A topology optimization method is used to take advantage of programmable anisotropy in LCEs to achieve target deformations.

Reconfigurable structures based on origami design are useful for multifunctional applications, such as deployable shelters, solar array packaging, and tunable antennas. Origami provides a framework to decompose a complex 2D to 3D transformation into a series of folding operations about predetermined foldlines. Recent optimization toolsets have begun to enable a systematic search of the design space to optimize not only geometry but also mechanical performance criteria as well. However, selecting optimal fold patterns for large folding operations is challenging as geometric nonlinearity influences fold choice throughout the evolution. The present work investigates strategies for design optimization to incorporate the current and future configurations of the structure in the performance evaluation. An optimization method, combined with finite-element analysis, is used to distribute mechanical properties within an initially flat structure to determine optimal crease patterns to achieve desired motions. Out-of-plane and twist displacement objectives are used in three examples. The influence of load increment and geometric nonlinearity on the choice of crease patterns is studied, and appropriate optimization strategies are discussed.

Kinematic synthesis to meet an approximate motion specification naturally forms a constrained optimization problem. Instead of using local methods, we conduct global design searches by direct computation of all critical points. The idea is not new, but performed at scale is only possible through modern polynomial homotopy continuation solvers. Such a complete computation finds all minima, including the global, which allows for a full exploration of the design space, whereas local solvers can only find the minimum nearest to an initial guess. We form equality-constrained objective functions that pertain to the synthesis of spherical four-bar linkages for approximate function generation. We consider the general case where all mechanism dimensions may vary and a more specific case that enables the placement of ground pivots. The former optimization problem is shown to permit 268 sets of critical points, and the latter permits 61 sets. Critical points are classified as saddles or minima through a post-process eigenanalysis of the projected Hessian. The discretization points are contained within the coefficients of the stationarity polynomials, so the algebraic structure of the synthesis equations remains invariant to the number of points. The results of our computational work were used to design a mechanism that coordinates the folding wings. We also use this method to parameterize mechanism dimensions for a family of hyperbolic curves.

This paper presents a mechanism design optimization for actuating the horizontal stabilizers of an aircraft using a rotating empennage without a vertical stabilizer. Birds do not have vertical stabilizers and rotate their tail feathers to control agile maneuvers. A rotating empennage concept will mimic this motion and enable the bio-inspired flight of a fixed wing aircraft. To maintain control, the bio-inspired rotating empennage will incorporate three degrees of freedom: independent rotation of each horizontal stabilizer and rotation of the empennage relative to the main axis of the fuselage. The primary benefits of an aircraft without a vertical stabilizer are reduced drag and weight which, in turn, results in a more efficient operation. In order to reduce inertia of the rotating empennage, the linear actuators that position the horizontal stabilizers will be placed within the fuselage. Mechanisms that couple the linear translation of the actuators with the rotation of the horizontal stabilizers ideally require a low peak force and short stroke from the actuator. With two conflicting objectives, a Pareto front optimization was conducted to determine appropriate link lengths of candidate solutions and to understand the effectiveness of alternate mechanisms. The study considers rack & pinon, scotch-yoke, slider-crank, inverted slider-crank, Watt II, and Stephenson III mechanisms.

Modern materials and manufacturing technologies have allowed the construction of morphing wings that are able to continuously vary certain airfoil parameters such as twist, camber, or control surface deflection as a function of span. This work presents a twist effectiveness parameter as a means of comparing the ideal aerodynamic efficiency of spanwise continuous control surfaces (morphing wings) and spanwise discrete control surfaces (standard wings). A numerical algorithm is used to compute the twist effectiveness of both continuous and discrete control-surface designs over a wide range of planform shapes with evenly spaced actuation for inviscid, incompressible flow. Results included here show that using continuous control surfaces instead of discrete control surfaces reduces induced drag by less than 5% for most applications.