Structural instability, in particular postbuckling resulted in predefined constraints, has been performing advantages in many applications given their promising mechanical characteristics. However, inadequate studies have been conducted to effectively control and tune the postbuckling behavior of bilaterally constrained nonuniform beams. This study develops postbuckling systems comprised of multiple nonuniform beams subjected to bilateral confinements. Theoretical model is developed using Euler-Bernoulli theory and small deformation assumptions to predict postbuckling response of the beam systems under quasi-static axial loading. To locate the minimum energy path of the deformed beam system, the minimization problem of total potential energies of the bi-walled beam systems is solved by Nelder-Mead algorithm. Snap-through transitions of buckled systems are shown by drops in the response curves. To validate the developed model with existing models in literature, the model was simplified to account for single uniform beam under displacement control. The proposed model is experimentally and numerically validated, and satisfactory agreements are obtained. Parametric studies are carried out to investigate the influence of varying the geometric parameters (i.e., length, thickness) of the nonuniform beams on the tunable systems. Using the presented theoretical model, the postbuckling events can be accurately controlled by the geometry properties of the nonuniform beams.

Many structures are subjected to varying forces, moving boundaries, and other dynamic conditions. Whether part of a vehicle, building, or active energy mitigation device, data on such changes can represent useful knowledge, but also presents challenges in its collection and analysis. In systems where changes occur rapidly, assessment of the system’s state within a useful time span is required to enable an appropriate response before the system’s state changes further. Rapid state estimation is especially important but poses unique difficulties. In determining the state of a structural system subjected to high-rate dynamic changes, measuring the frequency response is one method that can be used to draw inferences, provided the system is adequately understood and defined. The work presented here is the result of an investigation into methods to determine the frequency response, and thus state, of a structure subjected to high-rate boundary changes in real-time. In order to facilitate development, the Air Force Research Laboratory created the DROPBEAR, a testbed with an oscillating beam subjected to a continuously variable boundary condition. One end of the beam is held by a stationary fixed support, while a pinned support is able to move along the beam’s length. The free end of the beam structure is instrumented with acceleration, velocity, and position sensors measuring the beam’s vertical axis. Direct position measurement of the pin location is also taken to provide a reference for comparison with numerical models. This work presents a numerical investigation into methods for extracting the frequency response of a structure in real-time. An FFT based method with a rolling window is used to track the frequency of a data set generated to represent the range of the DROPBEAR, and is run with multiple window lengths. The frequency precision and latency of the FFT method is analyzed in each configuration. A specialized frequency extraction technique, Delayed Comparison Error Minimization, is implemented with parameters optimized for the frequency range of interest. The performance metrics of latency and precision are analyzed and compared to the baseline rolling FFT method results, and applicability is discussed.

In this paper, we propose a novel gradient index metamaterial lens to focus elastic wave energy in polymer pipes. We investigate multi-mode focusing of guided ultrasonic waves in a poly-vinyl chloride (PVC) pipe by designing and integrating an embedded gradient index (GRIN) lens within the pipe wall. The metamaterial lens is composed of equally spaced cylindrical brass inserts embedded into the pipe wall. All the inserts are of same height which is equal to the half-thickness of the pipe. Insert diameters are varied in circumferential direction to realize hyperbolic secant distribution of refractive index around the circumference of pipe. We explore focusing of three pipe wave modes commonly used for guided wave inspection of pipelines namely, L(0,2), L(0,1) and T(0,1), using a single lens design. We further verify the lens performance through numerical simulations estimating the amplification of wave energy in focal regions of the GRIN lens for these three modes. We also estimate attenuation of guided waves propagating in PVC pipe through experimental measurements.

Motivated by its success as a structural health monitoring solution, electromechanical impedance measurements have been utilized as a means for non-destructive evaluation of conventionally and additively manufactured parts. In this process, piezoelectric transducers are either directly embedded in the part under test or bonded to its surface. While this approach has proven to be capable of detecting manufacturing anomalies, instrumentation requirements of the parts under test have hindered its wide adoption. To address this limitation, indirect electromechanical impedance measurement, through instrumented fixtures or testbeds, has recently been investigated for part authentication and non-destructive evaluation applications. In this work, electromechanical impedance signatures obtained with piezoelectric transducers indirectly attached to the part under test, via an instrumented fixture, are numerically investigated. This aims to better understand the coupling between the instrumented fixture and the part under test and its effects ON sensitivity to manufacturing defects. For this purpose, numerical models are developed for the instrumented fixture, the part under test, and the fixture/part assembly. The frequency-domain spectral element method is used to obtain numerical solutions and simulate the electromechanical impedance signatures over the frequency range of 10–50 kHz. Criteria for selecting the frequency range that is most sensitive to defects in the part under test are proposed and evaluated using standard damage metric definitions. It was found that optimal frequency ranges can be preselected based on the fixture design and its dynamic response.

