Simple deformation measures for discrete elastic rods and ribbons

The discrete elastic rod method (Bergou et al. 2008 ACM Trans. Graph . 27 , 63:1–63:12. ( doi:10.1145/1360612.1360662 )) is a numerical method for simulating slender elastic bodies. It works by representing the centreline as a polygonal chain, attaching two perpendicular directors to each segment and defining discrete stretching, bending and twisting deformation measures and a discrete strain energy. Here, we investigate an alternative formulation of this model based on a simpler definition of the discrete deformation measures. Both formulations are equally consistent with the continuous rod model. Simple formulae for the first and second gradients of the discrete deformation measures are derived, making it easy to calculate the Hessian of the discrete strain energy. A few numerical illustrations are given. The approach is also extended to inextensible ribbons described by the Wunderlich model, and both the developability constraint and the dependence of the energy on the strain gradients are handled naturally.

Vibration of a Segmented Rod

This paper presents the governing equation of motion, boundary conditions and exact vibration frequencies of a segmented rod where the segments are connected by hinges with elastic rotational springs of constant stiffness. The mass of each segment is assumed to be evenly distributed along the length of the rod. Another discrete model called Hencky bar-chain model (short for HBM; which is equivalent to the finite difference model for discretizing continuous rod) assumes the rod mass to be lumped at the ends instead and a different set of boundary conditions are adopted clamped end. The vibration results of a clamped–clamped segment rod are compared with those of the HBM. It is shown that the HBM underestimates the vibration frequencies when compared to the segmented rod model for a finite number of segments while both models furnish vibration solutions that converge to the solutions of Euler beam for infinitely large number of segments.

Shedding new light on the generation of the visual chromophore

The visual phototransduction cascade begins with acis–transphotoisomerization of a retinylidene chromophore associated with the visual pigments of rod and cone photoreceptors. Visual opsins release their all-trans-retinal chromophore following photoactivation, which necessitates the existence of pathways that produce 11-cis-retinal for continued formation of visual pigments and sustained vision. Proteins in the retinal pigment epithelium (RPE), a cell layer adjacent to the photoreceptor outer segments, form the well-established “dark” regeneration pathway known as the classical visual cycle. This pathway is sufficient to maintain continuous rod function and support cone photoreceptors as well although its throughput has to be augmented by additional mechanism(s) to maintain pigment levels in the face of high rates of photon capture. Recent studies indicate that the classical visual cycle works together with light-dependent processes in both the RPE and neural retina to ensure adequate 11-cis-retinal production under natural illuminances that can span ten orders of magnitude. Further elucidation of the interplay between these complementary systems is fundamental to understanding how cone-mediated vision is sustained in vivo. Here, we describe recent advances in understanding how 11-cis-retinal is synthesized via light-dependent mechanisms.

RESEARCH ON THE FREQUENCY RELIABILITY SENSITIVITY AND RELIABILITY-BASED ROBUST DESIGN OF THE RANDOM VIBRATION SYSTEM OF CONTINUOUS ROD

The frequency reliability sensitivity in the stochastic dynamic structure system and reliability-based robust design were studied deeply in this paper. With the criterion that the absolute value of the difference between natural frequency and forcing frequency, the frequency reliability method of avoiding resonance was proposed. Then frequency reliability sensitivity theory was presented, which provided a preliminary efficient way to analyze how each random parameter contributed to the system reliability. Moreover, the frequency reliability-based robust design method was obtained by robust and optimization technology on the basis of the frequency reliability and sensitivity research in the paper, which helped designers to establish acceptable parameter values and to determine the fluctuations of the parameters for the safe operations. Meanwhile, a numerical example of the random vibration system of continuous rod was provided and studied. The effectiveness and accuracy of the proposed methods were well demonstrated.