Analysis of Wing Morphing via Frame Buckling

Adaptive structures have the ability to modify their shape and internal forces through sensing and actuation in order to maintain optimal performance under changing actions. Previous studies have shown that substantial whole-life energy savings with respect to traditional passive designs can be achieved through well-conceived adaptive design strategies. The whole-life energy comprises an embodied part in the material and an operational part for structural adaptation. Structural adaptation through controlled large shape changes allows a significant stress redistribution so that the design is not governed by extreme loads with long return periods. This way, material utilization is maximized and embodied energy is reduced. A design process based on shape optimization has been formulated to obtain shapes that are optimal for each load case. A geometrically non-linear force method is employed to control the structure into required shapes. This paper presents the experimental testing of a small-scale prototype adaptive structure produced by this design process. The structure is a simply supported planar truss. Shape adaptation is achieved through controlled length changes of turnbuckles that strategically replace some of the structural elements. The stress is monitored by strain sensors fitted on some of the truss elements. The nodal coordinates are monitored by an optical tracking system. Numerical predictions and measurements have a minimum Pearson correlation of 0.86 which indicates good accordance. Although scaling effects have to be further investigated, experimental testing on a small-scale prototype has been useful to assess the feasibility of the design and control methods outlined in this work. Results show that stress homogenization through controlled large shape changes is feasible.

This work presents the design, optimization and testing of a novel lattice-structure based morphing wing. The lattice-structure concept spans a large design space, including the possibility to vary among others material, number, distribution and the orientation of the lattice rods. The used parametrization scheme considers both the positioning of the Carbon Fiber Reinforced Polymer (CFRP) rods and their orientation in spherical coordinates within the wing, thus allowing to appropriately cover the design space, while reducing the set of variables during the design optimization procedure. The morphing deformations are relying on electromechanical servomotors. Design objectives include weight minimization and structural requirements, while achieving sufficient roll control. The local deformation induced by the electromechanical actuators is distributed by an internal skeleton structure across the rear section of the wing. An extensible skin is ensuring a smooth cambering and minimizes the required actuation energy. The in-house developed and validated simulation environment couples the aerodynamic pressure and the structural deformations, to accurately predict the aeroelastic response of the wing to aerodynamic and actuation forces, considering large deformations. In addition to the lattice structure, the aeroelastic optimization also considers the actuation layout, and the layup-thickness of the wing skin. Planform and airfoil shape are fixed to a NACA0012 airfoil with 80 cm span, and 30 cm chord. The structural and morphing behavior was evaluated on a technology demonstrator. The demonstrator provides large continuous shape changes, improving the aerodynamic performance and achieving large deflections and high rolling moment coefficients. This is mainly achieved by exploiting the interaction of the tailored internal structure and the actuation system. Since the deformation is distributed over a large portion of the wing, local stress concentrations are minimized, and actuation forces are reduced. Wing-up bending tests have been carried out, confirming the simulation results, respectively the load-carrying capability of the presented concept. Furthermore, actuation tests resulted in peak-to-peak trailing edge deflections of 31mm, respectively a rolling moment coefficient of 0.062, which are consistent with the simulation results and guarantee sufficient roll control.

Design and control of a prototype structure that adapts to loading through large shape changes

Materials and structures with shape morphing capabilities are attractive in aerospace, maritime vehicles and robotics: such systems offer lighter weight, better distributed stresses, simpler kinematics, smaller numbers of actuators and higher reliability. Current morphing materials are either very compliant to achieve large shape changes (metamaterials, compliant mechanisms, hydrogels), or very stiff but with infinitesimal shape changes that require large actuation forces (metallic or composite sandwich panels with piezoelectric actuation). Morphing efficiency and structural stiffness are therefore mutually exclusive properties in current engineering morphing materials, which limit the range of their application. Here we propose a design for a stiff morphing beam made of “meta-elements” with unusual combinations of elastic properties, and which can be actuated from a simple push/pull at the base. To capture the performance of the beam we propose and use three metrics: The “morphing amplitude”, the “morphing compliance” and “structural stiffness”. We develop nonlinear finite elements to explore a wide range of designs, and to show some inevitable tradeoffs of stiffness and morphing. To aid the design of the structure we propose ternary diagrams to select optimum combinations of properties for the meta-elements. Finally, we fabricated and tested three prototypes of stiff morphing beams to validate the approach.

