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Keywords = bending–torsion–axial coupling

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24 pages, 5243 KB  
Article
Multi-Segment Extendable Soft Manipulator Driven by a Pneumatic–Tendon Coupling Mechanism
by Hongxi Yang, Yufeng Zeng, Zeyu Zhong, Zhiyan Chen, Junxi Zhou, Zhicheng Ling, Ye Chen and Yunquan Li
Biomimetics 2025, 10(10), 643; https://doi.org/10.3390/biomimetics10100643 - 23 Sep 2025
Viewed by 444
Abstract
Continuum robots have garnered significant attention for their high flexibility and adaptability to complex environments. However, achieving the same level of high-precision control as rigid robots remains a significant challenge. This paper introduces an innovative Multi-Segment Extendable Soft Manipulator (MSESM) that employs a [...] Read more.
Continuum robots have garnered significant attention for their high flexibility and adaptability to complex environments. However, achieving the same level of high-precision control as rigid robots remains a significant challenge. This paper introduces an innovative Multi-Segment Extendable Soft Manipulator (MSESM) that employs a pneumatic–tendon hybrid drive mechanism. The design, utilizing off-the-shelf industrial bellows and 3D-printed components, allows the manipulator to achieve an extension ratio of up to 156.85%. By adopting a differential stiffness design, its bending stiffness was increased by approximately 4–5 times, its axial stiffness was increased by approximately 10 times, and its torsional resistance was enhanced, preventing inter-segment coupling during motion. At the control level, this paper proposes a hybrid control method that integrates a Constant Curvature (CC) physical prior with a data-driven neural network. Experimental results show that in tracking rectangular, triangular, and circular trajectories, this hybrid method reduced the average tracking error by 60.43% compared to a purely neural network-based controller, with the error reduction for the rectangular trajectory reaching 74.19%. This research validates a practical and effective approach for creating soft manipulators that successfully merge high flexibility with high-precision control. Full article
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22 pages, 5158 KB  
Article
Natural Frequencies of Composite Anisogrid Cylindrical Shell-Beams Carrying Rigid Bodies at the Boundaries: Smeared Approach, FEM Verification, and Minimum Mass Design
by Giovanni Totaro
Appl. Sci. 2025, 15(17), 9335; https://doi.org/10.3390/app15179335 - 25 Aug 2025
Viewed by 676
Abstract
In this paper, the natural frequencies of pure bending, axial–bending, and torsional-bending coupled modes of CFRP Anisogrid cylindrical shell-beams supporting non-structural masses and inertias at the boundaries are firstly analytically investigated and, secondly, verified by FEM. Indeed, the design of shell-beam elements in [...] Read more.
In this paper, the natural frequencies of pure bending, axial–bending, and torsional-bending coupled modes of CFRP Anisogrid cylindrical shell-beams supporting non-structural masses and inertias at the boundaries are firstly analytically investigated and, secondly, verified by FEM. Indeed, the design of shell-beam elements in various engineering applications is driven by the minimum frequency value that is necessary to achieve in order not to compromise the proper functionality of the assembly for which these elements are designed. In turn, this minimum frequency depends on the geometry, mass, and dynamics of the main components of the assembly. A typical point in space applications is to control the lowest frequency of the spacecraft body, commonly supported by a shell structure, in order to avoid the occurrence of resonance issues that may be induced by dynamic loads during the launch phase. As a rule, to keep the lowest frequency sufficiently high, in conjunction with non-structural masses, means to increase the stiffness and the mass of the load-carrying structure and, ideally, to identify the most efficient solution. In order to effectively address this topic, the analytical models of the natural frequencies of Anisogrid cylindrical shell-beams are finally introduced into an optimization routine as constraints on the fundamental frequency. This approach allows us to readily explore the various Anisogrid configurations and find the best candidate solutions in the framework of preliminary design. Full article
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41 pages, 3195 KB  
Article
A Stress Analysis of a Thin-Walled, Open-Section, Beam Structure: The Combined Flexural Shear, Bending and Torsion of a Cantilever Channel Beam
by David W. A. Rees
Appl. Sci. 2025, 15(15), 8470; https://doi.org/10.3390/app15158470 - 30 Jul 2025
Viewed by 996
Abstract
Channels with three standard symmetrical sections and one asymmetric section are mounted as cantilever beams with the web oriented vertically. A classical solution to the analysis of stress in each thin-walled cantilever channel is provided using the principle of wall shear flow superposition. [...] Read more.
