Point configurations that are asymmetric yet balanced

A configuration of particles confined to a sphere is balanced if it is in equilibrium under all force laws (that act between pairs of points with strength given by a fixed function of distance). It is straightforward to show that every sufficiently symmetrical configuration is balanced, but the converse is far from obvious. In 1957 Leech completely classified the balanced configurations in R^3, and his classification is equivalent to the converse for R^3. In this paper we disprove the converse in high dimensions. We construct several counterexamples, including one with trivial symmetry group.Comment: 10 page

Topology Optimization of Composite Self-Deployable Thin Shells with Cutouts

The paper presents topology optimization studies of selfs-deployable joints in thin-walled tubular structures. The joints are made entirely of ultra-thin, fiber reinforced composite materials. The objective of this research is to strategically position cutouts on the joints so that they can fold without failing, while maximizing the deployed bending stiffness. The optimal shape and position of cutouts are the results of concurrent topology optimization of these composite, thin-shell joints with geometrical non-linearities, due to their folding and self-deployable nature. Numerical methods to accurately detect failure are implemented and results from a novel level-set method for topology optimization are compared to results from classical parametric optimization and preliminary designs based on physical intuition

Poly[ethyl­enediammonium [tris­[μ3-hydrogenphosphato(2−)]dicadmium] monohydrate]

The title compound, {(C2H10N2)[Cd2(HPO4)3]·H2O}n, was synthesized under hydro­thermal conditions. The structure of this hybrid compound consists of CdO6, CdO5 and PO4 polyhedra arranged so as to build an anionic inorganic layer, namely [Cd2(HPO4)3]2−, parallel to the ab plane. The edge-sharing CdO6 octa­hedra form infinite chains running along the a axis and are linked by CdO5 and PO4 polyhedra. The ethyl­ene­diammonium cation and the water mol­ecule are located between two adjacent inorganic layers and ensure the cohesion of the structure via N—H⋯O and O—H⋯O hydrogen bonds

Topology optimization of 3D compliant actuators by a sequential element rejection and admission method

This work presents a sequential element rejection and admission (SERA) method for optimum topology design of three dimensional compliant actuators. The proposed procedure has been successfully applied to several topology optimization problems, but most investigations for compliant devices design have been focused on planar systems. This investigation aims to progress on this line, where a generalization of the method for three dimensional topology optimization is explored. The methodology described in this work is useful for the synthesis of high performance flexure based micro and nano manipulation applications demanding for both sensing and control of motion and force trajectories. In this case the goal of the topology optimization problem is to design an actuator that transfers work from the input point to the output port in a structurally efficient way. Here we will use the classical formulation where the displacement performed on a work piece modelled by a spring is maximized. The technique implemented works with two separate criteria for the rejection and admission of elements to efficiently achieve the optimum design and overcomes problems encountered by other evolutionary methods when dealing with compliant mechanisms design. The use of the algorithm is demonstrated through several numerical examples

CT Image Segmentation Using FEM with Optimized Boundary Condition

The authors propose a CT image segmentation method using structural analysis that is useful for objects with structural dynamic characteristics. Motivation of our research is from the area of genetic activity. In order to reveal the roles of genes, it is necessary to create mutant mice and measure differences among them by scanning their skeletons with an X-ray CT scanner. The CT image needs to be manually segmented into pieces of the bones. It is a very time consuming to manually segment many mutant mouse models in order to reveal the roles of genes. It is desirable to make this segmentation procedure automatic. Although numerous papers in the past have proposed segmentation techniques, no general segmentation method for skeletons of living creatures has been established. Against this background, the authors propose a segmentation method based on the concept of destruction analogy. To realize this concept, structural analysis is performed using the finite element method (FEM), as structurally weak areas can be expected to break under conditions of stress. The contribution of the method is its novelty, as no studies have so far used structural analysis for image segmentation. The method's implementation involves three steps. First, finite elements are created directly from the pixels of a CT image, and then candidates are also selected in areas where segmentation is thought to be appropriate. The second step involves destruction analogy to find a single candidate with high strain chosen as the segmentation target. The boundary conditions for FEM are also set automatically. Then, destruction analogy is implemented by replacing pixels with high strain as background ones, and this process is iterated until object is decomposed into two parts. Here, CT image segmentation is demonstrated using various types of CT imagery

Multicriterion structure/control design for optimal maneuverability and fault tolerance of flexible spacecraft

A multicriterion design problem for optimal maneuverability and fault tolerance of flexible spacecraft is considered. The maneuverability index reflects the time required to perform rest-to-rest attitude maneuvers for a given set of angles, with the postmaneuver spillover within a specified bound. The performance degradation is defined to reflect the maximum possible attitude error after maneuver due to the effect of faults. The fault-tolerant design is to minimize the worst performance degradation from all admissible faults by adjusting the design of the spacecraft. It is assumed that admissible faults can be specified by a vector of real parameters. The multicriterion design for optimal maneuverability and fault tolerance is shown to be well defined, leading to a minimax problem. Analysis for this nonsmooth problem leads to closed-form expressions of the generalized gradient of the performance degradation function with respect to the fault parameters and structural design variables. Necessary and sufficient conditions for the optimum are derived, and the closed-form expressions of the generalized gradients are applied for their interpretation. The bundle method is applicable to this minimax problem. Approximate methods which efficiently solve this minimax problem with relatively little computational difficulties are presented. Numerical examples suggest that it is possible to improve the fault tolerance substantially with relatively little loss in maneuverability.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45242/1/10957_2005_Article_BF02191852.pd

Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works

Inverse Design of Nanophotonic Devices with Structural Integrity

Computational inverse design has been a driving force behind the development of compact and highly efficient nanophotonic devices. However, due to fabrication constraints, devices have so far mostly been restricted to planar geometries. With recent developments, additive manufacturing techniques are poised to open up a vast design space for free-form nanophotonic devices, bringing with them a new set of inverse design challenges. The most urgent one is structural integrity. With a technique such as 3D laser lithography (nearly) every structure can be written, but not every structure is self supported and is with that feasible; free-floating elements are simply not an option. To address this challenge, we present here a method for the inverse design of nanophotonic devices that combines electromagnetic and structural topology optimization. To illustrate the proposed method, we present designs for a nanolens and a mode converter with structural integrity. We show that some of these designs achieve efficiencies comparable to those of conventional nanophotonic inverse design while maintaining structural integrity; and even slightly surpass them. This opens up new possibilities for photonic device design and may lead to the development of novel photonic devices for additive manufacturing