Membrane theory

2017 ◽  
Author(s):  
David J. Steigmann
Keyword(s):  
Three Dimensional ◽  
Thin Sheets ◽  
Two Dimensional ◽  
Leading Order ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
Small Thickness

This chapter develops two-dimensional membrane theory as a leading order small-thickness approximation to the three-dimensional theory for thin sheets. Applications to axisymmetric equilibria are developed in detail, and applied to describe the phenomenon of bulge propagation in cylinders.

Contact Temperature in Dry Bearings. Three Dimensional Theory and Verification

1981 ◽  
Vol 103 (2) ◽  
pp. 243-251 ◽  
Author(s):  
A. Floquet ◽  
D. Play
Keyword(s):  
Fourier Transform ◽  
Boundary Conditions ◽  
Experimental Verification ◽  
Three Dimensional ◽  
Contact Temperature ◽  
3D Analysis ◽  
New Work ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Infra Red

Boundary conditions were arbitrarily specified in an earlier two dimensional (2D) analysis of contact temperature. In this new work a general three dimensional (3D) Fourier transform solution is obtained from which for specific cases, the boundary conditions can be estimated. Further, experimental verification of 3D analysis was performed using infra-red technique.

Extension of the Prandtl–Batchelor theorem to three-dimensional flows slowly varying in one direction

2010 ◽  
Vol 654 ◽  
pp. 351-361 ◽  
Author(s):  
M. SANDOVAL ◽  
S. CHERNYSHENKO
Keyword(s):  
Flow Field ◽  
Small Parameter ◽  
Order Approximation ◽  
Three Dimensional ◽  
Inviscid Limit ◽  
Two Dimensional ◽  
Leading Order ◽  
Dimensional Flow ◽  
Two Dimensional Flow

According to the Prandtl–Batchelor theorem for a steady two-dimensional flow with closed streamlines in the inviscid limit the vorticity becomes constant in the region of closed streamlines. This is not true for three-dimensional flows. However, if the variation of the flow field along one direction is slow then it is possible to expand the solution in terms of a small parameter characterizing the rate of variation of the flow field in that direction. Then in the leading-order approximation the projections of the streamlines onto planes perpendicular to that direction can be closed. Under these circumstances the extension of the Prandtl–Batchelor theorem is obtained. The resulting equations turned out to be a three-dimensional analogue of the equations of the quasi-cylindrical approximation.

Directed fluid sheets

1976 ◽  
Vol 347 (1651) ◽  
pp. 447-473 ◽  
Keyword(s):  
Water Waves ◽  
Three Dimensional ◽  
Steady Motion ◽  
Finite Depth ◽  
Free Surface Flows ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Inviscid Fluids ◽  
Two Dimensional Flows

This paper is concerned mainly with incompressible inviscid fluid sheets but the incompressible linearly viscous fluid sheet is also considered. Our development is based on a direct formulation using the two dimensional theory of directed media called Cosserat surfaces . The first part of the paper deals with the formulation of appropriate nonlinear equations (which may include the effects of gravity and surface tension) governing the two dimensional motion of incompressible inviscid media for two categories, namely those ( a ) for two dimensional flows confined to a plane perpendicular to a specified direction and ( b ) for propagation of fairly long waves in a stream of variable initial depth. The latter development is a generalization of an earlier direct formulation of a theory of water waves when the fixed bottom of the stream is level (Green, Laws & Naghdi 1974). In the second part of the paper, special attention is given to a demonstration of the relevance and applicability of the present direct formulation to a variety of two dimensional problems of inviscid fluid sheets. These include, among others, the steady motion of a class of two-dimensional flows in a stream of finite depth in which the bed of the stream may change from one constant level to another, the related problem of hydraulic jumps, and a class of exact solutions which characterize the main features of the time-dependent free surface flows in the three dimensional theory of incompressible inviscid fluids.

scholarly journals The path integral of 3D gravity near extremality; or, JT gravity with defects as a matrix integral

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Henry Maxfield ◽  
Gustavo J. Turiaci
Keyword(s):  
Classical Solution ◽  
Path Integral ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
Matrix Integral ◽  
Pure Gravity ◽  
Extremal Limit ◽  
3D Gravity

Abstract We propose that a class of new topologies, for which there is no classical solution, should be included in the path integral of three-dimensional pure gravity, and that their inclusion solves pathological negativities in the spectrum, replacing them with a nonperturbative shift of the BTZ extremality bound. We argue that a two dimensional calculation using a dimensionally reduced theory captures the leading effects in the near extremal limit. To make this argument, we study a closely related two-dimensional theory of Jackiw-Teitelboim gravity with dynamical defects. We show that this theory is equivalent to a matrix integral.

