Morphing Structures Research Articles

Impact of continuously extending/retracting wall on Mack-mode evolution in hypersonic boundary layers

Structural morphing is regarded as a potential solution for future space transportation systems, necessitating aircraft capable of extensive altitude ranges, wide speed ranges, and multi-regime operations. The investigation of laminar-turbulent transition incorporating morphing effects aims to compensate for the lack of physical mechanisms in aircraft designs. This paper particularly focuses on the impact of a continuously extending or retracting wall in the chordwise direction on the evolution of inviscid Mack modes in a Mach 5.92 hypersonic boundary layer. Using the high-Reynolds-number asymptotic technique, a model is developed to quantify the morphing effect by an amplification factor, which includes both the scattering effect at the rigid-morphing junction and the successive modification of the Mack growth rate by the morphing velocity in the downstream region. Such a model enables us to conduct a comprehensive investigation across a wide parameter space defined by morphing speed and flow parameters. A critical frequency is identified near the most unstable second-mode frequency. For an extending wall, the oncoming Mack modes are suppressed for frequencies above this critical frequency and enhanced for frequencies below it. Conversely, the retracting-wall effect exhibits an inverse impact on the Mack modes. To validate the accuracy of the asymptotic predictions, the harmonic linearized Navier–Stokes calculations are performed, resulting in favorable agreements. This research sheds light on the complex interplay between wall morphing and the Mack-mode evolution, offering informative contributions to the understanding of the aerodynamic behaviors in hypersonic boundary layers.

Multi-layered morphing soft structure with high-performance embedded electrothermal artificial muscles along with touch and temperature sensors

Abstract In this paper, we present a novel multilayered morphing structure, having similar topology resembling the structures found in nature to grasp delicate objects effectively as well as sense contact force and temperature. The structure consists of two actuation layers, two U-shaped cooling channel layers, piezoelectric based touch sensors and temperature sensors. Employing shape memory alloy (SMA) spring actuators for bending and twisted and coiled polymer fishing line with nichrome (TCPFL NMC) artificial muscles for antagonistic return, the soft silicone-based composite skin exhibits unique capabilities of large bidirectional movement, avoid rigid passive springs for return motion, soft grasping, safe interaction with humans, and ease fabrication. The SMA (0.38 mm wire diameter) serves as relatively fast actuating muscle and the TCPFL NMC (0.8 mm fiber diameter) as a slow actuating (considering mainly heating cycle), which was programmed/designed to mimic the fast and slow twitching muscles found in nature. Bending and return operations of skin samples of length 100 mm and thickness of 9 mm, with three different widths 20 mm, 25 mm, 30 mm, were experimentally studied. The 25 mm wide multilayered soft skin demonstrated cyclic actuation with a maximum bending angle of ∼70°, which was attributed due to the active cooling. The fluidic channels for active cooling were fabricated using 3D printed PVA tubes, casting within the silicone in a mold and subsequently dissolving in a circulating water. The study also included the integration and voltage response of mini-piezodisk sensor PIC255 having a diameter of 2 mm and thickness of 0.15 mm, which was embedded at different depths within the silicone (on the surface, 1 mm depth and 2 mm depth). The multilayered soft skin was also able to detect the temperature of the object during grasping, suggesting its potential application as a soft gripper in robotic systems.

Integration of the passive energy balancing based actuation system into a camber morphing design

A spiral pulley mechanism can be used to passively balance the energy between the morphing structure and actuation system. Applying the energy balancing concept has the potential to improve the performance of the actuation system by reducing the external energy consumption. In the current study, the integration workflow for the passive energy balancing device is established and is adopted in a variable camber morphing wing. The design variables of the passive energy balancing system are optimised and the effects of the different parameters are discussed together with the adaptability of the passive energy balancing device when the load stiffness changes. An integrated demonstrator was also built to validate the mechanism by measuring the currents in the process of morphing actuation.

