Symmetry-Based Transformable and Foldable Plate Structures

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Valentina Beatini
Keyword(s):  
The Other ◽  
Rigid Plate ◽  
Plate Structures ◽  
Symmetry Operations

This paper presents a novel family of modular flat-foldable rigid plate structures composed by assemblies of 4R-linkages. First, in the field of foldable plates, the proposed system is characterized by being not only foldable but also transformable: the slope of one module over the other is capable of changing not only magnitude but also sign. This transformable behavior extends the range of application of foldable plates from simply larger–smaller configurations to substantially different configurations and usages. The transformable curve is obtained by means of symmetry operations on the spherical length of links. For each module, three configurations can be designed. Various examples are illustrated.

scholarly journals Curved composite beam with interlayer slip loaded by radial load

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
István Ecsedi ◽  
Ákos József Lengyel
Keyword(s):  
Linear Relationship ◽  
Cross Section ◽  
Cross Sections ◽  
Composite Beam ◽  
The Other ◽  
Radial Load ◽  
Rigid Plate ◽  
Shear Connection ◽  
First Case ◽  
Interlayer Slip

AbstractElastic two-layer curved composite beam with partial shear interaction is considered. It is assumed that each curved layer separately follows the Euler-Bernoulli hypothesis and the load slip relation for the flexible shear connection is a linear relationship. The curved composite beam at one of the end cross sections is fixed and the other end cross section is subjected by a concentrated radial load. Two cases are considered. In the first case the loaded end cross section is closed by a rigid plate and in the second case the radial load is applied immediately to it. The paper gives solutions for radial displacements, slips and stresses. The presented examples can be used as benchmark for the other types of solutions as given in this study.

Mobility and Kinematic Analysis of Foldable Plate Structures Based on Rigid Origami

2016 ◽  
Vol 8 (6) ◽  
Author(s):  
Jianguo Cai ◽  
Zelun Qian ◽  
Chao Jiang ◽  
Jian Feng ◽  
Yixiang Xu
Keyword(s):  
Kinematic Analysis ◽  
Jacobian Matrix ◽  
Null Space ◽  
Building Structures ◽  
Rigid Plate ◽  
Deployable Structures ◽  
Plate Structures ◽  
Constraint Equations ◽  
New Type ◽  
System Constraint

As one new type of deployable structures, foldable plate structures based on origami are more and more widely used in aviation and building structures in recent years. The mobility and kinematic paths of foldable origami structures are studied in this paper. Different constraints including the rigid plate, spherical joints, and the boundary conditions of linkages were first used to generate the system constraint equations. Then, the degree-of-freedom (DOF) of the foldable plate structures was calculated from the dimension of null space of the Jacobian matrix, which is the derivative of the constraint equations with respect to time. Furthermore, the redundant constraints were found by using this method, and multiple kinematic paths existing in origami structures were studied by obtaining all the solutions of constraint equations. Different solutions represent different kinematic configurations. The DOF and kinematic paths of a Miura-ori and a rigid deployable antenna were also investigated in detail.

Nonlinear Lid Technique: Application to Gap and Moonpool Resonance

2018 ◽  
Author(s):  
B. Lécuyer ◽  
M.-C. Rouault
Keyword(s):  
Free Surface ◽  
Degrees Of Freedom ◽  
Nonlinear Damping ◽  
The Other ◽  
Second Step ◽  
Plate Structures ◽  
Multi Body ◽  
Piston Mode ◽  
Quadratic Damping ◽  
Moonpool Resonance

This paper focuses on the implementation of a nonlinear Lid Technique, as done in the software Diodore™. Several dummy plates are used and modelled as mechanical structures with their own degrees of freedom, capable to account for nonlinear damping. The paper describes first the general equations governing the multi-body sea-keeping model including dummy plate structures, and the expression of the relative quadratic damping. In a second step, examples of applications with gap and moonpool are exposed, demonstrating the capability of the nonlinear Lid Technique with multiple plates to render not only the piston mode, but also the other modes of deformation of the free surface.

scholarly journals Different teaching way to space group and symmetry operation: polyhedral vs ball