Channels with three standard symmetrical sections and one asymmetric section are mounted as cantilever beams with the web oriented vertically. A classical solution to the analysis of stress in each thin-walled cantilever channel is provided using the principle of wall shear flow superposition. The latter is coupled with a further superposition between axial stress arising from bending and from the constraint placed on free warping imposed at the fixed end. Closed solutions for design are tabulated for the net shear stress and the net axial stress at points around any section within the length. Stress distributions thus derived serve as a benchmark structure for alternative numerical solutions and for experimental investigations. The conversion of the transverse free end-loading applied to a thin-walled cantilever channel into the shear and axial stress that it must bear is outlined. It is shown that the point at which this loading is applied within the cross-section is crucial to this stress conversion. When a single force is applied to an arbitrary point at the free-end section, three loading effects arise generally: bending, flexural shear and torsion. The analysis of each effect requires that this force’s components are resolved to align with the section’s principal axes. These forces are then considered in reference to its centroid and to its shear centre. This shows that axial stress arises directly from bending and from the constraint imposed on free warping at the fixed end. Shear stress arises from flexural shear and also from torsion with a load offset from the shear centre. When the three actions are combined, the net stresses of each action are considered within the ability of the structure to resist collapse from plasticity and buckling. The novelty herein refers to the presentation of the shear flow calculations within a thin wall as they arise from an end load offset from the shear centre. It is shown how the principle of superposition can be applied to individual shear flow and axial stress distributions arising from flexural bending, shear and torsion. Therein, the new concept of a ‘trans-moment’ appears from the transfer in moments from their axes through centroid G to parallel axes through shear centre E. The trans-moment complements the static equilibrium condition, in which a shift in transverse force components from G to E is accompanied by torsion and bending about the flexural axis through E. Full article
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18 pages, 33781 KB  
Article
New Experimental Single-Axis Excitation Set-Up for Multi-Axial Random Fatigue Assessments
by Luca Campello, Vivien Denis, Raffaella Sesana, Cristiana Delprete and Roger Serra
Machines 2025, 13(7), 539; https://doi.org/10.3390/machines13070539 - 20 Jun 2025
Viewed by 348
Abstract
Fatigue failure, generated by local multi-axial random state stress, frequently occurs in many engineering fields. Therefore, it is customary to perform experimental vibration tests for a structural durability assessment. Over the years, a number of testing methodologies, which differ in terms of the [...] Read more.
Fatigue failure, generated by local multi-axial random state stress, frequently occurs in many engineering fields. Therefore, it is customary to perform experimental vibration tests for a structural durability assessment. Over the years, a number of testing methodologies, which differ in terms of the testing machines, specimen geometry, and type of excitation, have been proposed. The aim of this paper is to describe a new testing procedure for random multi-axial fatigue testing. In particular, the paper presents the experimental set-up, the testing procedure, and the data analysis procedure to obtain the multi-axial random fatigue life estimation. The originality of the proposed methodology consists in the experimental set-up, which allows performing multi-axial fatigue tests with different normal-to-shear stress ratios, by choosing the proper frequency range, using a single-axis exciter. The system is composed of a special designed specimen, clamped on a uni-axial shaker. On the specimen tip, a T-shaped mass is placed, which generates a tunable multi-axial stress state. Furthermore, by means of a finite element model, the system dynamic response and the stress on the notched specimen section are estimated. The model is validated through a harmonic acceleration base test. The experimental tests validate the numerical simulations and confirm the presence of bending–torsion coupled loading. Full article
(This article belongs to the Section Machines Testing and Maintenance)
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14 pages, 3272 KB  
Article
Research on Multi-Objective Optimization of Helical Gear Shaping Based on an Improved Genetic Algorithm
by Shengmao Zhou and Dehai Zhang
Machines 2025, 13(4), 295; https://doi.org/10.3390/machines13040295 - 2 Apr 2025
Cited by 1 | Viewed by 626
Abstract
Traditional design and shaping methods of helical gears may have difficulties in meeting the requirements of multiple performance indicators simultaneously, such as tooth surface accuracy, load-carrying capacity, and transmission efficiency. This study attempts to overcome these limitations through a multi-objective optimization method and [...] Read more.
