Finite Element Simulation of Dense Wire Packings

A finite element program is presented to simulate the process of packing and coiling elastic wires in two- and three-dimensional confining cavities. The wire is represented by third order beam elements and embedded into a corotational formulation to capture the geometric nonlinearity resulting from large rotations and deformations. The hyperbolic equations of motion are integrated in time using two different integration methods from the Newmark family: an implicit iterative Newton-Raphson line search solver, and an explicit predictor-corrector scheme, both with adaptive time stepping. These two approaches reveal fundamentally different suitability for the problem of strongly self-interacting bodies found in densely packed cavities. Generalizing the spherical confinement symmetry investigated in recent studies, the packing of a wire in hard ellipsoidal cavities is simulated in the frictionless elastic limit. Evidence is given that packings in oblate spheroids and scalene ellipsoids are energetically preferred to spheres.Comment: 17 pages, 7 figures, 1 tabl

Integrating rotation from angular velocity

Abstract\ud The integration of the rotation from a given angular velocity is often required in practice. The present paper explores how the choice of the parametrization of rotation, when employed in conjuction with different numerical time-integration schemes, effects the accuracy and the computational efficiency. Three rotation parametrizations – the rotational vector, the Argyris tangential vector and the rotational quaternion – are combined with three different numerical time-integration schemes, including classical explicit Runge–Kutta method and the novel midpoint rule proposed here. The key result of the study is the assessment of the integration errors of various parametrization–integration method combinations. In order to assess the errors, we choose a time-dependent function corresponding to a rotational vector, and derive the related exact time-dependent angular velocity. This is then employed in the numerical solution as the data. The resulting numerically integrated approximate rotations are compared with the analytical solution. A novel global solution error norm for discrete solutions given by a set of values at chosen time-points is employed. Several characteristic angular velocity functions, resulting in small, finite and fast oscillating rotations are studied

Stability and power optimality in time-periodic flapping wing structures

This paper investigates the nonlinear dynamics of a vehicle with two flexible flapping wings. The body dynamics and the wings\u27 deformation are monolithically grouped into a single system of equations, with aerodynamics accounted for by a quasi-steady blade element method. A periodic shooting method is then used to locate closed orbits of this non-autonomous system, and Floquet multipliers assess the linearized stability about the nonlinear orbit. This framework is then exposed to a gradient based optimizer, in order to quantify the role of wing planform variables, wing structure variables, and kinematic actuation variables in obtaining vehicles with superior open-loop stability characteristics, and/or low-power requirements

History of Branch County, Michigan,

Author's name in caption title.Mode of access: Internet

History of Hillsdale county. Michigan, with illustrations and biographical sketches of some of its prominent men and pioneers.

History of Hillsdale county, by Crisfield Johnson. History of the townships and villages of Hillsdale county.Mode of access: Internet

History of Branch county, Michigan, with illustrations and biographical sketches of some of its prominent men and pioneers.

1 p. l., 7-347 p. : front., illus., plates, ports., map, facsim. ; 31 cm.Author's name in caption title