scholarly journals Discussion: “Analysis of Plane Stress in Polar Coordinates and With Varying Thickness” (Conway, H. D., 1959, ASME J. Appl. Mech., 26, pp. 437–439)

1960 ◽  
Vol 27 (2) ◽  
pp. 372-372
Author(s):  
V. S. Musick
Keyword(s):  
Plane Stress ◽  
Polar Coordinates ◽  
Varying Thickness

Waves From Suddenly Punched Hole in Plate Subjected to Uniaxial Tension Field

1979 ◽  
Vol 46 (4) ◽  
pp. 873-877 ◽  
Author(s):  
J. B. Haddow ◽  
A. Mioduchowski
Keyword(s):  
Numerical Solution ◽  
Uniaxial Tension ◽  
Plane Stress ◽  
Finite Time ◽  
Gas Dynamics ◽  
Polar Coordinates ◽  
Governing Equations ◽  
Spatial Variables ◽  
Independent Variables ◽  
Stress Components

The plane-stress unloading waves emanating from a suddenly punched circular hole in a thin plate subjected to a uniform uniaxial tension field are considered. It is assumed that the plate is linearly elastic and that the plugging of the hole takes place over a finite time with the stress components at the circumference of the hole decreasing, linearly with time, to zero. A modification of the method of near characteristics, introduced by Sauer [1], for problems of gas dynamics with two or three spatial variables is used to obtain a numerical solution to the governing equations, which have three independent variables, time and two plane polar coordinates. The numerical results obtained approach those for the well-known statical solution, for a hole in a plate subjected to a tension field [2], as the time after the arrival of the wave front becomes large.

Analysis of Plane Stress in Polar Co-ordinates and With Varying Thickness

1959 ◽  
Vol 26 (3) ◽  
pp. 437-439
Author(s):  
H. D. Conway
Keyword(s):  
General Solution ◽  
Plane Stress ◽  
Stress Function ◽  
Constant Thickness ◽  
Numerical Example ◽  
Arbitrary Power ◽  
Varying Thickness

Abstract The biharmonic stress-function equation for plane stress in polar co-ordinates is generalized by assuming that the thickness varies with the radius. In order to make this equation tractable, the thickness is assumed to be proportional to an arbitrary power of the radius. Michell’s general solution for the constant-thickness case is then generalized for this variation of thickness. As a numerical example, the solution is given for the problem of a segmental plate bent by end couples, the constant-thickness version of this well-known problem being due to Golovin.

Non-Polar Variation of Latitude

1972 ◽  
Vol 1 ◽  
pp. 93-101 ◽  
Author(s):  
S. Yumi
Keyword(s):  
Polar Motion ◽  
Polar Coordinates ◽  
Normal Variation ◽  
Latitude Variation ◽  
Local Trend

ABSTRACTAnalysing the residual latitude of the station, local trend in latitude variation other than by the polar motion was found.Residual latitude was calculated for each of 26 stations which gave the continuous records of observation during 6 years comprising — 1962 — 1967 as a difference between observed variation of latitude and – normal variation calculated by the polar coordinates Iderived from all the results of 26 stations.As far as the results during these six years are concerned, local trend at any station it seemed to be expressed in terms of 3λ.Assumed effect of local trend on the coordinates values of the instantaneous pole is also discussed.

Computing cell tractions from particle displacements on silicone rubber substrata

1994 ◽  
Vol 52 ◽  
pp. 162-163
Author(s):  
Tim Oliver ◽  
Akira Ishihara ◽  
Ken Jacobsen ◽  
Micah Dembo
Keyword(s):  
Plane Stress ◽  
Linear Elasticity ◽  
Silicone Rubber ◽  
Mathematical Analysis ◽  
Elastic Recovery ◽  
Video Images ◽  
Cell Traction Forces ◽  
Latex Beads ◽  
Cell Traction ◽  
Better Than

In order to better understand the distribution of cell traction forces generated by rapidly locomoting cells, we have applied a mathematical analysis to our modified silicone rubber traction assay, based on the plane stress Green’s function of linear elasticity. To achieve this, we made crosslinked silicone rubber films into which we incorporated many more latex beads than previously possible (Figs. 1 and 6), using a modified airbrush. These films could be deformed by fish keratocytes, were virtually drift-free, and showed better than a 90% elastic recovery to micromanipulation (data not shown). Video images of cells locomoting on these films were recorded. From a pair of images representing the undisturbed and stressed states of the film, we recorded the cell’s outline and the associated displacements of bead centroids using Image-1 (Fig. 1). Next, using our own software, a mesh of quadrilaterals was plotted (Fig. 2) to represent the cell outline and to superimpose on the outline a traction density distribution. The net displacement of each bead in the film was calculated from centroid data and displayed with the mesh outline (Fig. 3).

The solution problem of Dirihle for equation of Laplace in polar coordinates by method Monte Carlo

2018 ◽  
Vol 2 ◽  
pp. 114-122
Author(s):  
Yu.I. Nikolayenko ◽  
◽  
V.G. Ilvovsky ◽  
S.V. Moiseenko ◽  
◽  
...  
Keyword(s):  
Monte Carlo ◽  
Polar Coordinates ◽  
Solution Problem

scholarly journals Gauge invariance, polar coordinates and inflation

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ali Akil ◽  
Xi Tong
Keyword(s):  
Coordinate System ◽  
Effective Potential ◽  
Gauge Invariance ◽  
Polar Coordinates ◽  
Quantum Corrections ◽  
Background Current ◽  
Gauge Invariant ◽  
Gauge Dependence ◽  
Current Term ◽  
Invariant Current

Abstract We point out the necessity of resolving the apparent gauge dependence in the quantum corrections of cosmological observables for Higgs-like inflation models. We highlight the fact that this gauge dependence is due to the use of an asymmetric background current which is specific to a choice of coordinate system in the scalar manifold. Favoring simplicity over complexity, we further propose a practical shortcut to gauge-independent inflationary observables by using effective potential obtained from a polar-like background current choice. We demonstrate this shortcut for several explicit examples and present a gauge-independent prediction of inflationary observables in the Abelian Higgs model. Furthermore, with Nielsen’s gauge dependence identities, we show that for any theory to all orders, a gauge-invariant current term gives a gauge-independent effective potential and thus gauge-invariant inflationary observables.

Sign in / Sign up

Export Citation Format

Share Document