2014 ◽  
Vol 70 (a1) ◽  
pp. C1389-C1389
Author(s):  
Jian Zhou ◽  
Hejing Wang
Keyword(s):  
Teaching Practice ◽  
Symmetry Plane ◽  
Symmetry Operation ◽  
The Other ◽  
Space Group ◽  
Fundamental Knowledge ◽  
Crystallographic Symmetry ◽  
Position Shift ◽  
Symmetry Operations

To introduce the regulations of space group combining with a symmetry operation, put an orientation ball at a position shift away from the lattice tops is a good way [1]. However, based on the fundamental knowledge of "lattice", it often occurs that the tops of a lattice "should be" the positions of "atom balls" thought by most beginnings in teaching practice. This "thought" leads them never deduce out those regulations in symmetry operations and often misleads a wrong conclusion. As a beginning one wishes watching movies and pictures instead of mathematical deduction or vector calculation. It easily arises that a lattice has eight tops with atom balls. This "idea" lets the orientation balls shifting away from the lattice tops become difficult to understand. Nevertheless, the balls with a sign of "comma" in the middle are also difficult to understand that they can stand for a certain orientation because ball is circle. "Tops" and "directions" are two troubles in learning crystallographic symmetry and symmetry operations for those beginnings. How to guide them to overcome the two fences is an important step that will lead those beginnings to a never understanding status, on one hand, or let them understand throughout all regulations of space group(s) combining with a symmetry operation on the other. From teaching practice, a polyhedral at lattice tops could overcome both difficulties at position and in orientation. First, a polyhedral is always in orientation, even it is a cubic. This is easily understood. Secondly the centre of a polyhedral could easily meet with the tops of a lattice; it lets students easily understand "a lattice has eight tops occupied – a natural thought by beginnings". This way let them easily understand and deduce all regulations in crystallographic symmetry operations, such as a body-centred lattice combining with a symmetry plane (m) produces n symmetry operation at 1/4t, etc. see figures below.

Convex Polyhedra with Regular Faces

1966 ◽  
Vol 18 ◽  
pp. 169-200 ◽  
Author(s):  
Norman W. Johnson
Keyword(s):  
The Other ◽  
Convex Polyhedra ◽  
Regular Polygons ◽  
Platonic Solids ◽  
Geometric Figures ◽  
Regular Polyhedra ◽  
The Subject ◽  
Symmetry Operations

An interesting set of geometric figures is composed of the convex polyhedra in Euclidean 3-space whose faces are regular polygons (not necessarily all of the same kind). A polyhedron with regular faces is uniform if it has symmetry operations taking a given vertex into each of the other vertices in turn (5, p. 402). If in addition all the faces are alike, the polyhedron is regular.That there are just five convex regular polyhedra—the so-called Platonic solids—was proved by Euclid in the thirteenth book of the Elements (10, pp. 467-509). Archimedes is supposed to have described thirteen other uniform, “semi-regular” polyhedra, but his work on the subject has been lost.

The summary of nonrigid molecules: the Schrödinger supergroup

1967 ◽  
Vol 298 (1453) ◽  
pp. 184-203 ◽  
Keyword(s):  
Semidirect Product ◽  
Careful Analysis ◽  
The Other ◽  
Symmetry Groups ◽  
Total Group ◽  
Nonrigid Molecules ◽  
New Type ◽  
Symmetry Operations

The symmetry groups of nonrigid molecules possess two subgroups: one is that of all the symmetry operations of the Schrödinger group of the molecule and the other is a group of a new type of operation called an isodynamic operation. The total group, which is called the Schrödinger supergroup, is a semidirect product of the Schrödinger group and the isodynamic group. Examples are given for borondifluoride methyl, ethane, dimethylacetylene and borontrimethyl. It is shown that in certain cases the double groups of the isodynamic group have to be used. The results do not agree always with those recently given by Longuet-Higgins: a careful analysis of the nature of symmetry and isodynamic operations indicates the origin of the discrepancy.