A starfish-inspired 4D self-healing morphing structure

Inspired by the starfish's unique ability to achieve flexibility and posture-holding with minimal energy expenditure, we present a novel bioinspired morphing structure. Our two-component design, consisting of a thermoplastic mesh and elastomeric jacket, effectively mimics the functions of the starfish's ossicles, mutable collagenous tissues, and derma. This structure exhibits a remarkable combination of self-healing, time-dependent shape memory, and self-posture-holding properties. Systematic variations in mesh geometry demonstrate precise control over structural stiffness and thermal response, enabling customization for specific applications. The structure's scalability and ease of fabrication further enhance its adaptability. We experimentally demonstrate the potential of our biomimetic morphing structure using several prototypes. This work lays the foundation for developing a new type of versatile morphing structures with applications in diverse fields, including robotics, biomedical devices, and adaptive structures.

Dynamic stability and response of morphing wing structure with time-varying stiffness

Abstract Morphing, adaptable or smart structures are being used in mechanical and aerospace applications in recent years. These structures often have the property of time-varying stiffness or inertial properties, which can cause parametric instability issues that are not well understood. This paper examines the dynamic stability and response of a morphing aircraft wing with periodically time-varying structural stiffness. The wing is modeled as a beam with coupled bending-torsion motion, and parametrically excited stiffness. Aerodynamic loads introduce aerodynamic damping and aerodynamic stiffness to the wing structure. The dynamic and aeroelastic equation of motion resembles a coupled, damped Mathieu-type equation but differs with asymmetric damping and stiffness matrices, and symmetric inertial matrix. Further, these equations are functions of airspeed, magnitude and frequency of parametric excitation. Initially, dynamic stability of the wing is analyzed using Floquet theory, and the instability regions are numerically quantified by stability charts. Subsequently, dynamic responses in the stable and unstable regions are investigated with a Floquet-based Harmonic balance method. The findings reveal that, at zero airspeed, the combination instabilities are eliminated by varying the bending and torsional stiffness with equal magnitudes and frequency. However, as airspeed increases, instability regions shift unevenly, leading to the emergence of new instabilities. Furthermore, the response analysis within stable regions uncovers several unfavorable zones for operating the variable stiffness, where response decay is slower. The results clearly show that parametric excitation can cause unusual phenomena that significantly impact the operation of morphing wings with variable stiffness, which needs to be thoroughly investigated for successful implementation.

Design and modeling of a programmable morphing structure with variable stiffness capability

The development of structures capable of both dynamic shape morphing and stiffness modulation has significant potential in various applications. However, such structures often suffer from bulkiness and control complexity. This paper addresses these challenges by exploring a scaled structure that integrates morphing capabilities and variable stiffness within a compact configuration. For the first time, we establish a comprehensive set of design criteria and obtain the previously unexplored design space, focusing on geometric parameters including layer thickness, target shape radius, the number of scales, and the number of periods per scale. Through extensive finite element simulations, we evaluate the impact of material property and geometric parameters on the performance of the scaled structure, emphasizing the role of coefficient of friction. Our findings identify a critical threshold for the coefficient of friction above which morphing ability is hindered. Additionally, we uncover a trade-off between morphing capability and stiffness variation ability, which we overcome by modifying the surface structure of the scales. The optimal design is found to be a superellipse shape with an exponent of ∼1.9. The practical potential of this structure is demonstrated through three applications: a soft gripper, a phone stand, and a foldable box, showcasing its versatility in real-world scenarios. This research provides a foundational approach for designing morphing scaled structures, offering valuable insights into optimizing morphing capability and stiffness variation ability for broader engineering applications.

Nonlinear effect on stable state and snap-through bistability of square composite laminate

Bistable structures with the elastic instability caused by buckling are confirmed to perform significantly in micro-electromechanical systems, metamaterials, energy harvester, vibration isolation and morphing structures. The target of this paper is to explore the dynamic responses of cross-ply bistable composite laminate, focusing on the nonlinear effect of the single- and double-well vibration. Both theoretical and finite element (FE) methods are employed to simulate the nonlinear vibration and dynamic snap-through of bistable composite laminate under the foundation excitation at the center. In the theoretical model, the governing equations are established via Lagrange's equation based on the first-order shear deformation theory, von Karman nonlinear strain-displacement relation and Rayleigh-Ritz method. The fourth-order Runge-Kutta method is adopted to solve the governing equations, and the numerical results are validated by FE model. Subsequently, the details of the dynamic responses are analyzed to identify the nonlinear effects in the form of bifurcation diagram, phase portrait, time history, Poincare maps and amplitude spectrum. The dynamic responses are examined for a series of excitation parameters in both time and frequency domain. Through fixed frequency and frequency sweep tests, the nonlinear phenomenon of the single- and double-well vibrations are analyzed including superharmonic resonance, stiffness softening, hysteresis phenomenon, various periodic and chaotic vibration. The diverse responses to external inputs contribute significantly to efficiently predicting mechanical behaviors in real-world conditions, thereby offering indispensable theoretical support for structural design applications.