Traditional design and shaping methods of helical gears may have difficulties in meeting the requirements of multiple performance indicators simultaneously, such as tooth surface accuracy, load-carrying capacity, and transmission efficiency. This study attempts to overcome these limitations through a multi-objective optimization method and achieve the comprehensive optimization of multiple performance indicators. This paper aims to boost gear system power transmission and cut vibration and noise. It assesses gear shaping impacts via normal load per unit length of the helical gear surface and gear vibration amplitude. Traditional gear shaping schemes were first determined using classic theories and formulas. Then, an improved genetic algorithm was applied to seek optimal helical gear shaping parameters. An eight-degree-of-freedom lumped mass model of the helical gear transmission system, considering bending–torsion–axial coupling, was developed based on Newton’s second law and solved via the fourth-order Runge–Kutta method. Comparisons showed that the traditional shaping scheme reduced the maximum normal load per unit length by 20.6% and the system’s vibration amplitude by 18.3%. In contrast, the improved genetic algorithm achieved greater reductions of 26.34% and 27.2%, respectively. Both methods effectively decreased the maximum normal load per unit length and system vibration amplitude, with the improved genetic algorithm yielding superior results. This work offers a key theoretical basis and reference for enhancing load transmission, reducing costs, and mitigating vibration and noise in gear transmission systems. Full article
(This article belongs to the Section Machine Design and Theory)
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22 pages, 650 KB  
Article
Integrated Dynamic Analysis of Thin-Walled Beams: Coupled Bidirectional Bending, Torsion, and Axial Vibrations Under Axial Loads
by Yunjie Yu, Huanxia Wei, Baojing Zheng, Dongfang Tian and Lingli He
Appl. Sci. 2024, 14(23), 11390; https://doi.org/10.3390/app142311390 - 6 Dec 2024
Cited by 2 | Viewed by 1464
Abstract
This paper proposes a beam model integrating the Timoshenko beam theory with Vlasov beam theory to capture the coupled behavior of bidirectional bending, torsion, and axial vibration in thin-walled beams subjected to axial loads. Our model incorporates the effects of shear deformation, rotational [...] Read more.
This paper proposes a beam model integrating the Timoshenko beam theory with Vlasov beam theory to capture the coupled behavior of bidirectional bending, torsion, and axial vibration in thin-walled beams subjected to axial loads. Our model incorporates the effects of shear deformation, rotational inertia, and axial loads, offering a comprehensive approach to complex dynamic behaviors. By utilizing Hamilton’s principle, we derived a complete set of coupled dynamic equations and boundary conditions. The highlight of this model is its capacity to accurately predict the dynamic response of thin-walled beams under multifaceted loading conditions, surpassing traditional models by integrating coupled axial vibrations. This research significantly advances the understanding of the dynamic behavior of thin-walled beams, providing a precise analytical tool for structural design and safety assessment. The robustness and accuracy of the proposed model were validated through extensive theoretical analysis and empirical validation, equipping engineers with critical insights to optimize the design of engineering structures subjected to complex dynamic loads. Full article
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23 pages, 5734 KB  
Article
Nonlinear Slippage of Tensile Armor Layers of Unbonded Flexible Riser Subjected to Irregular Loads
by Qingsheng Liu, Zhongyuan Qu, Xiaoya Liu, Jiawei He, Gang Wang, Sicong Wang and Feng Chen
J. Mar. Sci. Eng. 2024, 12(5), 818; https://doi.org/10.3390/jmse12050818 - 14 May 2024
Cited by 3 | Viewed by 1334
Abstract
The unbonded flexible riser has been increasingly applied in the ocean engineering industry to transport oil and gas resources from the seabed to offshore platforms. The slippage of helical layers, especially the tensile armor layers of unbonded flexible risers, contribute to the nonlinear [...] Read more.