Stromatoporoids from the Famennian (Devonian) Wabamun Formation, Normandville oilfield, north–central Alberta, Canada

1988 ◽  
Vol 62 (03) ◽  
pp. 411-419 ◽  
Author(s):  
Colin W. Stearn
Keyword(s):  
Patch Reef ◽  
Abundant Species ◽  
The Other ◽  
North Central ◽  
Biotic Crisis

Stromatoporoids are the principal framebuilding organisms in the patch reef that is part of the reservoir of the Normandville field. The reef is 10 m thick and 1.5 km2in area and demonstrates that stromatoporoids retained their ability to build reefal edifices into Famennian time despite the biotic crisis at the close of Frasnian time. The fauna is dominated by labechiids but includes three non-labechiid species. The most abundant species isStylostroma sinense(Dong) butLabechia palliseriStearn is also common. Both these species are highly variable and are described in terms of multiple phases that occur in a single skeleton. The other species described areClathrostromacf.C. jukkenseYavorsky,Gerronostromasp. (a columnar species), andStromatoporasp. The fauna belongs in Famennian/Strunian assemblage 2 as defined by Stearn et al. (1988).

D. The Line Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 207-244
Author(s):  
R. P. Kraft
Keyword(s):  
Variable Stars ◽  
The Other ◽  
Line Spectrum ◽  
Afternoon Session ◽  
Empirical Information ◽  
Pulsating Variable Stars ◽  
Almost Continuous ◽  
Informal Approach

(Ed. note:Encouraged by the success of the more informal approach in Christy's presentation, we tried an even more extreme experiment in this session, I-D. In essence, Kraft held the floor continuously all morning, and for the hour and a half afternoon session, serving as a combined Summary-Introductory speaker and a marathon-moderator of a running discussion on the line spectrum of cepheids. There was almost continuous interruption of his presentation; and most points raised from the floor were followed through in detail, no matter how digressive to the main presentation. This approach turned out to be much too extreme. It is wearing on the speaker, and the other members of the symposium feel more like an audience and less like participants in a dissective discussion. Because Kraft presented a compendious collection of empirical information, and, based on it, an exceedingly novel series of suggestions on the cepheid problem, these defects were probably aggravated by the first and alleviated by the second. I am much indebted to Kraft for working with me on a preliminary editing, to try to delete the side-excursions and to retain coherence about the main points. As usual, however, all responsibility for defects in final editing is wholly my own.)

C. The Continuous Spectrum of Pulsating Variable Stars

1967 ◽  
Vol 28 ◽  
pp. 177-206
Author(s):  
J. B. Oke ◽  
C. A. Whitney
Keyword(s):  
Continuous Spectrum ◽  
Variable Stars ◽  
Velocity Fields ◽  
The Other ◽  
Line Spectrum ◽  
Direct Information ◽  
Thermodynamic Structure ◽  
Diagnostic Interpretation ◽  
Pulsating Variable Stars ◽  
The Continuum

Pecker:The topic to be considered today is the continuous spectrum of certain stars, whose variability we attribute to a pulsation of some part of their structure. Obviously, this continuous spectrum provides a test of the pulsation theory to the extent that the continuum is completely and accurately observed and that we can analyse it to infer the structure of the star producing it. The continuum is one of the two possible spectral observations; the other is the line spectrum. It is obvious that from studies of the continuum alone, we obtain no direct information on the velocity fields in the star. We obtain information only on the thermodynamic structure of the photospheric layers of these stars–the photospheric layers being defined as those from which the observed continuum directly arises. So the problems arising in a study of the continuum are of two general kinds: completeness of observation, and adequacy of diagnostic interpretation. I will make a few comments on these, then turn the meeting over to Oke and Whitney.

Observing programme for the 24-inch/36-inch Schmidt telescope

1966 ◽  
Vol 24 ◽  
pp. 337
Author(s):  
W. Iwanowska
Keyword(s):  
The Other ◽  
Schmidt Telescope ◽  
Flint Glass

A new 24-inch/36-inch//3 Schmidt telescope, made by C. Zeiss, Jena, has been installed since 30 August 1962, at the N. Copernicus University Observatory in Toruń. It is equipped with two objective prisms, used separately, one of crown the other of flint glass, each of 5° refracting angle, giving dispersions of 560Å/mm and 250Å/ mm respectively.

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