ABSTRACTThe quasi-binary eutectic NiAl-9% Mo with faceted molybdenum fibers was subjected to both thermal annealing conditions and to annealing under thermal cycling conditions to determine the microstructural stability of this alloy. The static temperature tests were run at 0.85TM- 0.97TMin an argon gas atmosphere. The thermal cycling tests were performed between temperatures of 700°C and 1200°C by induction heating disk-shaped specimens in an argon gas atmosphere using time-temperature heating and cooling profiles to approximate potential engine applications. To quantify microstructural changes, the fiber size and size distribution and number of fibers per unit area were measured as a function of time at temperature. The overall results demonstrate that the directionally solidified eutectic NiAl-9Mo subjected to thermal fatigue conditions exhibits cell boundary coarsening and large shape changes, whereas the microstructure under static stress-free annealing is stable.

System-level aircraft conceptual design can be viewed as a high-dimensional, multidisciplinary design optimization (MDO) problem involving potentially thousands of design variables across multiple subsystems and design conditions. Recent advances in modeling and adjoint-based sensitivity analysis have enabled the use of low-fidelity physics-based models to solve this complex problem in a computationally efficient manner using established MDO algorithms. However, integrating higher-fidelity aerodynamic simulations into comprehensive, large-scale MDO of aircraft concepts remains challenging. This is in large part due to the increased computational cost and the large geometric changes that may occur at the conceptual design stage. Since many mid- to high-fidelity aerodynamic solvers require conforming surface meshes, there is a need for a general deformation method that efficiently updates surface mesh nodes based on changes to the design geometry in a differentiable manner. In this paper, we aim to fill this need by developing such a method using a two-step process: 1) recompute intersections between components given large geometric changes and 2) deform the surface mesh using thin plate splines to conform to the updated intersections. The method is reasonably efficient and all steps are differentiable. We test our method on a simple tube-and-wing geometry for which we translate and rotate the wing with respect to the fuselage. The method performs well for all considered rotation angles (±10 degrees) with over 95% of triangles being of acceptable quality. For translations, the performance is similar up to 1.5 times the chord length. We couple the method with a panel-method aerodynamic solver, confirming its applicability in aircraft conceptual design.

The Reproducing Kernel Particle Method (RKPM) is one of several so-called meshfree methods of structural analysis and has been applied in this paper to the gradient-based shape optimization of two-dimensional automotive components. As indicated by the term meshfree, no mesh is required, but rather a field of points, or particles, are distributed within the domain of the problem. Three standard linear examples are chosen to allow a comprehensive comparison between the optimization with the RKPM and the state-of-art optimization tool in Unigraphics Version 18 (UG V18). The results show that the optimization analysis with the RKPM is able to accommodate very large shape changes required in the optimization process without doing particle re-adaptation, and provides accurate solutions of the objective and constraint functions and their gradients, therefore facilitates a fast convergence of the gradient-based optimization algorithm.

A finite element based shape optimization program has been developed for three‐dimensional shell structures which allows for multiple edge movement and large shape changes. This program automatically performs shape optimization by linking together adaptive mesh generation, substructuring and optimization algorithms with a commercial finite element analysis program, MSC/NASTRAN. This paper examines the robustness of the shape optimization program by varying the initial shape and design parameters for three examples. This is performed to determine the conditions under which similar optimum shapes will be generated for different initial conditions.

Morphing technology enables aerospace vehicles to achieve a broader range of operational modes. Computational aeroelastic and design analysis tools of these vehicles must be able to handle arbitrarily large deformations and shape changes. The objective of this study is to improve aircraft performance, expand its flight envelope, replace conventional control surfaces, reduce drag, and reduce vibration/flutter by morphing technology. This paper presents a revolutionary approach to solve aeroelastic instabilities of air vehicles undergoing large deformation and arbitrarily large shape change. The technology was implemented in a CFD code and demonstrated for several solid-fluid interaction and morphing telescope wing problems. This innovative technology casts structure/body-dynamics equations in an Eulerian reference frame, so that the dependent variables for the fluid and solids are continuous and coupled. The volume of solid tracks the evolution of solid-fluid interface, while implicit formulation embeds the interaction forces into the solution procedure. The method is devoid of troublesome moving mesh or tedious grid regeneration issues. The developed technology will provide the lacking design and analysis capability in conceptualizing how vehicles should safely change shape during flight.

Experimental and theoretical results are presented on the evolution of large elastic deformation, non-uniform curvature, shape changes and geometric instability in substrates of Si wafers with metal films. The critical diameter and thickness of the Si wafer, for which large deformation and shape instability occur, are identified, as functions of the line tension in the film (which is the product of the biaxial stress in the film and the film thickness). Observations of the curvature and shape variations along the wafer diameter and geometry-dependence of the shape instability compare favorably with those predicted by detailed finite element analyses.

