Three Dimensional Pattern Grading Based on Deformable Body Features and 3D Developable Surface

2011 ◽  
Vol 4 (2) ◽  
pp. 115-128 ◽  
Author(s):  
Haiqiao Huang
Keyword(s):  
Deformable Body ◽  
Three Dimensional ◽  
Developable Surface ◽  
Pattern Grading

Design of a Two-Piece Brassiere Cup From its Data Points Toward its Automation

2020 ◽  
Author(s):  
Kotaro Yoshida ◽  
Hidefumi Wakamatsu ◽  
Eiji Morinaga ◽  
Takahiro Kubo
Keyword(s):  
Three Dimensional ◽  
Developable Surface ◽  
Two Dimensional ◽  
Trial And Error ◽  
Design Efficiency ◽  
Developable Surfaces ◽  
Data Points ◽  
Dimensional Shape ◽  
The Given ◽  
Three Dimensional Shape

Abstract A method to design the two-dimensional shapes of patterns of two piece brassiere cup is proposed when its target three-dimensional shape is given as a cloud of its data points. A brassiere cup consists of several patterns and their shapes are designed by repeatedly making a paper cup model and checking its three-dimensional shape. For improvement of design efficiency of brassieres, such trial and error must be reduced. As a cup model for check is made of paper not cloth, it is assumed that the surface of the model is composed of several developable surfaces. When two lines that consist in the developable surface are given, the surface can be determined. Then, the two-piece brassiere cup can be designed by minimizing the error between the surface and given data points. It was mathematically verified that the developable surface calculated by our propose method can reproduce the given data points which is developable surface.

The calculation of three-dimensional turbulent boundary layers in incompressible flow

1969 ◽  
Vol 37 (4) ◽  
pp. 625-642 ◽  
Author(s):  
J. F. Nash
Keyword(s):  
Shear Stress ◽  
Incompressible Flow ◽  
Energy Equation ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Turbulent Energy ◽  
Two Dimensions ◽  
Turbulent Shear ◽  
Developable Surface ◽  
Turbulent Shear Stress

A method is described for calculating the development of a three-dimensional turbulent boundary layer, over a flat or developable surface, in incompressible flow. The method involves the numerical integration of the equations of motion by an explicit finite-difference method. The shear stress is determined by a parallel integration of the turbulent energy equation modified by the inclusion of empirical functions of a form which has proved successful in two dimensions, and the additional assumption is made that the turbulent shear stress acts in the direction of the rate of strain of the mean motion. The treatment of the turbulent energy equation follows closely the work of Bradshaw, Ferriss & Atwell (1967) in two dimensions.Comparison with experiment is found to be substantially more difficult than in two dimensions. Particular difficulty is encountered in translating the recorded details of the experiment into boundary conditions for the calculation. The comparisons submitted here give some indication that the method as a whole performs satisfactorily, but they do not provide a definitive assessment of the validity of the basic assumptions. A plea is made for an experiment to supply data in a suitable form for making a more careful assessment of methods of this type.

Swimming due to transverse shape deformations

2009 ◽  
Vol 631 ◽  
pp. 127-148 ◽  
Author(s):  
EVA KANSO
Keyword(s):  
Potential Flow ◽  
Deformable Body ◽  
Three Dimensional ◽  
Point Vortices ◽  
Vortex Wake ◽  
Balance Laws ◽  
Reactive Force ◽  
Slender Bodies ◽  
Shape Changes ◽  
Shape Deformations

Balance laws are derived for the swimming of a deformable body due to prescribed shape changes and the effect of the wake vorticity. The underlying balances of momenta, though classical in nature, provide a unifying framework for the swimming of three-dimensional and planar bodies and they hold even in the presence of viscosity. The derived equations are consistent with Lighthill's reactive force theory for the swimming of slender bodies and, when neglecting vorticity, reduce to the model developed in Kanso et al. (J. Nonlinear Sci., vol. 15, 2005, p. 255) for swimming in potential flow. The locomotion of a deformable body is examined through two sets of examples: the first set studies the effect of cyclic shape deformations, both flapping and undulatory, on the locomotion in potential flow while the second examines the effect of the wake vorticity on the net locomotion. In the latter, the vortex wake is modelled using pairs of point vortices shed periodically from the tail of the deformable body.