A machine learning algorithm that performs multifidelity domain decomposition is introduced. While the design of complex systems can be facilitated by numerical simulations, the determination of appropriate physics couplings and levels of model fidelity can be challenging. The proposed method automatically divides the computational domain into subregions and assigns required fidelity level, using a small number of high fidelity simulations to generate training data and low fidelity solutions as input data. Unsupervised and supervised machine learning algorithms are used to correlate features from low fidelity solutions to fidelity assignment. The effectiveness of the method is demonstrated in a problem of viscous fluid flow around a cylinder at Re ≈ 20. Ling et al. built physics-informed invariance and symmetry properties into machine learning models and demonstrated improved model generalizability. Along these lines, we avoid using problem dependent features such as coordinates of sample points, object geometry or flow conditions as explicit inputs to the machine learning model. Use of pointwise flow features generates large data sets from only one or two high fidelity simulations, and the fidelity predictor model achieved 99.5% accuracy at training points. The trained model was shown to be capable of predicting a fidelity map for a problem with an altered cylinder radius. A significant improvement in the prediction performance was seen when inputs are expanded to include multiscale features that incorporate neighborhood information.

It has been amply demonstrated that the development of SMA actuators has a great potential of application in several branches of industry. Obviously, the efficiency of the actuators depends both on the inherent features of the materials they are made of and the geometric characteristics of the devices. This work considers a particular type of actuator first conceived by [1], consisting in the association of two cantilever beams, the first presenting the shape memory effect and the second presenting the superelastic effect, coupled mechanically so as to guarantee two equilibrium positions and thus a stand-alone cyclic actuator, in which the superelastic beam provides the bias action. Numerical simulations of the behavior of the actuator are performed using the commercial finite element software COMSOL, which implements the Boyd-Lagoudas thermomechanical model. The goal of the simulations is to characterize the actuation range of the actuator, in terms of maximum displacement obtained at the tip. The effect of the dimensions of the beams on the tip displacement under some load scenarios is investigated. The results provide guidelines for the design of the actuator to fulfill specific requirements, also suggesting the use of numerical optimization for the optimal design of the actuator accounting for constraints.

In this paper, an hybrid mass dampers (HMD) and its control law are studied. Based on a optimal tuned mass damper (TMD), it is a one degree of freedom (dof) mass-spring system associated with an electromagnetic system. The passive damping is provided by the coil-magnet combination coupled with a tunable load. The passive resonator has been modify to become “dual”, a second coil-magnet combination has been had on the same dof to create an active part. The control law is a modified velocity feedback with phase compensator. The proposed hybrid system controller is hyperstable and ensure a fail-safe behavior. The HMD is experimentally tested at 1:1 scale. It is carried out on a main structure suspended by flexible blades. The numerical model, with experimental parameters identification, provides good results. Under shock disturbance, experimental results show the ability of this system to react quickly and dissipate energy in comparison with the passive one.

Dispersion relations describe the frequency-dependent nature of elastic waves propagating in structures. Experimental determination of dispersion relations of structural components, such as the floor of a building, can be a tedious task, due to material inhomogeneity, complex boundary conditions, and the physical dimensions of the structure under test. In this work, data-driven modeling techniques are utilized to reconstruct dispersion relations over a predetermined frequency range. The feasibility of this approach is demonstrated on a one-dimensional beam where an exact solution of the dispersion relations is attainable. Frequency response functions of the beam are obtained numerically over the frequency range of 0–50kHz. Data-driven dynamical model, constructed by the vector fitting approach, is then deployed to develop a state-space model based on the simulated frequency response functions at 16 locations along the beam. This model is then utilized to construct dispersion relations of the structure through a series of numerical simulations. The techniques discussed in this paper are especially beneficial to such scenarios where it is neither possible to find analytical solutions to wave equations, nor it is feasible to measure dispersion curves experimentally. In the present work, actual experimental data is left for future work, but the complete framework is presented here.

