 27.04.2022).
5. Митрофанов О.В. Проектирование несущих панелей из композитных материалов по закритическому состоянию: обзор
и актуальные задачи // Естественные и технические науки. 2021. № 11 (162). С. 224-226. DOI: 10.25633/ETN.2021.11.17
6. Михайловский К.В., Баранов-ски С.В. Методика проектирования крыла из полимерных композиционных материалов на основе параметрического моделирования. Часть 3. Выбор и обоснование оптимальных схем армирования силовых элементов // Известия высших учебных заведений. Машиностроение. 2018. № 5 (698). С. 75-84. DOI: 10.18698/0536-1044-2018-5-75-84
7. Татарников О.В., Пху Вэй Аунг, Найнг Лин Аунг. Выбор оптимальной конструктивно-силовой схемы лонжеронного композитного крыла // Известия высших учебных заведений. Машиностроение. 2021. № 12 (741). С. 90-99. DOI: 10.18698/05361044-2021-12-90-99
8. Больших А.А., Еремин В.П. Применение метода параметрической оптимизации в задачах проектирования пассажирских авиалайнеров [Электронный ресурс] // Инженерный журнал: наука и инновации. 2020. № 10 (106). 14 c. DOI: 10.18698/2308-60332020-10-2022 (дата обращения: 27.04.2022).
9. Гузева Т.А., Малышева Г.В. Особенности разработки конструкторско-техно-логических решений при проектировании деталей из полимеров и композитов // Технология металлов. 2022. № 4. C. 35-41. DOI: 10.31044/1684-2499-2022-0-4-35-41
10. Martinez D.W. A comprehensive review on the application of 3D printing in the aerospace industry / D.W. Martinez, M. Espino, J.R. Dizon, H.M. Cascolan, J.L. Crisostomo // Key engineering materials. 2022. Vol. 913. Pp. 27-34. DOI: 10.4028/p-94a9zb
11. Azarov A.V., Kolesnikov V.A., Khazi-ev A.R. Development of equipment for composite 3D printing of structural elements for aerospace applications [Электронный ресурс] // IOP conference series: materials science and engineering. 2020. Vol. 934. ID: 012049. DOI: 10.1088/1757-899X/934/1/012049 (дата обращения: 27.04.2022).
12. Song L., Gao T., Tang L. An all-movable rudder designed by thermo-elastic topology optimization and manufactured by addi-
tive manufacturing [Электронный ресурс] // Computers and structures. 2021. Vol. 243. ID: 106405. DOI: 10.1016/j.compstruc.2020.106405 (дата обращения: 27.04.2022).
13. Азаров А.В., Бабичев А.А., Разин А.Ф. Оптимальное проектирование сетчатой композитной панели крыла самолета при одноосном сжатии // Механика композиционных материалов и конструкций. 2020. Т. 26, № 4. С. 490-500. DOI: 10.33113/mkmk. ras.2020.26.04.490_500.04
14. Zhu J.H., Zhang W.H., Xia L. Topology optimization in aircraft and aerospace structures design // Archives of computational methods in engineering. 2016. No. 23. Pp. 595-622. DOI: 10.1007/s11831-015-9151-2
15. Юргенсон С.А. Конструкционные элементы на основе метаматериалов / С.А. Юргенсон, Е.В. Ломакин, Б.Н. Федулов, А.Н. Фе-доренко // Вестник Пермского национального исследовательского политехнического университета. Механика. 2020. № 4. С. 211-219. DOI: 10.15593/perm.mech/2020.4.18
16. Dubois A., Farhat C., Abukhwe-jah A.H. Parameterization framework for aeroe-lastic design optimization of bio-inspired wing structural layouts // 57th AIAA/ASCE/AHS/ ASC structures, structural dynamics, and materials conference. USA, San Diego, 4-8 January 2016. Vol. 2016-0485. Pp. 1-16. DOI: 10.2514/6.2016-0485
17. Soboyejo W., Daniel L. (Eds.). Bioin-spired structures and design. Cambridge: Cambridge University press, 2020. 360 p. DOI: 10.1017/9781139058995
18. Singh K. Hybrid optimization of curvi-line-arly stiffened shells using parallel processing / K. Singh, W. Zhao, M. Jrad, R.K. Ka-pania [Электронный ресурс] // Journal of aircraft. 2019. Vol. 56, no. 3. Pp. 1068-1079.
DOI: 10.2514/1.C035069 (дата обращения: 27.04.2022).
19. Барановски С.В., Михайловский К.В.
Структурно-оптимизированная конструкция крыла из полимерных композиционных материалов. Часть 1. Криволинейные силовые элементы // Ученые записки ЦАГИ. 2020. Т. 51, № 2.
C. 79-86.
20. Zhao W., Kapania R.K. Bilevel programming weight minimization of composite flying-wing aircraft with curvilinear spars and ribs [Электронный ресурс] // AIAA Journal. 2019. Vol. 57, no. 6. Pp. 2594-2608. DOI: 10.2514/1.J057892 (дата обращения: 27.04.2022).
21. De S., Jrad M., Kapania R.K. Structural optimization of internal structure of aircraft wings with curvilinear spars and ribs [Электронный ресурс] // Journal of aircraft. 2019. Vol. 56, no. 2. Pp. 707-718. DOI: 10.2514/1. C034818 (дата обращения: 27.04.2022).
22. Stanford B.K., Jutte C.V. Comparison of curvilinear stiffeners and tow steered composites for aeroelastic tailoring of aircraft wings // Computers & Structures. 2017. Vol. 183, no. 15. Pp. 48-60. DOI: 10.1016/j.compstruc.2017.01.010
23. Vescovini R. A sem-analytical approach for the analysis of variable-stiffness panels with curvilinear stiffeners / R. Vescovini, V. Oliveri,
D. Pizzi, L. Dozio, P.M. Weaver // International Journal of Solids and Structures. 2020. Vol. 188-189. Pp. 244-260. DOI: 10.1016/ j.ijsolstr.2019.10.011
24. Salcedo M.K. Computational analysis of size, shape and structure of insect wings [Электронный ресурс] / M.K. Salcedo, J. Hoffmann, S. Donoughe, L. Mahadevan // Biology Open. 2019. Vol. 8, no. 10. ID: bio040774. DOI: 10.1242/bio.040774 (дата обращения: 27.04.2022).
Information about the authors
Sergey V. Baranovski, Candidate of Technical Sciences, Associate Professor of the Rocket-Space Composite Structures Chair, Bauman Moscow State Technical University, serg1750@mail.ru.
Zay Yar Lin, Trainee of the Rocket-Space Composite Structures Chair, Bauman Moscow State Technical University, zayarlinngate321@gmail.com.
Научный Вестник МГТУ ГА
Civil Aviation High Technologies
Том 26, № 02, 2023
Vol. 26, No. 02, 2023
Сведения об авторах
Барановски Сергей Владиславович, кандидат технических наук, доцент кафедры ракетно-космических композитных конструкций Московского государственного технического университета им. Н.Э. Баумана, serg1750@mail.ru.
Зай Я Лин, стажер-практикант кафедры ракетно-космических композитных конструкций Московского государственного технического университета им. Н.Э. Баумана, zayarlin-ngate321@gmail.com.
Поступила в редакцию 10.10.2022 Received 10.10.2022
Принята в печать 23.03.2023 Accepted for publication 23.03.2023