The unbonded flexible riser has been increasingly applied in the ocean engineering industry to transport oil and gas resources from the seabed to offshore platforms. The slippage of helical layers, especially the tensile armor layers of unbonded flexible risers, contribute to the nonlinear hysteresis phenomenon, which is a research hotspot and difficulty. In this paper, on the basis of a typical eight-layer unbonded flexible riser model, the nonlinear slippage of a tensile armor layer and the corresponding nonlinear behavior of an unbonded flexible riser subjected to irregular external loads are studied by numerical modeling with detailed cross-sectional properties of the helical layers, and are verified through a theoretical method considering the coupled effect of the external loads on the unbonded flexible riser. Firstly, the balance equation of each layer considering the effect of external loads is established based on functional principles, and the overall theoretical model of the unbonded flexible riser is set up in consideration of the contact between adjacent layers. Secondly, the numerical modeling of each separate layer within the unbonded flexible riser, including the actual geometry of the carcass and pressure armor layer, is established, and solid elements are applied to all the interlayers, thus simulating the nonlinear contact and friction between and within interlayers. Finally, after verification through test data, the behavior of the unbonded flexible riser under the cyclic axial force, torsion, bending moment, and irregular external and internal pressure is studied. The results show that the tensile armor layer can slip under irregular loads. Additionally, some suggestions related to the analysis of unbonded flexible risers under irregular loads are drawn in the end. Full article
(This article belongs to the Section Ocean Engineering)
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9 pages, 420 KB  
Proceeding Paper
Partial Differential Equations of Motion for a Single-Link Flexible Manipulator
by Mohammed Bouanane, Rachad Oulad Ben Zarouala and Abdellatif Khamlichi
Eng. Proc. 2021, 11(1), 40; https://doi.org/10.3390/ASEC2021-11120 - 17 Mar 2022
Cited by 2 | Viewed by 1684
Abstract
Robot manipulators have played an enormous role in the industry during the twenty-first century. Due to the advances in materials science, lightweight manipulators have emerged with low energy consumption and positive economic aspect regardless of their complex mechanical model and control techniques problems. [...] Read more.
Robot manipulators have played an enormous role in the industry during the twenty-first century. Due to the advances in materials science, lightweight manipulators have emerged with low energy consumption and positive economic aspect regardless of their complex mechanical model and control techniques problems. This paper presents a dynamic model of a single link flexible robot manipulator with a payload at its free end based on the Euler–Bernoulli beam theory with a complete second-order deformation field that generates a complete second-order elastic rotation matrix. The beam experiences an axial stretching, horizontal and vertical deflections, and a torsional deformation ignoring the shear due to bending, warping due to torsion, and viscous air friction. The deformation and its derivatives are assumed to be small. The application of the extended Hamilton principle while taking into account the viscoelastic internal damping based on the Kelvin–Voigt model expressed by the Rayleigh dissipation function yields both the boundary conditions and the coupled partial differential equations of motion that can be decoupled when the manipulator rotates with a constant angular velocity. Equations of motion solutions are still under research, as it is required to study the behavior of flexible manipulators and develop novel ways and methods for controlling their complex movements. Full article
(This article belongs to the Proceedings of The 2nd International Electronic Conference on Applied Sciences)
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17 pages, 20846 KB  
Article
On the Free Vibration and the Buckling Analysis of Laminated Composite Beams Subjected to Axial Force and End Moment: A Dynamic Finite Element Analysis
by MirTahmaseb Kashani and Seyed M. Hashemi
Appl. Mech. 2022, 3(1), 210-226; https://doi.org/10.3390/applmech3010015 - 23 Feb 2022
Cited by 4 | Viewed by 3028
Abstract
This work presents the bending–torsion coupled free vibration analysis of prestressed, layered composite beams subjected to axial force and end moment using the traditional finite element method (FEM) and dynamic finite element (DFE) techniques. Current trends in the literature, in terms of different [...] Read more.