Contact Loading of a Rubber Disk

1985 ◽  
Vol 13 (1) ◽  
pp. 3-15 ◽  
Author(s):  
R. A. Ridha ◽  
K. Satyamurthy ◽  
L. R. Hirschfelt ◽  
R. E. Holle
Keyword(s):  
Close Agreement ◽  
Deformable Body ◽  
Three Dimensional ◽  
Computational Method ◽  
Element Analysis ◽  
Contact Loading ◽  
Contact Algorithm ◽  
The Finite Element Analysis ◽  
Deformable Bodies ◽  
Rigid Surfaces

Abstract A computational method is described for the analysis of deformable bodies loaded against rigid surfaces. The deformable body is modeled by three-dimensional isoparametric elements. A contact algorithm determines the nodes that come into contact with each loading step; the finite element analysis computes the size and shape of the footprint and the distribution of contact pressure in the footprint. The procedure is illustrated by analysis of the contact of a rubber disk. The close agreement, shown between the computed and measured results for the rubber disk, demonstrates the potential of the technique for 3D contact analysis of pneumatic tires.

scholarly journals Three-Dimensional Lattice Boltzmann Simulation of Two-Phase Flow Containing a Deformable Body with a Viscoelastic Membrane

2011 ◽  
Vol 9 (5) ◽  
pp. 1397-1413 ◽  
Author(s):  
Toshiro Murayama ◽  
Masato Yoshino ◽  
Tetsuo Hirata
Keyword(s):  
Lattice Boltzmann ◽  
Present Method ◽  
Deformable Body ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Spherical Body ◽  
The Body ◽  
Elastic Model ◽  
Two Phase ◽  
Lattice Boltzmann Simulation

AbstractThe lattice Boltzmann method (LBM) with an elastic model is applied to the simulation of two-phase flows containing a deformable body with a viscoelastic membrane. The numerical method is based on the LBM for incompressible two-phase fluid flows with the same density. The body has an internal fluid covered by a viscoelastic membrane of a finite thickness. An elastic model is introduced to the LBM in order to determine the elastic forces acting on the viscoelastic membrane of the body. In the present method, we take account of changes in surface area of the membrane and in total volume of the body as well as shear deformation of the membrane. By using this method, we calculate two problems, the behavior of an initially spherical body under shear flow and the motion of a body with initially spherical or biconcave discoidal shape in square pipe flow. Calculated deformations of the body (the Taylor shape parameter) for various shear rates are in good agreement with other numerical results. Moreover, tank-treading motion, which is a characteristic motion of viscoelastic bodies in shear flows, is simulated by the present method.

scholarly journals Ultra-fast escape of a deformable jet-propelled body

2013 ◽  
Vol 721 ◽  
pp. 367-385 ◽  
Author(s):  
G. D. Weymouth ◽  
M. S. Triantafyllou
Keyword(s):  
Shape Change ◽  
Deformable Body ◽  
Three Dimensional ◽  
Inviscid Flow ◽  
Added Mass ◽  
Internal Cavity ◽  
Mass Energy ◽  
Fast Start ◽  
Escape Speed ◽  
Rigid Shell

AbstractIn this work a cephalopod-like deformable body that fills an internal cavity with fluid and expels it to propel an escape manoeuvre, while undergoing a drastic external shape change through shrinking, is shown to employ viscous as well as mainly inviscid hydrodynamic mechanisms to power an impressively fast start. First, we show that recovery of added-mass energy enables a shrinking rocket in a dense inviscid flow to achieve greater escape speed than an identical rocket in a vacuum. Next, we extend the shrinking body results of Weymouth & Triantafyllou (J. Fluid Mech., vol. 702, 2012, pp. 470–487) to three-dimensional bodies and show that three hydrodynamic mechanisms must be combined to achieve rapid escape performance in a viscous fluid: added-mass energy recovery; flow separation elimination; and an optimized energy storage and recovery. In particular, we show that the mechanism of separation elimination achieved through rapid body shrinking, coordinated with the mechanism of recovering the initially imparted added-mass energy, is critical to achieving a high escape speed. Hence a flexible, collapsing body can be vastly superior to a rigid-shell jet-propelled body.

scholarly journals Concentrated force effects in the method of boundary state

2020 ◽  
pp. 34-44
Author(s):  
Максим Владимирович Поликарпов ◽  
Виктор Борисович Пеньков
Keyword(s):  
Deformable Body ◽  
Three Dimensional ◽  
Physical Nature ◽  
Stress Strain ◽  
Concentrated Force ◽  
Boundary State ◽  
Boundary States ◽  
Special Solutions ◽  
Concentrated Forces ◽  
State Method

Данная статья посвящена развитию метода граничных состояний на класс задач механики твердого деформируемого тела, включающих сингулярности физического характера. Сформировано множество специальных решений, соответствующих сосредоточенным силовым воздействиям на поверхности гладкого трехмерного тела. Каждое специальное решение включено в базисы пространств внутренних и граничных состояний. В качестве примеров эффективности использования специальных решений методом граничных состояний построены напряжённо-деформированные состояния тел шарообразной формы под воздействием сосредоточенных сил. This article is devoted to the development of the method of boundary states into a class of problems of mechanics of a solid deformable body, including singularities of a physical nature. Many special solutions have been formed corresponding to concentrated force actions on the surface of a smooth three-dimensional body. Each special solution is included in the bases of spaces of internal and boundary states. As examples of the effectiveness of using special solutions using the boundary state method, stress-strain states of spherical bodies are constructed under the influence of concentrated forces.

