Compressibility of Two-Dimensional Cavities of Various Shapes

1986 ◽  
Vol 53 (3) ◽  
pp. 500-504 ◽  
Author(s):  
R. W. Zimmerman
Keyword(s):  
Closed Form Solution ◽  
Mapping Function ◽  
Complex Stress ◽  
Form Solution ◽  
Hydrostatic Compression ◽  
Biaxial Compression ◽  
Cavity Surface ◽  
Uniform Pressure ◽  
Two Dimensional ◽  
Stress Functions

Muskhelishvili-Kolosov complex stress functions are used to find the stresses and displacements around two-dimensional cavities under plane strain or plane stress. The boundary conditions considered are either uniform pressure at the cavity surface with vanishing stresses at infinity, or a traction-free cavity surface with uniform biaxial compression at infinity. A closed-form solution is obtained for the case where the mapping function from the interior of the unit circle to the region outside of the cavity has a finite number of terms. The area change of the cavity due to hydrostatic compression at infinity is examined for a variety of shapes, and is found to correlate closely with the square of the perimeter of the hole.

scholarly journals Analytic Solution for Systems of Two-Dimensional Time Conformable Fractional PDEs by Using CFRDTM

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Abir Chaouk ◽  
Maher Jneid
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Analytic Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
Fractional Pdes ◽  
Differential Transform ◽  
Computational Work ◽  
Similar Solutions

In this study we use the conformable fractional reduced differential transform (CFRDTM) method to compute solutions for systems of nonlinear conformable fractional PDEs. The proposed method yields a numerical approximate solution in the form of an infinite series that converges to a closed form solution, which is in many cases the exact solution. We inspect its efficiency in solving systems of CFPDEs by working on four different nonlinear systems. The results show that CFRDTM gave similar solutions to exact solutions, confirming its proficiency as a competent technique for solving CFPDEs systems. It required very little computational work and hence consumed much less time compared to other numerical methods.

scholarly journals Performance of New Austrian Tunneling Method (NATM) in Weak Rock Case Study

2018 ◽  
Vol 7 (4.20) ◽  
pp. 40
Author(s):  
Heba Kamal ◽  
. .
Keyword(s):  
Finite Element ◽  
Closed Form Solution ◽  
Side Wall ◽  
Form Solution ◽  
Two Dimensional ◽  
Phase 2 ◽  
Actual Case ◽  
Tunneling Method ◽  
New Austrian Tunneling Method

The decline in the over ground utilizable space and increment in development of metro structures, cut and cover structures are winding up fairly difficult to conceptualize and build. In this examination, a nonlinear two dimensional limited component investigation was completed to show the New Austrian Tunneling Method (NATM) burrow developed in frail shake utilizing the business limited component with joint programming PHASE 2.The validity of the numerical modeling procedure performed by the author was checked by making back-analysis for an actual case study of Strengen Tunnel which is one of the biggest expressways in western Austria.  A comprehensive parametric study was performed on a hypothetical circle tunnel. Two dimensional numerical simulations with the finite element with joint software PHASE 2 have been performed to ground behaviour with   the results of the numerical analysis are presented and   discussed for recommendations for future work. In general the tangential stress at side wall and crown  obtained from  finite element with joints are  nearly equal or higher than the closed form solution and equivalent continuum.                                                                                   

scholarly journals Block-Wise Two-Dimensional Maximum Margin Criterion for Face Recognition

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Xiao-Zhang Liu ◽  
Guan Yang
Keyword(s):  
Feature Extraction ◽  
Matrix Multiplication ◽  
Closed Form Solution ◽  
Image Data ◽  
Form Solution ◽  
Two Dimensional ◽  
Maximum Margin ◽  
Maximum Margin Criterion ◽  
Bilateral Projection ◽  
Characteristics Of Image

Maximum margin criterion (MMC) is a well-known method for feature extraction and dimensionality reduction. However, MMC is based on vector data and fails to exploit local characteristics of image data. In this paper, we propose a two-dimensional generalized framework based on a block-wise approach for MMC, to deal with matrix representation data, that is, images. The proposed method, namely, block-wise two-dimensional maximum margin criterion (B2D-MMC), aims to find local subspace projections using unilateral matrix multiplication in each block set, such that in the subspace a block is close to those belonging to the same class but far from those belonging to different classes. B2D-MMC avoids iterations and alternations as in current bilateral projection based two-dimensional feature extraction techniques by seeking a closed form solution of one-side projection matrix for each block set. Theoretical analysis and experiments on benchmark face databases illustrate that the proposed method is effective and efficient.

Effects of Geometry on the Performance of a Downhole Orbital Vibrator

2002 ◽  
Vol 124 (2) ◽  
pp. 77-82
Author(s):  
Robert R. Reynolds ◽  
Jack H. Cole ◽  
Zhen Yuan
Keyword(s):  
Pressure Field ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
Confined Water ◽  
Dimensional Model ◽  
Concentric Cylinder ◽  
Fe Method ◽  
Two Dimensional Model ◽  
Special Case

The influence of geometry on the pressure field within the confined, water-filled annulus between a central, vibrating cylinder and an outer, rigid enclosure is determined. A two-dimensional model is constructed using the finite element (FE) method and parameters are identified to characterize the eccentricity of the nominal cylinder position, the size of the annulus relative to the inner cylinder and the degree to which the annulus is not circular (i.e., it is elliptic). The FE solution is verified using a closed-form solution for the special case of a concentric cylinder and annulus. It is shown that the system acts as a force multiplier. Analyses of the asymmetrical geometries indicate that while the pressure field on the surface of the cylinder and enclosure can be highly asymmetric, the system is relatively insensitive to minor variations in annulus shape except when the vibrating cylinder is not centrally located within the fluid region or the annulus size itself is small.