Size-Dependent Finite Element Analysis of Functionally Graded Flexoelectric Shell Structures Based on Consistent Couple Stress Theory

The functionally graded (FG) flexoelectric material is a potential material to determine the structural morphing of aircrafts. This work proposes the penalty 20-node element based on the consistent couple stress theory for analyzing the FG flexoelectric plate and shell structures with complex geometric shapes and loading conditions. Several numerical examples are examined and prove that the new element can predict the size-dependent behaviors of FG flexoelectric plate and shell structures effectively, showing good convergence and robustness. Moreover, the numerical results reveal that FG flexoelectric material exhibits better bending performance and higher flexoelectric effect compared to homogeneous materials. Moreover, the increase in the material length scale parameter leads to a gradual increase in the natural frequencies of the out-of-plane modes of FG flexoelectric plate/shell, while the natural frequencies of the in-plane modes change minimally, resulting in the occurrence of mode-switching phenomena.

Hamiltonian formalism for bistable-multilayered plates under non-mechanical stimuli

Bistable multilayered plates have attracted significant attention as morphing and adaptive structures, renowned for their unprecedented exceptional performance. However, accurately predicting both their shape and internal stresses poses formidable challenges due to their geometrically nonlinear nature. For the first time, this paper introduces a Hamiltonian formalism aimed at achieving high-resolution analysis of nonlinear multilayered plates subjected to non-mechanical stimuli, including hygro-thermo-electro-magneto-elastic responses. A canonical system is strategically developed to compute membrane behaviors, yielding symplectic dual differential equations for in-plane field variables. This method elegantly decouples out-of-plane variables from the full-state vector, leading to an exact analytical solution in the membrane problem. To predict the bending behaviors, the first variation of the Hamiltonian energy density function, expressed as a power series of the transverse deflection, ensures flexural equilibrium. The power series effectively captures all admissible out-of-plane deformations, enabling a smooth transition between linear and nonlinear plate responses, including pitchfork bifurcation and limit points. The validity and accuracy of the proposed method are rigorously assessed through convergence tests and satisfaction of boundary conditions across various equilibria, ranging from monostability to bistability. It is cross-verified with high-fidelity finite-element methods (FEM), showing excellent agreements in both deformations and stress resultants. This research presents a physics-based methodology that unveils a parametric interplay between in-plane and out-of-plane field variables, serving as an efficient approach for analyzing adaptive and morphing structures.

Theoretical and experimental investigations on a data-driven trajectory planning scheme for dynamic shape control of piezo-actuated compliant morphing structures

Piezo-actuated compliant morphing structures can transmit motion and force via elastic deformation with lower weight, simplified design, and higher accuracy, a typical example is the variable camber wing. However, the rapid shape change of compliant structures is a challenging control problem because it often results in a high level of vibration due to the structural flexibility necessary to achieve the morphing requirement. This study presents a model-free data-driven trajectory planning approach based on spline curves and surrogate-based optimization (SBO) to obtain smooth “rest-to-rest” morphing trajectories. The macro-fiber composite (MFC) patches are used for piezoelectric actuators to generate elastic deformation. The flexible beam and variable camber wing are used for both linear numerical simulation and experimental tests with various nonlinearities and uncertainties. An optimization criterion is proposed to minimize both transient and residual vibrations during the “rest-to-rest” motion. An extraordinarily terminal displacement error function is added to eliminate the effects of the hysteresis and creep of the actuator. The control inputs, i.e., voltage profiles for the MFCs, are defined using cubic spline curves via only a few control points. Then, the optimization problem is solved by employing a Kriging surrogate model-based algorithm integrated with the expected improvement (EI) infilling-sampling criterion, which constructs an efficient algorithm similar to reinforcement learning. The optimal morphing trajectories can be highly efficiently obtained by using only 4 control points and less than 150 samplings. The experimental results of both the plate model and the variable camber wing model show that the proposed method can not only achieve a smooth dynamic morphing trajectory with minimized vibration but also automatically compensate for hysteresis and creep. The proposed method provides an effective means for the rapid realization of an optimized morphing trajectory for compliant morphing structures.