scholarly journals Möbius bands, unstretchable material sheets and developable surfaces

2016 ◽  
Vol 472 (2192) ◽  
pp. 20160459 ◽  
Author(s):  
Yi-chao Chen ◽  
Eliot Fried
Keyword(s):  
Equilibrium Shape ◽  
Three Dimensional ◽  
Dimensional Euclidean Space ◽  
Developable Surface ◽  
Rectangular Region ◽  
Isometric Mapping ◽  
Developable Surfaces ◽  
Planar Region ◽  
Möbius Band ◽  
Modelling Strategies

A Möbius band can be formed by bending a sufficiently long rectangular unstretchable material sheet and joining the two short ends after twisting by 180 ° . This process can be modelled by an isometric mapping from a rectangular region to a developable surface in three-dimensional Euclidean space. Attempts have been made to determine the equilibrium shape of a Möbius band by minimizing the bending energy in the class of mappings from the rectangular region to the collection of developable surfaces. In this work, we show that, although a surface obtained from an isometric mapping of a prescribed planar region must be developable, a mapping from a prescribed planar region to a developable surface is not necessarily isometric. Based on this, we demonstrate that the notion of a rectifying developable cannot be used to describe a pure bending of a rectangular region into a Möbius band or a generic ribbon, as has been erroneously done in many publications. Specifically, our analysis shows that the mapping from a prescribed planar region to a rectifying developable surface is isometric only if that surface is cylindrical with the midline being the generator. Towards providing solutions to this issue, we discuss several alternative modelling strategies that respect the distinction between the physical constraint of unstretchability and the geometrical notion of developability.

scholarly journals GENERAL REFERENCE FRAMES AND THEIR ASSOCIATED SPACE MANIFOLDS

2011 ◽  
Vol 08 (01) ◽  
pp. 155-165 ◽  
Author(s):  
MAYEUL ARMINJON ◽  
FRANK REIFLER
Keyword(s):  
Quantum Mechanics ◽  
Reference Frame ◽  
Reference Frames ◽  
Deformable Body ◽  
Three Dimensional ◽  
Differentiable Manifold ◽  
Hamiltonian Operator ◽  
Formal Definition ◽  
General Reference ◽  
Time Coordinate

We propose a formal definition of a general reference frame in a general spacetime, as an equivalence class of charts. This formal definition corresponds with the notion of a reference frame as being a (fictitious) deformable body, but we assume, moreover, that the time coordinate is fixed. This is necessary for quantum mechanics, because the Hamiltonian operator depends on the choice of the time coordinate. Our definition allows us to associate rigorously with each reference frame F, a unique "space" (a three-dimensional differentiable manifold), which is the set of the world lines bound to F. This also is very useful for quantum mechanics. We briefly discuss the application of these concepts to Gödel's universe.

Infinitesimally affine deformations of a hypersurface

2016 ◽  
Vol 23 (2) ◽  
pp. 209-220
Author(s):  
Nikos Kadianakis ◽  
Fotios I Travlopanos
Keyword(s):  
Continuum Mechanics ◽  
Deformable Body ◽  
Affine Connection ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Decomposition Theorem ◽  
General Context ◽  
Necessary And Sufficient ◽  
Straight Lines ◽  
The Continuum

Affine deformations serve as basic examples in the continuum mechanics of deformable three-dimensional bodies (usually referred to as homogeneous deformations). They preserve parallelism of straight lines, and are often used as an approximation to general deformations. However, when the deformable body is a membrane, a shell or an interface modeled by a surface, parallelism is defined by the affine connection of this surface. In this work we study the infinitesimally affine time-dependent deformations (motions) of such a continuum, but in a more general context, by considering that it is modeled by a Riemannian hypersurface. First we prove certain equivalent formulas for the variation of the connection of the hypersurface. Some of these formulas are expressed in terms of geometrical quantities, and others in terms of kinematical quantities of the deforming continuum. The latter is achieved by using an adapted version of the polar decomposition theorem, frequently used in continuum mechanics to analyze motion. We also apply our results to special motions like tangential and normal motions. Further, we find necessary and sufficient conditions for this variation to be zero (infinitesimal affine motions), providing insight on the form of these motions and the kind of hypersurfaces that allow such motions. Finally, we give some specific examples of mechanical interest which demonstrate motions that are infinitesimally affine but not infinitesimally isometric.

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