Editorial: Left ventricular dysfunction after open repair of simple confenital heart defects in infants and children

Highly redundant modular robots may undergo large shape changes which significantly affect the geometry and dynamics of the robot. In these motions, the shape change may induce a tipping or rolling behavior of the robot. The paper describes the dynamic modeling, locomotion planning, control and simulation of such rolling motions for the Tetrobot modular robots. The motion is described by the path profiles of controlled nodes, the tipping criteria and dynamic tipping motion and an impact-reaction model of contact with the ground. These phases of motion are described using Newton-Euler dynamic equations and the principle of conservation of angular momentum. In the paper, a two-phase planning and switching control sequence is introduced to achieve stable and reliable motion of a Tetrobot modular robot. Simulation results illustrate the tipping behavior of a tetrahedron, the dynamic contact and rolling of an icosahedral Tetrobot and dynamic control of the rolling Tetrobot. The resulting models are useful to analyze and control both intentional rolling as a new mode of mobility as well as the avoidance of unintentional tipping and rolling during task execution.

WC-(Fe, Ni, C) cemented carbides can be successfully transformation-toughened by careful control of binder composition and taking into consideration the effect of thermal residual stress on the transformation characteristics of the binder. An additional degree of control on the metastability of the binder phase can be achievedvia thermomechanical treatments. These treatments consist of transforming an austenitic binder to martensite by cooling in liquid nitrogen followed by a suitable high temperature heat treatment to reaustenitize it. Thein situ deformation of the binder caused by the large shape and volume changes that accompany its transformation to martensite thus provides the mechanical component of the thermomechanical treatment. Subsequent heat treatments not only reaustenitize the binder but also modify its susceptibility to undergo stress-induced transformation. It is shown that the hardness/fracture toughness behavior of WC-(Fe, Ni, C) cemented carbides can be significantly improved by the application of such treatments. A qualitative explanation for the enhancements in fracture toughness provided by thermomechanical treatments is offered based on a careful examination of the changes in phase constitution of the binder that occur during these treatments.

In this work, we propose a new kind of soft-rigid hybrid actuator composed mainly of soft chambers and rigid frames. Compared with the well-known fiber-reinforced soft actuators, the hybrid actuators are able to ensure the design of noncircular cross-sectional shapes. It is demonstrated that rigid frames are capable of providing geometric constraints, reducing the ineffective deformation, and improving the energy utilization for the hybrid actuators with noncircular cross-sections. The essential characteristics of rigid constraints and flexible constraints are obtained by simulation and experiments on specimens with three different cross-sectional shapes. Furthermore, a spring-fluid film model is introduced to characterize the behavior of a representative hybrid linear actuator and a bending actuator with a rectangular cross-section, and it is also proved by the corresponding experiments. The change of the cross-sectional shape of fiber-reinforced soft actuators under pressurization is also explained theoretically as a contrast. Then, two application examples, namely, a robotic gripper and a caudal fin formed from linear actuators, are designed and demonstrated, showing the advantages and potential applications of the proposed geometric confined hybrid actuators. The proposed soft-rigid hybrid actuators combine the properties of soft and rigid materials, expand the design scope of the compliant actuators, and provide new solutions for robotics, especially for soft robots with specific requirements for their shapes or profiles.

The concept of morphing structures refers to devices that exhibit large scale shape changes, whilst maintaining load bearing capability, in response to distinctive operating conditions. This behavior comes from combinations of non-linear material or kinematic responses. Here, we limit our interests to shell type structures made from low strain, elastic materials that exhibit highly nonlinear kinematic behavior. Often, but not necessarily, the response can be bistable. Models predicting the multistability of shells often present a compromise between computational efficiency and accuracy of results. Moreover, they deal mainly with regular domains, such as rectangular or elliptical planforms. Few studies have been done to investigate the performance and the possible advantages of exploiting multistable structures with more general domains. In the present work, the multistability of thin shallow composite shells with irregular domains is investigated. An accurate and computationally efficient energy-based model is developed, in which the membrane and the bending components of the total strain energy are decoupled using the semi-inverse formulation of the constitutive equations. Transverse displacements are approximated using Legendre polynomials and the membrane problem is solved in isolation by combining compatibility conditions and equilibrium equations. The result is the total potential energy as a function of curvatures only. Stable shapes are recovered by minimizing the total energy with respect to curvature. The accurate evaluation of the membrane energy is a key step in order to accurately capture the bifurcation points. Here the membrane problem is solved using the Differential Quadrature Method (DQM), which provides accuracy at a relatively small computational cost. However, DQM is limited to rectangular domains. For this reason, blending functions are used to map the irregular physical domain into a regular computational domain. This approach allows multistable shells with arbitrary convex planforms to be described without affecting the computational efficiency and the accuracy of the proposed model.