Numerical analysis of an innovative solar collector utilizing bistable composite laminates and macro fiber composite actuators

Innovative designs for solar collectors have attracted substantial academic and industrial interests owing to the high efficiency of solar panels in the recent past. This paper proposes the analysis and numerical design of a novel solar collector model composed of bistable laminates bonded with Macro Fiber Composite (MFC) actuators and solar cells. The bistable cross-ply laminate serves as the steering mechanism in this design by providing multiple stable shapes for the innovative solar collector design. Bistable morphing structures have received growing interest in aerospace structures and wind turbines due to their rapid shape-changing ability in response to changes in operating conditions, and this paper aims to integrate them more into the solar energy sector. The snap-through and snap-back motion of bistable laminates can be controlled by the voltage inputs of MFC actuators. The change of bistable laminate shape holds the solar cell in a position approximately at the latitude angle of the place to capture maximum solar energy. A systematic finite element parametric study has been performed to identify the optimum size and location of MFC actuators to achieve an energy-efficient snap-through and snap-back transition. As a result, a numerical design of a solar collector with six bistable elements has been proposed. In order to check the feasibility of the proposed designs, a numerical study has been performed to evaluate the total energy output and to optimize the solar panel tilt angle. ASHRAE’s solar irradiation model proposed in the literature has been used to identify the optimum solar panel tilt angle for maximum annual solar irradiation. This innovative solar collector model has demonstrated promising results, holds the potential for widespread application across various engineering domains, and paves the way for increased adoption of intelligent structures in everyday life.

The regenerative solar system. Unified theory of physics

The Euler’s holomorphic regenerative universe is a quantum-gravitational theory of Earth development recognizing that oxygen, hydrogen, nitrogen and carbon dioxide in the Earth’s hydrosphere engender biological processes along with living organisms able to reshape the planet as surely as any physical force, but with delayed effects, the so-called torsional/gravitational buckling lag. Herein, the environmental sciences as a Vernadsky’s hypothesis precursor to these, become vital for preserving biological recurrent cycles, their nature being artificially changed by a vicious human intervention. The present paper describes the thermal gravitational mechanism of a solar system associated with the regenerative processes of molecular structures (in biology called metabolism or growth) at the quantum-gravitational scale, too slow to be perceived. The term “morph” (or the concept of “morphing” in aeronautics, in mathematics called topological holomorphism) originates from ancient Greeks and refers to the shape, figure, or other related aspects of an evolving entity. Therefore, morphing/morphism pertains to the process of modifying the original form or appearance of a particular object or system. The planets of solar system like “cosmic organisms” can manipulate the curvature and twist of their surfaces to maintain precise control over their recurrent cyclical complex motions (double, orbital and sideral rotations) by the thermal gravitational waves. The out of order function of the thermal gravitational mechanism can lead to the global warming effects associated with both reshaping (earthquakes, fires, floods) surfaces and morphing (as a whole energy metabolism) mutations, crucial for perpetuity of human beings. At the same time, the concept of quantum-gravity light with a topological dual isomorphic structure solves the fundamental problem of a unified theory of physical forces, as kinematic fast dynamo electromagnetic forces for splitting quanta bonded into atomic structures, and persistent (long time) gravitational forces for non-splitting quanta bonded into thermomolecular morphing structures. The only problem remains to gauge such multiple cooperative physical phenomena induced by light, which is solved by diverse reciprocity/equivalence theorems and corresponding conversion factors.