The adaptation of a wing contour is important for most aircraft, because of the different flight states. That’s why an enormous number of mechanisms exists and reaches from conventional slats and flaps to morphing mechanisms, which are integrated in the wing. Especially integrated mechanisms reduce the number of gaps at the wing skin and produce less turbulent flow. However these concepts are located at a certain section of the wing. This leads to morphing and fixed wing sections, which are located next to each other. Commonly, the transition between these sections is not designed or a wing fence is used. If the transition is not designed, the wing has a step with an activated morphing mechanism and that produces additional vortices. A new skin design will be presented in order to smooth the contour between a fixed wing and a morphing wing. Here the transition between a droop nose and a fixed wing is considered. The skin material is a mix of ethylene propylene diene monomer rubber and glass-fiber reinforced plastic. The rubber is the baseline material, while the glass-fiber is added as stripes in chord-wise direction. In span-wise direction the glass fiber is connected with the rubber. The rubber carries the loads in span-wise direction and reduces the required actuation force. The glass fiber stiffens the skin locally in chord wise direction and keeps the basic contour of the skin. Some geometrical parameters within the skin layup can be varied to change the transition along the span or to reduce the maximum strain within the skin. The local strain maximum is a result of the material transition with different modules. One design of a leading edge was manufactured with an existing mold and it has a span of 200 mm. There are two essential aspects from a structural point of view. One is a nearly continuous deformation along the span and the second is the maximum strain in the rubber. Both aspects are investigated in an experiment and the results are compared with a simulation model. The results show a reliable concept and its numerical model, which will be assigned to a full scale demonstrator. This demonstrator will have a span of 1000 mm and will show the smooth skin transition between a droop nose and a fixed wing.

Magnetorheological fluid is a special smart fluid which can show different rheological properties under different magnetic flux densities due to its magnetically sensitive structure. This makes the fluid able to be manipulated and semi-actively controlled for various applications such as dampers, clutches and brakes. To provide an effective damping it is necessary to create an appropriate control algorithm. In order to design a structure with magnetorheological fluid and to get an idea for a control approach, the physics of the fluid motion has to be modelled. Computational Fluid Dynamics is an effective tool to model any fluid behaviour or any fluid involved structure. For magnetorheological devices, despite number of numerical models available in the literature, a befitting model is not yet presented. In this study a mapped rheological model is proposed and used in a magnetorheological damper simulation. The results are compared with other models and experimental data. It is shown that the new mapped model is effective and better than old approaches. It also showed a good agreement with the experimental data.

Impulsive energy provides a promising source for energy harvesting techniques due to their high amplitude and abundance in a living environment. The sensitivity to excitation of bistable energy harvesters makes them feasible for impulsive-type events. In this paper, a novel impulsively-excited bistable energy harvester with rotary structure and plectrum is proposed to achieve plucking-based frequency up-conversion. The input excitation is converted to plucking force on the bistable energy harvester, so as to help it go into the high-energy orbit. The piezoelectric and electromagnetic transduction mechanisms are combined by incorporating a coil to the structure in order to overcome the increase of damping introduced by the bistable configuration. As a result, high-energy output and broadband performance could be realized. Impact mechanics is employed to develop a comprehensive model, which could be used to analyze the nonlinear dynamics and predict the system responses under various plucking velocities and overlap lengths. Numerical simulation shows that the bistable energy harvester could experience large-amplitude oscillation under impulsive excitation and the hybrid configuration outperforms the standalone ones under high damping ratio and low coupling coefficient. The proposed design is targeted to be applied on the turnstile gates of the subway station. Less human effort would be needed when passengers pass the turnstile gate due to the snap-through motion of bistability.

