Origami devices have the ability to spatially reconfigure between 2D and 3D states through folding motions. The precise mapping of origami presents a novel method to spatially tune radio frequency (RF) devices, including adaptive antennas, sensors, reflectors, and frequency selective surfaces (FSSs). While conventional RF FSSs are designed based upon a planar distribution of conductive elements, this leaves the large design space of the out of plane dimension underutilized. We investigated this design regime through the computational study of four FSS origami tessellations with conductive dipoles. The dipole patterns showed increased resonance shift with decreased separation distances, with the separation in the direction orthogonal to the dipole orientations having a more significant effect. The coupling mechanisms between dipole neighbours were evaluated by comparing surface charge densities, which revealed the gain and loss of coupling as the dipoles moved in and out of alignment via folding. Collectively, these results provide a basis of origami FSS designs for experimental study and motivates the development of computational tools to systematically predict optimal fold patterns for targeted frequency response and directionality.
Origami structures morph between 2D and 3D conformations along predetermined fold lines that efficiently program the form, function and mobility of the structure. The transfer of origami concepts to engineering design shows potential for many applications including solar array packaging, tunable antennae, and deployable sensing platforms. However, the enormity of the design space and the complex relationship between origami-based geometries and engineering metrics places a severe limitation on design strategies based on intuition. This motivates the development of design tools based on optimization to identify optimal fold patterns for geometric and functional objectives. The present work proposes a topology optimization method using mechanical analysis to distribute fold line properties within a reference crease pattern to achieve a target actuation. By increasing the fold stiffness, unnecessary folds are effectively removed from the design solution, which allows fundamental topologies for actuation to be identified. A series of increasingly refined reference grids were analyzed and several actuating mechanisms were predicted. The fold stiffness optimization was then followed by a node position optimization, which determined that only two of the predicted topologies were fundamental and the solutions from higher density grids were variants or networks of these building blocks. This two-step optimization approach provides a valuable check of the grid dependency of the design and offers an important step toward systematic incorporation of origami design concepts into new, novel and reconfigurable engineering devices.
In this paper, the topology optimization methodology for the synthesis of distributed actuation system with specific applications to the morphing air vehicle is discussed. The main emphasis is placed on the topology optimization problem formulations and the development of computational modeling concepts. For demonstration purposes, the inplane morphing wing model is presented. The analysis model is developed to meet several important criteria: It must allow large rigid-body displacements, as well as variation in planform area, with minimum strain on structural members while retaining acceptable numerical stability for finite element analysis. Preliminary work has indicated that addressed modeling concept meets the criteria and may be suitable for the purpose. Topology optimization is performed on the ground structure based on this modeling concept with design variables that control the system configuration. In other words, states of each element in the model are design variables and they are to be determined through optimization process. In effect, the optimization process assigns morphing members as 'soft' elements, non-morphing load-bearing
members as 'stiff' elements, and non-existent members as 'voids.' In addition, the optimization process determines the location and relative force intensities of distributed actuators, which is represented computationally as equal and opposite nodal forces with soft axial stiffness. Several different optimization problem formulations are investigated to understand their potential benefits in solution quality, as well as meaningfulness of formulation itself. Sample in-plane morphing problems are solved to demonstrate the potential capability of the methodology introduced in this paper.
In this paper, the optimal location of a distributed network of actuators within a scissor wing mechanism is investigated. The analysis begins by developing a mechanical understanding of a single cell representation of the mechanism. This cell contains four linkages connected by pin joints, a single actuator, two springs to represent the bidirectional behavior of a flexible skin, and an external load. Equilibrium equations are developed using static analysis and the principle of virtual work equations. An objective function is developed to maximize the efficiency of the unit cell model. It is defined as useful work over input work. There are two constraints imposed on this problem. The first is placed on force transferred from the external source to the actuator. It should be less than the blocked actuator force. The other is to require the ratio of output displacement over input displacement, i.e., geometrical advantage (GA), of the cell to be larger than a prescribed value. Sequential quadratic programming is used to solve the optimization problem. This process suggests a systematic approach to identify an optimum location of an actuator and to avoid the selection of location by trial and error. Preliminary results show that optimum locations of an actuator can be selected out of feasible regions according to the requirements of the problem such as a higher GA, a higher efficiency, or a smaller transferred force from external force. Results include analysis of single and multiple cell wing structures and some experimental comparisons.