Smart polymer composites with vertically oriented boron nitride and carbon fiber for heat management: Magneto-thermal responsiveness

Emerging structural materials for aerospace deformable structures, soft robotics, and advanced smart electronic devices necessitate reversible, lockable, and reprogrammable shape transformation capabilities. A challenge in this realm is heat accumulation in high-power density devices, which limited impedes broader applications of these materials. This study introduces magneto-thermal coupling response and efficient heat dissipation to structural composite, facilitating reversible and reprogrammable material deformation. Our composites prepared using bi-directional freeze casting strategy demonstrated excellent thermal management capabilities. When the composites were applied to the chip heat dissipation, the chip temperature was significantly reduced by 36.3 °C from 112.2 °C. Furthermore, the integration of a flexible boron nitride nanosheets (BNNS)/carbon fibers (CFs) network with magnetic Fe3O4 particles and phase-change material enables effective magneto-thermal response. This magnetically controlled thermal deformation behavior of composites provides a promising avenue for the development of multimodal morphing structures for soft robotics and aerospace applications.

Easy-to-actuate multi-compatible truss structures with prescribed reconfiguration

Multi-stable structures attract great interest because they possess special energy landscapes with domains of attraction around the stable states. Consequently, multi-stable structures have the potential to achieve prescribed reconfiguration with only a few lightweight actuators (such as shape-memory alloy springs), and do not need constant actuation to be locked at a stable state. However, most existing multi-stability designs are based on assembling bi-stable unit cells, which contain multitudes of distractive stable states, diminishing the feasibility of reconfiguration actuation. Another type is by introducing prestress together with kinematic symmetry or nonlinearity to achieve multi-stability, but the resultant structure often suffers the lack of stiffness. To help address these challenges, we firstly introduce the constraints that a truss structure is simultaneously compatible at multiple (more than two) prescribed states. Then, we solve for the design of multi-stable truss structures, named multi-compatible structures in this paper, where redundant stable states are limited. Secondly, we explore minimum energy paths connecting the designed stable states, and compute for a simple and inaccurate pulling actuation guiding the structure to transform along the computed paths. Finally, we fabricated four prototypes to demonstrate that prescribed reconfigurations with easy-actuation have been achieved and applied a quadra-stable structure to the design of a variable stiffness gripper. Altogether, our full-cycle design approach contains multi-stability design, stiffness design, minimum-energy-path finding, and pulling actuation design, which highlights the potential for designing morphing structures with lightweight actuation for practical applications.

Chaotic snap-through vibrations of bistable asymmetric deployable composite laminated cantilever shell under foundation excitation and application to morphing wing

The realization of the dynamic snap-through behaviors provides the new design ideas in the fields of the morphing aircraft and piezoelectric energy harvesting. This paper studies 1:2 internal resonance, nonlinear vibrations and chaotic snap-through phenomena of the bistable asymmetric composite laminated (BSCL) cantilever shell with the lower-frequency and higher-frequency primary resonances for the first time. The transverse foundation excitation subjects to the fixed end of the bistable cantilever shell. The perturbation analysis of two-degrees-of-freedom nonlinear ordinary differential equations is carried out by using the first-order approximate multiple scale method. The analytical results of the frequency-amplitude and force-amplitude response curves are obtained under the small foundation excitation. The obtained results reveal that the BSCL cantilever shell exhibits the double-jumping characteristics when 1:2 internal and primary resonances occur. There is a continuous energy exchange back and forth between two modes of the bistable laminated cantilever shell. As the foundation excitation increases, the BSCL cantilever shell exhibits saturation phenomenon. Numerical simulations are finished to further investigate the effects of the large excitation on the chaotic, quasi-periodic and snap-through vibrations for the BSCL cantilever shell. The vibration experiment is carried out to investigate the internal resonance and dynamic snap-though motions of the BSCL cantilever shell. Using the snap-though behaviors of the BSCL cantilever shell, we obtain the morphing structure of the aircraft wing.