Ultrasonic atomization of bulk liquids has received extensive attention in the past few decades due to the ability to produce controlled droplet sizes, a necessity for many industries such as spray coating and aerosol drug delivery. Despite the increase in attention, one novel application of this technology has been overlooked until recently, and that is the moisture removal capabilities of atomization. The first ever ultrasonic dryer, created by researchers at Oak Ridge National Lab in 2016, applies the mechanisms of atomization to mechanically remove moisture from clothing. The process utilizes the ultrasonic vibrations created by a piezoelectric transducer in direct contact with a wet fabric to rupture the liquid-vapor boundary of the retained water. Once ruptured, smaller droplets are ejected from the bulk liquid and are actively removed from the fabric pores. The mechanisms of droplet ejection from this event are related to both capillary waves forming on the liquid surface (Capillary Wave Theory), as well as the implosion of cavitation bubbles formed from the hydraulic shocks propagating from the transducer (Cavitation Theory). In this work, we present an analytical model for predicting the moisture removal rate of a wet fabric exposed to ultrasonic vibrations, and connect the atomization events to a global variable, acceleration, in order to decouple the relationship between the transducer and applied voltage. The acceleration governing atomization is predicted using a verified numerical model. The numerical model is shown to assist in developing ultrasonic drying by means of efficiently evaluating transducer design changes.

Future manned space missions will require thermal control systems that can adapt to larger fluctuations in temperature and heat flux that exceed the capabilities of current state-of-the-art systems. These missions will demand novel space radiators that can vary the heat rejection rate of the system to maintain the crew cabin at habitable temperatures throughout the entire mission. Current systems can provide a turndown ratio (defined as the ratio of maximum to minimum heat rejection) of 3:1 under adverse conditions. However, future missions are projected to demand thermal control systems that can provide a turndown ratio of more than 6:1. A novel radiator concept, known as the morphing radiator, varies the system heat rejection rate by altering the shape of the radiator that is exposed to space. This shape change is accomplished through the use of shape memory alloys, a class of active materials that exhibit thermomechanically-driven phase transformations and can be used as both sensors and actuators in thermal control applications. In past efforts, prototype morphing radiators have been tested in a relevant thermal environment, demonstrating the feasibility and scalability of the concept. This work summarizes the progress towards testing a high-performance morphing radiator in a relevant thermal environment and details the development of an efficient numerical model that predicts the mechanical response of an arbitrary morphing radiator configuration due to changes in temperature. Model predictions are then validated against previous experimental results, demonstrating the usefulness of the model as a design tool for future morphing radiator prototypes.

Computational modeling, instrumented linkages, optical technologies, MRI, and radiographic techniques have been widely used to study knee motion after total knee replacement (TKR) surgery. Information provided by these methods has helped designers to develop implants with better clinical performance and surgeons to obtain an improved understanding of the stability and mobility of the joint. Correspondingly, overall patient satisfaction with respect to the reduction in pain and recovery of normal functioning of the joint has been improving. However, about 20% of patients are still not fully satisfied with their surgical outcomes. The main obstacle in the current state-of-the-art is that a comprehensive post-operative understanding of knee balance is still unavailable, mostly due to a lack of in vivo data collected from the joint after surgery. This work presents an attempt to develop a self-powered instrumented knee implant for in vivo data acquisition. The knee sensory system in this study utilizes several embedded piezoelectric transducers in the tibial bearing of the knee replacement in order to provide sensing and energy harvesting capabilities. Through a series of analytical modeling, finite element simulation, and experimental testing, the performance of the suggested system is evaluated and a dimensionally optimized design of an instrumented TKR is achieved. More specifically, a comprehensive platform is established in order to combine the knowledge of embedded piezoelectric sensors and energy harvesters, musculoskeletal modeling of the knee joint, multiphysics finite element modeling, additive manufacturing techniques, image processing, and experimental knee loading simulation in order to achieve the experimentally validated and optimized instrumented knee implant design. The cumulative work presented in this article encompasses three main studies performed on the sensing performance of the proposed design: first, preliminary parametric studies of the effect of local dimensional and material parameters on the electromechanical behavior of the embedded sensory system; second, investigation of the ability to sense total force and center of pressure location; and third, evaluation of an enhanced system with the ability to sense compartmental forces and contact locations. Additionally, the energy harvesting capacity of the system is investigated to ensure the achievement of a fully self-powered sensory system. Results obtained from the experimental analysis of the system demonstrate the successful sensing and energy harvesting performance of the designs achieved in this study.

