139 research outputs found
多自由度剛体折紙構造の設計と幾何学的非線形解析
京都大学新制・課程博士博士(工学)甲第24576号工博第5082号新制||工||1973(附属図書館)京都大学大学院工学研究科建築学専攻(主査)教授 大崎 純, 教授 竹脇 出, 教授 聲高 裕治学位規則第4条第1項該当Doctor of Philosophy (Engineering)Kyoto UniversityDFA
Non-Parametric Shape Design of Free-Form Shells Using Fairness Measures and Discrete Differential Geometry
A non-parametric approach is proposed for shape design of free-form shells discretized into triangular mesh. The discretized forms of curvatures are used for computing the fairness measures of the surface. The measures are defined as the area of the offset surface and the generalized form of the Gauss map. Gaussian curvature and mean curvature are computed using the angle defect and the cotangent formula, respectively, defined in the field of discrete differential geometry. Optimization problems are formulated for minimizing various fairness measures for shells with specified boundary conditions. A piecewise developable surface can be obtained without a priori assignment of the internal boundary. Effectiveness of the proposed method for generating various surface shapes is demonstrated in the numerical examples
Equilibrium path and stability analysis of rigid origami using energy minimization of frame model
This paper presents a method of equilibrium path analysis and stability analysis of an equilibrium state for a rigid origami, which consists of rigid flat faces connected by straight crease lines (folding lines) and can be folded and unfolded without deformation of its faces. This property is well suited to the application to deployable structures and morphing building envelopes consisting of stiff panels. In this study, a frame model which consists of hinges and rigid frame members is used to model the kinematics of a rigid origami. Faces and crease lines of a rigid origami are represented by frame members and hinges, respectively. External loads are applied to the nodes of a frame model, and the displacements of some nodes are fixed. Small rotational stiffness proportional to the length of a crease line is assumed in each hinge to uniquely determine the equilibrium state, which is obtained by solving the optimization problem for minimizing the total potential energy under the conditions so that the displacements of the nodes and the members are compatible. The optimization problem is solved by the augmented Lagrangian method, and the positive definiteness of the Hessian of the augmented Lagrangian is investigated to determine the stability of the equilibrium state. Equilibrium path analyses are carried out and bifurcations of the equilibrium paths are investigated for examples with waterbomb patterns
Real and complexified configuration spaces for spherical 4-bar linkages
This note is a complete library of symbolic parametrized expressions for both
real and complexified configuration spaces of a spherical 4-bar linkage.
Building upon the previous work from Izmestiev, (2016, Section 2), this library
expands on the expressions by incorporating all four folding angles across all
possible linkage length choices, along with the polynomial relation between
diagonals (spherical arcs). Furthermore, a complete MATLAB app script is
included, enabling visualization and parametrization. The derivations are
presented in a detailed manner, ensuring accessibility for researchers across
diverse disciplines.Comment: arXiv admin note: substantial text overlap with arXiv:2307.1220
The Great Space Weather Event during February 1872 Recorded in East Asia
The study of historical great geomagnetic storms is crucial for assessing the
possible risks to the technological infrastructure of a modern society, caused
by extreme space-weather events. The normal benchmark has been the great
geomagnetic storm of September 1859, the so-called "Carrington Event". However,
there are numerous records of another great geomagnetic storm in February 1872.
This storm, about 12 years after the Carrington Event, resulted in comparable
magnetic disturbances and auroral displays over large areas of the Earth. We
have revisited this great geomagnetic storm in terms of the auroral and sunspot
records in the historical documents from East Asia. In particular, we have
surveyed the auroral records from East Asia and estimated the equatorward
boundary of the auroral oval to be near 24.3 deg invariant latitude (ILAT), on
the basis that the aurora was seen near the zenith at Shanghai (20 deg magnetic
latitude, MLAT). These results confirm that this geomagnetic storm of February
1872 was as extreme as the Carrington Event, at least in terms of the
equatorward motion of the auroral oval. Indeed, our results support the
interpretation of the simultaneous auroral observations made at Bombay (10 deg
MLAT). The East Asian auroral records have indicated extreme brightness,
suggesting unusual precipitation of high-intensity, low-energy electrons during
this geomagnetic storm. We have compared the duration of the East Asian auroral
displays with magnetic observations in Bombay and found that the auroral
displays occurred in the initial phase, main phase, and early recovery phase of
the magnetic storm.Comment: 28 pages, 5 figures, accepted for publication in the Astrophysical
Journal on 31 May 201
A Great Space Weather Event in February 1730
Aims. Historical records provide evidence of extreme magnetic storms with
equatorward auroral extensions before the epoch of systematic magnetic
observations. One significant magnetic storm occurred on February 15, 1730. We
scale this magnetic storm with auroral extension and contextualise it based on
contemporary solar activity. Methods. We examined historical records in East
Asia and computed the magnetic latitude (MLAT) of observational sites to scale
magnetic storms. We also compared them with auroral records in Southern Europe.
We examined contemporary sunspot observations to reconstruct detailed solar
activity between 1729 and 1731. Results. We show 29 auroral records in East
Asian historical documents and 37 sunspot observations. Conclusions. These
records show that the auroral displays were visible at least down to 25.8{\deg}
MLAT throughout East Asia. In comparison with contemporary European records, we
show that the boundary of the auroral display closest to the equator surpassed
45.1{\deg} MLAT and possibly came down to 31.5{\deg} MLAT in its maximum phase,
with considerable brightness. Contemporary sunspot records show an active phase
in the first half of 1730 during the declining phase of the solar cycle. This
magnetic storm was at least as intense as the magnetic storm in 1989, but less
intense than the Carrington event.Comment: 30 pages, 5 figures, and 2 tables, accepted for publication in
Astronomy & Astrophysics on 25 April 2018. The figures and
transcriptions/translations of historical documents are partially omitted in
this manuscript due to the condition of reproduction. They are available in
the publisher versio
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