Shape-retaining beam-like morphing structures via localized snap through

In this study, we present a concept of morphing structure – featuring an arch mounted on a compliant base – that can be reconfigured via snap-through buckling and leverages bistability to retain its morphed shape. We show that one-dimensional arrays of such units yield beam-like structures that, upon localized snapping, can attain multiple, morphologically distinct stable shapes. Units are modeled using discrete elastic rods, a reduced-order formulation for beams and beam structures, and the results are validated via experiments. We leverage our model to understand the influence of the geometrical design parameters on the response and final shape of a unit. We then show that the morphed shapes of arrays of units can be predicted by concatenating results of simulations on single units, and leverage this idea to inverse-design structures that can be snapped into target stable shapes. Ultimately, our work suggests an up-scalable way to create shape-retaining morphing structures with target stable shapes.

Multistable compliant linkages with multiple kinematic paths separated by energy barriers

Multistable morphing structures can reconfigure between different stable states that are separated by energy barriers, and one-degree-of-freedom (1-DOF) mechanisms have many merits, like simple actuation. This paper combines the two and proposes a new family of reconfigurable compliant linkages with many (2−6) 1-DOF kinematic paths that are separated by energy barriers. This new type of design is an extension of multistable structures, where each stable state corresponds to not just one configuration but a 1-DOF configuration space, i.e., a kinematic path. Components of the linkages are made elastically compliant, therefore enabling the switch between two isolated compatible paths with multi-stability. A generation-selection hybrid design algorithm to follow prescribed reconfigurable paths is proposed, and a minimum energy path (MEP) finding method to guide actuation to switch between different kinematic paths is developed. Four design examples with 2–3 reconfigurable paths and their experiments are presented, and the effectiveness of this method is verified. This work provides a fresh perspective to design the single-DOF reconfigurable mechanisms with larger design space, more reconfigurable kinematic paths, and easier reconfiguration actuation.

Structural morphing in the viral portal vertex of bacteriophage lambda.

The tailed bacteriophages possess a distinct portal vertex that consists of a ring of 12 portal proteins associated with a 5-fold capsid shell. This portal protein is crucial in multiple stages of virus assembly and infection. Our research focused on examining the structures of the portal vertex in both its preliminary prohead state and the fully mature virion state of bacteriophage lambda. By analyzing these structures, we were able to understand how the portal protein undergoes conformational changes during maturation, the mechanism by which it prevents DNA from escaping, and the process of DNA spirally gliding.

Photo Switchable 4D Printing Remotely Controlled Responsive and Mimetic Deformation Shape Memory Polymer Nanocomposites

AbstractPhoto‐triggered shape morphing structures can be found in myriads of areas. Utilizing light as a switch can effectively control and regulate the precise deformation of structures. However, the integration of photo‐switching functions in shape‐morphing structures with complex geometries remains a challenge. Here, photoswitchable digital light processing based 4D printing high‐resolution and highly complex geometries, based on UV curable WO2.9 nanoparticle doped shape memory polymer nanocomposites is reported, which are highly deformable (stretchability up to ≈1000% at rubbery state) and fatigue resistant (repeatedly loaded >1200 times at ambient temperature). The presence of just trace WO2.9 nanoparticles (<0.20 wt.‰) contributes to the controlled photothermal property of nanocomposite via selective absorption of light, which enables reversibly photoswitchable (>50 times), spatial and remote control of 4D printing shape morphing structures. These findings offer a promising approach to expanding the applications of photo‐triggered shape‐morphing structures.

A Preliminary Evaluation of Morphing Horizontal Tail Design for UAVs

Morphing structures are a relatively new aircraft technology currently being investigated for a variety of applications, from civil to military. Despite the lack of literature maturity and its complexity, morphing wings offer significant aerodynamic benefits over a wide range of flight conditions, enabling reduced aircraft fuel consumption and airframe noise, longer range and higher efficiency. The aim of this study is to investigate the impact of morphing horizontal tail design on aircraft performance and flight mechanics. This study is conducted on a 1:5 scale model of a Preceptor N-3 Pup at its trim condition, of which the longitudinal dynamics is implemented in MATLAB release 2022. Starting from the original horizontal tail airfoil NACA 0012 with the elevator deflected at the trim value, this is modified by using the X-Foil tool to obtain a smooth morphing airfoil trailing edge shape with the same CLα. By comparing both configurations and their influence on the whole aircraft, the resulting improvements are evaluated in terms of stability in the short-period mode, reduction in the parasitic drag coefficient CD0, and increased endurance at various altitudes.