Revised Theory for the Quantitative Analysis of Fabric Hand

1980 ◽  
Vol 102 (1) ◽  
pp. 25-31 ◽  
Author(s):  
V. L. Alley
Keyword(s):  
Quantitative Analysis ◽  
Internal Pressure ◽  
Quantitative Measure ◽  
Extraction Process ◽  
Two Dimensional ◽  
Membrane Theory ◽  
Dimensional Theory ◽  
One Dimensional ◽  
Fabric Hand ◽  
Specimen Weight

A revision and extension of theory is presented on the nozzle extraction process for obtaining “Handle Moduli” as a quantitative measure of fabric hand. The original one dimensional theory is replaced with a two dimensional membrane theory and a different internal pressure hypothesis is proposed which gives better agreement between tests from different orifice sizes. Conversion relationships between the original and revised data are given and the interaction of specimen weight on “hand” measurements is formulated.

Influence of Rotatory Inertia and Shear on Flexural Motions of Isotropic, Elastic Plates

1951 ◽  
Vol 18 (1) ◽  
pp. 31-38 ◽  
Author(s):  
R. D. Mindlin
Keyword(s):  
Uniqueness Theorem ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Dimensional Theory ◽  
Rotatory Inertia ◽  
One Dimensional ◽  
Edge Conditions

Abstract A two-dimensional theory of flexural motions of isotropic, elastic plates is deduced from the three-dimensional equations of elasticity. The theory includes the effects of rotatory inertia and shear in the same manner as Timoshenko’s one-dimensional theory of bars. Velocities of straight-crested waves are computed and found to agree with those obtained from the three-dimensional theory. A uniqueness theorem reveals that three edge conditions are required.

In Search of Dominance: The Case of the Missing Dimension

2005 ◽  
Vol 100 (2) ◽  
pp. 559-566 ◽  
Author(s):  
Arthur E. Stamps
Keyword(s):  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Dimensional Theory

Some previous researchers have found that affect can be described in terms of two dimensions (pleasure and arousal), while others have noted three dimensions are needed (pleasure, arousal, and dominance). The competing claims were tested by creating stimuli with factors previously demonstrated to elicit responses of arousal or dominance, asking respondents to rate the stimuli, and contrasting correlations between ratings and the stimulus factors. Under the two-dimensional theory, the planned contrasts should be zero, while under the three-dimensional theory, the planned contrasts should be nonzero. Results supported the three-dimensional model.

On the theory of water waves

1974 ◽  
Vol 338 (1612) ◽  
pp. 43-55 ◽  
Keyword(s):  
Water Waves ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Dimensional Theory ◽  
De Vries ◽  
Set Up ◽  
Propagation Of Waves

The aim of this paper is to formulate a two-dimensional theory for the propagation of fairly long water waves. The approach differs from the usual in that the theory is set up via two-dimensional postulates. Subsequently, it is shown how a simple three-dimensional approxi­mation enables us to relate the two-dimensional theory to the three-dimensional theory. The resulting equations are used to discuss the unidirectional propagation of waves. lt is shown how the results obtained from the theory proposed here are related to the results of Korteweg & de Vries (1895) and to those of Benjamin, Bona & Mahony (1972).

Evaluation of the Theory for the Flow Pattern of a Hydrofoil of Finite Span

1960 ◽  
Vol 4 (01) ◽  
pp. 13-29
Author(s):  
Paul Kaplan ◽  
John P. Breslin ◽  
Winnifred R. Jacobs
Keyword(s):  
Surface Wave ◽  
Flow Field ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Limited Data ◽  
Flow Properties ◽  
Dimensional Theory ◽  
Finite Span ◽  
Wave Elevation ◽  
Experimental Values

Expressions for various properties of the flow field aft of a finite-span hydrofoil in smooth water are presented and discussed in this paper. Potential functions for the motion that have been derived previously on the basis of linearized free-surface theory serve as the basic terms from which the flow field is derived. Both two-dimensional and three-dimensional theories are used, and the expressions derived for the surface-wave elevation and downwash from the various theories are compared with experimental values. As a result of this study, it is shown that three-dimensional effects are of great importance and hence terms derived from the two-dimensional theory do not accurately represent the true flow properties. Recommended formulas, whose validity is demonstrated by the comparison with the limited data presented herein, are given for the evaluation of both the surface-wave amplitude and downwash.

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