This research investigates a quasi-zero stiffness (QZS) property from the pressurized fluidic origami cellular solid, and examines how this QZS property can be harnessed for low-frequency base excitation isolation. The QZS property originates from the nonlinear geometric relations between folding and internal volume change, and it is directly correlated to the design parameters of the constituent Miura-Ori sheets. Two different structures are studied to obtain a design guideline for achieving QZS: one is identical stacked Miura-Ori sheets (ismo) and the other is non-identical stacked Miura-Ori sheets (nismo). Further dynamic analyses based on numerical simulation and harmonic balance method, indicate that the QZS from pressurized fluidic origami can achieve effective base excitation isolation at low frequencies. Results of this study can become the foundation of origami-inspired metamaterials and metastructures with embedded dynamic functionalities.

The present study concerns with the performance of a skid landing gear (SLG) system of a rotorcraft impacting the ground at a vertical sink rate of 5.0 m/s. The impact attitude is per chapter 527 of the Airworthiness Manual (AWM) of Transport Canada Civil Aviation and FAR Part 27 of the U.S. Federal Aviation Regulation. A single degree of freedom helicopter model is investigated under two rotor lift factors 0.67 and 1.0. Three Configurations are evaluated: a) A conventional SLG; b) SLG equipped with a passive viscous damper and c) SLG incorporated with a magnetorheological energy absorber. The non-dimensional solutions of the helicopter model show that the passive damper system could reduce the maximum acceleration experienced by the helicopter occupants by 21% and 19.8% in comparison to the undamped system for the above rotor lift factors, respectively. However, the passive damper fails to constrain the non-dimensional energy absorption stroke of the damper within the given 18 cm maximum stroke and a bottoming out of the damper piston was noticed. Therefore, the alternative and successful choice was to employ a magnetorheological energy absorber (MREA). To improve the MREA controllability and to resettle the payload with no oscillations, i.e. in one cycle, two different Bingham numbers for compression stroke and rebound stroke were defined in the non-dimensional solution. Several simulations were conducted for different values of Bingham numbers. Among these numerical simulation results, the solution that implemented the optimum Bingham numbers was found to be the only one feasible solution. In this case the MREA with optimum Bingham number for compression could utilize the full energy absorption stroke to attain soft landing. In the rebound stroke, the generated optimal on-state damping force successfully controls the bounce of the payload until the payload settles down to its original equilibrium position with no oscillations.

Postbuckling response, long considered mainly as a failure limit state is gaining increased interest for smart applications, such as energy harvesting, frequency tuning, sensing, actuation, etc. Cylindrical shells have received less attention as structural form to harness elastic instabilities due to their increased modeling complexity and high imperfection sensitivity. Yet, preliminary experimental and computational evidence indicates that the elastic postbuckling response of cylindrical shells can be controlled and potentially managed. Further, cylindrical shells offer desirable features for the design of mechanical devices and adaptive structures that other forms cannot attain without additional external constraints. This paper presents a study on tailoring the elastic postbuckling response of thin-walled cylindrical shells under compression by means of non-uniform wall stiffness distributions. The pattern of stiffness distribution was designed by discretizing the shell surface into cells and thickening selected cells with respect to a baseline uniform wall thickness. Diverse patterns were characterized in the way of how they affect the postbuckling response through numerical simulations using the finite element method. Results show that the elastic postbuckling response can be tailored into three response types: softening, sustaining, and stiffening; and that number, sequence/time and location/space of localized buckling events can be designed. This work provides new knowledge on the means to design the cylindrical shells with controlled elastic postbuckling behavior for applications in smart materials, mechanical devices, and adaptive structures.