This work presents the bending–torsion coupled free vibration analysis of prestressed, layered composite beams subjected to axial force and end moment using the traditional finite element method (FEM) and dynamic finite element (DFE) techniques. Current trends in the literature, in terms of different types of modeling techniques and constraints, were briefly examined. The Galerkin-type weighted residual method was applied to convert the coupled differential equations of motion into a discrete problem using a polynomial interpolation function in the finite element method. In the dynamic finite element method, trigonometric shape functions were implemented to describe the equations in terms of nodal displacements. The eigenvalue problem resulting from the discretization along the length of the beam was solved in order to determine the system’s natural frequencies and modes. The results, showing the effects of axial load, end moment, and combined loading on natural frequencies, are discussed and are followed by some concluding remarks. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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18 pages, 2049 KB  
Article
Dynamic Finite Element Modelling and Vibration Analysis of Prestressed Layered Bending–Torsion Coupled Beams
by MirTahmaseb Kashani and Seyed M. Hashemi
Appl. Mech. 2022, 3(1), 103-120; https://doi.org/10.3390/applmech3010007 - 16 Jan 2022
Cited by 11 | Viewed by 5526
Abstract
Free vibration analysis of prestressed, homogenous, Fiber-Metal Laminated (FML) and composite beams subjected to axial force and end moment is revisited. Finite Element Method (FEM) and frequency-dependent Dynamic Finite Element (DFE) models are developed and presented. The frequency results are compared with those [...] Read more.
Free vibration analysis of prestressed, homogenous, Fiber-Metal Laminated (FML) and composite beams subjected to axial force and end moment is revisited. Finite Element Method (FEM) and frequency-dependent Dynamic Finite Element (DFE) models are developed and presented. The frequency results are compared with those obtained from the conventional FEM (ANSYS, Canonsburg, PA, USA) as well as the Homogenization Method (HM). Unlike the FEM, the application of the DFE formulation leads to a nonlinear eigenvalue problem, which is solved to determine the system’s natural frequencies and modes. The governing differential equations of coupled flexural–torsional vibrations, resulting from the end moment, are developed using Euler–Bernoulli bending and St. Venant torsion beam theories and assuming linear harmonic motion and linearly elastic materials. Illustrative examples of prestressed layered, FML, and unidirectional composite beam configurations, exhibiting geometric bending-torsion coupling, are studied. The presented DFE and FEM results show excellent agreement with the homogenization method and ANSYS modeling results, with the DFE’s rates of convergence surpassing all. An investigation is also carried out to examine the effects of various combined axial loads and end moments on the stiffness and fundamental frequencies of the structure. An illustrative example, demonstrating the application of the presented methods to the buckling analysis of layered beams is also presented. Full article
(This article belongs to the Special Issue Mechanical Design Technologies for Beam, Plate and Shell Structures)
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28 pages, 6746 KB  
Article
Nonlocal Analysis of the Flexural–Torsional Stability for FG Tapered Thin-Walled Beam-Columns
by Masoumeh Soltani, Farzaneh Atoufi, Foudil Mohri, Rossana Dimitri and Francesco Tornabene
Nanomaterials 2021, 11(8), 1936; https://doi.org/10.3390/nano11081936 - 27 Jul 2021
Cited by 11 | Viewed by 3217
Abstract
This paper addresses the flexural–torsional stability of functionally graded (FG) nonlocal thin-walled beam-columns with a tapered I-section. The material composition is assumed to vary continuously in the longitudinal direction based on a power-law distribution. Possible small-scale effects are included within the formulation according [...] Read more.
