930 research outputs found
Multiparameter actuation of a neutrally-stable shell: a flexible gear-less motor
We have designed and tested experimentally a morphing structure consisting of
a neutrally stable thin cylindrical shell driven by a multiparameter
piezoelectric actuation. The shell is obtained by plastically deforming an
initially flat copper disk, so as to induce large isotropic and almost uniform
inelastic curvatures. Following the plastic deformation, in a perfectly
isotropic system, the shell is theoretically neutrally stable, owning a
continuous manifold of stable cylindrical shapes corresponding to the rotation
of the axis of maximal curvature. Small imperfections render the actual
structure bistable, giving preferred orientations. A three-parameter
piezoelectric actuation, exerted through micro-fiber-composite actuators,
allows us to add a small perturbation to the plastic inelastic curvature and to
control the direction of maximal curvature. This actuation law is designed
through a geometrical analogy based on a fully non-linear inextensible
uniform-curvature shell model. We report on the fabrication, identification,
and experimental testing of a prototype and demonstrate the effectiveness of
the piezoelectric actuators in controlling its shape. The resulting motion is
an apparent rotation of the shell, controlled by the voltages as in a
"gear-less motor", which is, in reality, a precession of the axis of principal
curvature.Comment: 20 pages, 9 figure
Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies
We consider a bi-dimensional sheet consisting of two orthogonal families of inextensible fibres. Using the representation due to Rivlin and Pipkin for admissible placements, i.e. placements preserving the lengths of the inextensible fibres, we numerically simulate a standard bias extension test on the sheet, solving a non-linear constrained optimization problem. Several first and second gradient deformation energy models are considered, depending on the shear angle between the fibres and on its gradient, and the results obtained are compared. The proposed numerical simulations will be helpful in designing a systematic experimental campaign aimed at characterizing the internal energy for physical realizations of the ideal pantographic structure presented in this paper
A variational model for anisotropic and naturally twisted ribbons
We consider thin plates whose energy density is a quadratic function of the
difference between the second fundamental form of the deformed configuration
and a "natural" curvature tensor. This tensor either denotes the second
fundamental form of the stress-free configuration, if it exists, or a target
curvature tensor. In the latter case, residual stress arises from the
geometrical frustration involved in the attempt to achieve the target
curvature: as a result, the plate is naturally twisted, even in the absence of
external forces or prescribed boundary conditions. Here, starting from this
kind of plate energies, we derive a new variational one-dimensional model for
naturally twisted ribbons by means of Gamma-convergence. Our result
generalizes, and corrects, the classical Sadowsky energy to geometrically
frustrated anisotropic ribbons with a narrow, possibly curved, reference
configuration
Wire mesh design
We present a computational approach for designing wire meshes, i.e., freeform surfaces composed of woven wires arranged in a regular grid. To facilitate shape exploration, we map material properties of wire meshes to the geometric model of Chebyshev nets. This abstraction is exploited to build an efficient optimization scheme. While the theory of Chebyshev nets suggests a highly constrained design space, we show that allowing controlled deviations from the underlying surface provides a rich shape space for design exploration. Our algorithm balances globally coupled material constraints with aesthetic and geometric design objectives that can be specified by the user in an interactive design session. In addition to sculptural art, wire meshes represent an innovative medium for industrial applications including composite materials and architectural façades. We demonstrate the effectiveness of our approach using a variety of digital and physical prototypes with a level of shape complexity unobtainable using previous methods
Diffuse interface models of locally inextensible vesicles in a viscous fluid
We present a new diffuse interface model for the dynamics of inextensible
vesicles in a viscous fluid. A new feature of this work is the implementation
of the local inextensibility condition in the diffuse interface context. Local
inextensibility is enforced by using a local Lagrange multiplier, which
provides the necessary tension force at the interface. To solve for the local
Lagrange multiplier, we introduce a new equation whose solution essentially
provides a harmonic extension of the local Lagrange multiplier off the
interface while maintaining the local inextensibility constraint near the
interface. To make the method more robust, we develop a local relaxation scheme
that dynamically corrects local stretching/compression errors thereby
preventing their accumulation. Asymptotic analysis is presented that shows that
our new system converges to a relaxed version of the inextensible sharp
interface model. This is also verified numerically. Although the model does not
depend on dimension, we present numerical simulations only in 2D. To solve the
2D equations numerically, we develop an efficient algorithm combining an
operator splitting approach with adaptive finite elements where the
Navier-Stokes equations are implicitly coupled to the diffuse interface
inextensibility equation. Numerical simulations of a single vesicle in a shear
flow at different Reynolds numbers demonstrate that errors in enforcing local
inextensibility may accumulate and lead to large differences in the dynamics in
the tumbling regime and differences in the inclination angle of vesicles in the
tank-treading regime. The local relaxation algorithm is shown to effectively
prevent this accumulation by driving the system back to its equilibrium state
when errors in local inextensibility arise.Comment: 25 page
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