Controlled drug delivery (CDD) technology has received extensive attention in the past three decades due to numerous advantages of this technology when compared to the conventional methods. Despite recent efforts and substantial achievements, controlled drug releasing systems still face major challenges in practice, including chemical issues with synthesizing biocompatible drug containers and releasing the pharmaceutical compounds at the targeted location with a controlled time rate. In this work, we present experimentally-validated acoustic-thermoelastic mathematical modeling to show the feasibility of using shape memory polymers (SMPs) and focused ultrasound (FU) technology for designing a novel drug-delivery system. SMPs represent a new class of materials that have the ability of storing a temporary shape and returning to their permanent or original shape when subjected to external stimuli such as heat. FU is used as a trigger for noninvasively stimulating SMP-based drug capsules. FU has a superior capability to localize the heating effect, thus initiating the shape recovery process only in selected parts of the polymer. A multiphysics model is developed, which optimizes the design of a SMP-based CDD system using acoustic-thermoelastic analysis of a filament as the constituting base structure and quantifies its activation through FU. The analytical and numerical models are divided into three parts. The first part studies the acoustic behavior of SMPs using Khokhlov-Zabolotskaya-Kuznetsov (KZK) model. The equation solves for acoustic pressure field in a hybrid time-frequency domain using operator-splitting method and examines the effects of absorption, diffraction and nonlinear distortion on the propagating wave in the medium. The second part provides a numerical model based on Penne’s Bioheat equation to estimate the thermal field developed in SMPs as a result of focused acoustic pressure field. The third part provides a numerical framework to predict the mechanical stresses developed in SMPs under FU and consequent shape recovery. The mechanical model is formulated by a compressible neo-Hookean constitutive equation, which assumes the SMPs behave as a thermoelastic material and predicts the shape memory effect under FU. Experimental validation is performed using a FU transducer in a water tank. The recovery of thermally responsive SMPs under FU predicted by our model shows a good accordance with the experiments. The modeling results are used to optimize parameters such as nonlinear properties, input frequency, source power and dimensional effects to achieve maximum shape recovery.

Origami-inspired mechanical metamaterials could exhibit extraordinary properties that originate almost exclusively from the intrinsic geometry of the constituent folds. While most of current state of the art efforts have focused on the origami’s static and quasi-static scenarios, this research explores the dynamic characteristics of degree-4 vertex (4-vertex) origami folding. Here we characterize the mechanics and dynamics of two 4-vertex origami structures, one is a stacked Miura-ori (SMO) structure with structural bistability, and the other is a stacked single-collinear origami (SSCO) structure with locking-induced stiffness jump; they are the constituent units of the corresponding origami metamaterials. In this research, we theoretically model and numerically analyze their dynamic responses under harmonic base excitations. For the SMO structure, we use a third-order polynomial to approximate the bistable stiffness profile, and numerical simulations reveal rich phenomena including small-amplitude intrawell, large-amplitude interwell, and chaotic oscillations. Spectrum analyses reveal that the quadratic and cubic nonlinearities dominate the intrawell oscillations and interwell oscillations, respectively. For the SSCO structure, we use a piecewise constant function to describe the stiffness jump, which gives rise to a frequency-amplitude response with hardening nonlinearity characteristics. Mainly two types of oscillations are observed, one with small amplitude that coincides with the linear scenario because locking is not triggered, and the other with large amplitude and significant nonlinear characteristics. The method of averaging is adopted to analytically predict the piecewise stiffness dynamics. Overall, this research bridges the gap between the origami quasi-static mechanics and origami folding dynamics, and paves the way for further dynamic applications of origami-based structures and metamaterials.

Along with recent advancements in novel materials and manufacturing processes, the interest in morphing wings has increased in order to further improve the aerodynamic performance of flying bodies. The morphing wing can be tailored to deliver superior performance, compared to its non-morphing counterparts, for multiple operating conditions and in varying flows. In particular, the morphing wing is implemented for drag reduction and lift enhancement, and hence, the maneuverability, adaptability, and capability of the morphing wing can encompass an even wider spectrum by changing the wing shape. In this research, an existing morphing UAV wing design, Spanwise Morphing Trailing Edge (SMTE), actuated by bending Macro Fiber Composites (MFCs), is considered to generate the spanwise sinusoidal variations on the trailing edge of the morphing wing. A comparative aerodynamic study of the morphing wing by varying the spatial frequency ( i.e. , number of waves along the span) and the phase shift ( i.e. , wave shape along the span) at different angles of attack is conducted through analytical approaches and numerical Computational Fluid Dynamic (CFD) simulations, which are validated with previous experimental measurements. The analytical approach uses the three-dimensional (3D) Prandtl lifting line theory, and the CFD modeling in turbulence flow solves the 3D Reynolds-Averaged Navier-Stokes (RANS) equations with the k-ω Shear Stress Transport (SST) turbulence model. Note that the numerical simulations of a morphing wing focus on the pre-stall condition to estimate the aerodynamic performance. This work extends a prior study about a nominal flight condition testing a morphing wing at multiple flight conditions to evaluate multi-point 1 performance. The results show that there are governing aerodynamic efficiency zones of the lift-to-drag ratio, endurance, and aircraft range within a zone of angles of attack. Therefore, the morphing wing is shown to have a good aerodynamic performance as compared to the non-morphing wing.