This paper addresses the flexural–torsional stability of functionally graded (FG) nonlocal thin-walled beam-columns with a tapered I-section. The material composition is assumed to vary continuously in the longitudinal direction based on a power-law distribution. Possible small-scale effects are included within the formulation according to the Eringen nonlocal elasticity assumptions. The stability equations of the problem and the associated boundary conditions are derived based on the Vlasov thin-walled beam theory and energy method, accounting for the coupled interaction between axial and bending forces. The coupled equilibrium equations are solved numerically by means of the differential quadrature method (DQM) to determine the flexural–torsional buckling loads associated to the selected structural system. A parametric study is performed to check for the influence of some meaningful input parameters, such as the power-law index, the nonlocal parameter, the axial load eccentricity, the mode number and the tapering ratio, on the flexural–torsional buckling load of tapered thin-walled FG nanobeam-columns, whose results could be used as valid benchmarks for further computational validations of similar nanosystems. Full article
(This article belongs to the Special Issue Advanced Mechanical Modeling of Nanomaterials and Nanostructures)
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15 pages, 4666 KB  
Article
Measurement of Stress Waves Propagation in Percussive Drilling
by Diego Scaccabarozzi and Bortolino Saggin
Sensors 2021, 21(11), 3677; https://doi.org/10.3390/s21113677 - 25 May 2021
Cited by 8 | Viewed by 3348
Abstract
This work describes the results of a test campaign aimed to measure the propagation of longitudinal, torsional, and flexural stress waves on a drill bit during percussive rock drilling. Although the stress wave propagation during percussive drilling has been extensively modeled and studied [...] Read more.
This work describes the results of a test campaign aimed to measure the propagation of longitudinal, torsional, and flexural stress waves on a drill bit during percussive rock drilling. Although the stress wave propagation during percussive drilling has been extensively modeled and studied in the literature, its experimental characterization is poorly documented and generally limited to the detection of the longitudinal stress waves. The activity was performed under continuous drilling while varying three parameters, the type of concrete, the operator feeding force, and the drilling hammer rotational speed. It was found that axial stress wave frequencies and spectral amplitudes depend on the investigated parameters. Moreover, a relevant coupling between axial and torsional vibrations was evidenced, while negligible contribution was found from the bending modes. A finite element model of the drill bit and percussive element was developed to simulate the impact and the coupling between axial and torsional vibrations. A strong correlation was found between computed and measured axial stress spectra, but additional studies are required to achieve a satisfactory agreement between the measured and the simulated torque vibrations. Full article
(This article belongs to the Section Physical Sensors)
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26 pages, 827 KB  
Article
A Comprehensive Framework for Coupled Nonlinear Aeroelasticity and Flight Dynamics of Highly Flexible Aircrafts
by Chi Zhang, Zhou Zhou, Xiaoping Zhu and Lina Qiao
Appl. Sci. 2020, 10(3), 949; https://doi.org/10.3390/app10030949 - 1 Feb 2020
Cited by 4 | Viewed by 3895
Abstract
A framework to model and analyze the coupled nonlinear aeroelasticity and flight dynamics of highly flexible aircrafts is presented. The methodology is based on the dynamics of 3D co-rotational beams. The coupling of axial, bending and torsional effects is added to the stiffness [...] Read more.
A framework to model and analyze the coupled nonlinear aeroelasticity and flight dynamics of highly flexible aircrafts is presented. The methodology is based on the dynamics of 3D co-rotational beams. The coupling of axial, bending and torsional effects is added to the stiffness and mass matrices of Euler–Bernoulli beam to capture the most relevant characteristics of a real wing structure. The finite-state aerodynamic model is coupled with the structural model to simulate the unsteady aerodynamics. A scheme of mixed end-point and mid-point time-marching algorithms is proposed and applied into the implicit predictor–corrector integration, where the end-point algorithm is used in the predictor step for efficiency and mid-point algorithm in corrector step for accuracy. The ground, body and airflow axes for flight dynamics are re-defined by the global and elemental ones for structural dynamics, followed by the redefinitions of local Euler angles and airflow angles of each element. The framework can be used for quick analyses of flexible aircrafts in conceptual and preliminary design phases, including linear and nonlinear trim, aerodynamic load estimation, stability assessment, time-domain simulations and flight performance evaluations. The results show the payload mass and its distributions will significantly affect the trim state and longitudinal stability of highly flexible aircrafts. Full article
(This article belongs to the Section Mechanical Engineering)
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