Stress Concentration Factors at an Elliptical Hole on the Interface Between Bonded Dissimilar Half-Planes Under Bending Moment

1996 ◽  
Vol 63 (1) ◽  
pp. 7-14 ◽  
Author(s):  
Mohamed Salama ◽  
Norio Hasebe
Keyword(s):  
Stress Concentration ◽  
Elliptical Hole ◽  
Bending Moment ◽  
Mapping Function ◽  
Complex Stress ◽  
Function Technique ◽  
Rational Mapping ◽  
Stress Functions ◽  
Stress Concentration Factors ◽  
Thin Plate Bending

The problem of thin plate bending of two bonded half-planes with an elliptical hole on the interface and interface cracks on its both sides is presented. A uniformly distributed bending moment applied at the remote ends of the interface is considered. The complex stress functions approach together with the rational mapping function technique are used in the analysis. The solution is obtained in closed form. Distributions of bending and torsional moments, the stress concentration factor as well as the stress intensity factor, are given for all possible dimensions of the elliptical hole, various material constants, and rigidity ratios.

Two-Dimensional Elastohydrodynamic Lubrication Part 1: The Associated Dry Contact Problem

1988 ◽  
Vol 202 (5) ◽  
pp. 347-353 ◽  
Author(s):  
R W Hall ◽  
M D Savage
Keyword(s):  
Contact Problem ◽  
Contact Zone ◽  
Closed Form Solution ◽  
Surface Displacement ◽  
Form Solution ◽  
Two Dimensional ◽  
Fourier Cosine ◽  
Cosine Series ◽  
Ehd Lubrication ◽  
Dry Contact

Associated with each elastohydrodynamic (EHD) lubrication problem there is a dry contact problem with the same contact zone, |x| a, surface displacement, υ(x), and pressure distribution, p(x). This paper considers the two-dimensional dry contact problem and shows how Poritsky's closed-form solution can be used to derive results of fundamental importance to EHD lubrication. In particular, it is shown that singularities in pressure and pressure gradient arise from discontinuities in dυ/dx and d2υ/dx2. In addition, with υ(x) expressed as a Fourier cosine series of the form υ(x) = Σn Bn cos nη (where x = a cos η, 0 ≤ η ≤ π), it follows that at the end points of the contact zone, Reynolds boundary conditions are natural conditions yielding straightforward conditions on the Fourier coefficients, Bn.

scholarly journals Exact Solutions for Certain Nonlinear Autonomous Ordinary Differential Equations of the Second Order and Families of Two-Dimensional Autonomous Systems

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
M. P. Markakis
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Autonomous Systems ◽  
Closed Form Solution ◽  
First Integrals ◽  
Form Solution ◽  
Second Order ◽  
Two Dimensional ◽  
First Order ◽  
Abel Equations

Certain nonlinear autonomous ordinary differential equations of the second order are reduced to Abel equations of the first kind ((Ab-1) equations). Based on the results of a previous work, concerning a closed-form solution of a general (Ab-1) equation, and introducing an arbitrary function, exact one-parameter families of solutions are derived for the original autonomous equations, for the most of which only first integrals (in closed or parametric form) have been obtained so far. Two-dimensional autonomous systems of differential equations of the first order, equivalent to the considered herein autonomous forms, are constructed and solved by means of the developed analysis.

The Pressure Field Around a Vibrating Cylinder in a Fluid Annulus

2001 ◽  
Author(s):  
Robert R. Reynolds ◽  
Jack H. Cole ◽  
Zhen Yuan
Keyword(s):  
Pressure Field ◽  
Closed Form Solution ◽  
Form Solution ◽  
Two Dimensional ◽  
Confined Water ◽  
Dimensional Model ◽  
Concentric Cylinder ◽  
Fe Method ◽  
Two Dimensional Model ◽  
Special Case

Abstract The influence of geometry on the pressure field within the confined, water-filled annulus between a central, vibrating cylinder and an outer, rigid enclosure is determined. A two dimensional model is constructed using the finite element (FE) method and parameters are identified to characterize the eccentricity of the nominal cylinder position, the size of the annulus relative to the inner cylinder and the degree to which the annulus is not circular (i.e. it is elliptic). The FE solution is verified using a closed form solution for the special case of a concentric cylinder and annulus. It is shown that the system acts as a force multiplier. Analyses of the asymmetrical geometries indicate that while the pressure field on the surface of the cylinder and enclosure can be highly asymmetric, the system is relatively insensitive to minor variations in annulus shape except when the vibrating cylinder is not centrally located within the fluid region or the annulus size itself is small.

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