Force Stream Function Method Applied to Classical Griffith’s Crack Problem

2007 ◽  
Vol 129 (8) ◽  
pp. 1080-1082
Author(s):  
Xiang Wu ◽  
Joseph Genin
Keyword(s):  
Stress Analysis ◽  
Stream Function ◽  
Function Method ◽  
General Relation ◽  
Crack Problem ◽  
Numerical Results ◽  
Analysis Procedure ◽  
New Method ◽  
Fluid Stream ◽  
Linear Fracture

In a previous paper (Wu, X., and Genin, J., 2003, J. Strain Anal. Eng. Des., 38(2), pp. 181–185), we presented a new stress analysis procedure, the force stream function method. It established a general relationship between a fluid stream function and a force stream function through pure elasticity examples. Here, we expand its applications to the field of linear fracture. A brief review of the new method is provided at the paper’s beginning. When applied to the classical Griffith’s crack problem, the corresponding fluid stream function of a flow past a normal plate is conveniently used as an analog for the crack problem. Numerical results are employed to verify the general relation in this particular case. The significance of the new force stream function method and some difficulties of its applications are discussed in the paper’s conclusion.

Force stream function method

2003 ◽  
Vol 38 (2) ◽  
pp. 181-185 ◽  
Author(s):  
X Wu ◽  
J Genin
Keyword(s):  
Stream Function ◽  
Stress Function ◽  
Function Method ◽  
Analysis Procedure ◽  
Airy Stress Function ◽  
Fluid Stream ◽  
Simple Tension ◽  
Elasticity Problems ◽  
Tension Plate ◽  
The Relationship

A new stress analysis procedure, the force stream function method, is introduced. A general relationship between a fluid stream function and a force stream function is established. Simultaneously, the relationship between an Airy stress function and the force stream function is also presented. Classic elasticity problems, such as a simple tension plate with a circular hole in it and torsional problems are revisited using the method.

A New Method for Detecting the Diameter and Spatial Location of Tiny Through-Hole

2011 ◽  
Vol 189-193 ◽  
pp. 4186-4190 ◽  
Author(s):  
Zhi Gen Fei ◽  
Jun Jie Guo ◽  
Chang Shi Li
Keyword(s):  
Image Processing ◽  
Function Method ◽  
Optical Axis ◽  
Spatial Location ◽  
Processing Technique ◽  
New Method ◽  
Image Processing Technique ◽  
Experimental Platform ◽  
Digital Image Processing Technique ◽  
Through Hole

Aiming at the problem that the traditional plunged-bar method is difficult to meet the measurement requirement of spatial location of thin and small through-hole, in this paper, the digital image processing technique combined with sub-pixel detection technique is employed, and a new method is proposed to detect the tiny through-holes. The evaluating function method based on the “roundness” of the image of hole is presented to find out the posture parameters of CCD where the optical axis of CCD is parallel to the centerline of hole. Therefore, the spatial location of hole can be easily obtained by these posture parameters. Meanwhile, the diameter of hole can be achieved by means of image measuring technology at calculated posture of CCD. Owing to the non-contact measurement, this method is particularly suitable for those small through-holes drilled on the soft and easy-deformed object. The experiment results on the experimental platform illustrate the feasibility and validity of this method.

A Penalty-Free Method with Trust Region for Nonlinear Semidefinite Programming

2015 ◽  
Vol 32 (01) ◽  
pp. 1540006 ◽  
Author(s):  
Zhongwen Chen ◽  
Shicai Miao
Keyword(s):  
Semidefinite Programming ◽  
Objective Function ◽  
Penalty Function ◽  
Trust Region ◽  
Numerical Results ◽  
New Method ◽  
Penalty Parameter ◽  
Nonlinear Semidefinite Programming ◽  
Globally Convergent ◽  
Nonlinear Objective Function

In this paper, we propose a class of new penalty-free method, which does not use any penalty function or a filter, to solve nonlinear semidefinite programming (NSDP). So the choice of the penalty parameter and the storage of filter set are avoided. The new method adopts trust region framework to compute a trial step. The trial step is then either accepted or rejected based on the some acceptable criteria which depends on reductions attained in the nonlinear objective function and in the measure of constraint infeasibility. Under the suitable assumptions, we prove that the algorithm is well defined and globally convergent. Finally, the preliminary numerical results are reported.

Seismogram synthesis for multi-layered media with irregular interfaces by global generalized reflection/transmission matrices method. II. Applications for 2D SH case

1995 ◽  
Vol 85 (4) ◽  
pp. 1094-1106
Author(s):  
Xiaofei Chen
Keyword(s):  
Present Article ◽  
Analytical Solutions ◽  
Scattering Problem ◽  
Layered Media ◽  
Synthetic Seismograms ◽  
Numerical Results ◽  
New Method ◽  
New Formulation ◽  
Series Study

Abstract As the second part of a series study attempting to present a new method of seismogram synthesis for the irregular multi-layered media problems, the present article is devoted to discussing the aspects of the implementation of our new formulation developed earlier in part I of this series study (Chen, 1990). In this article, we have verified the validity of the formulation by comparing our numerical results with the existing analytical solutions for the scattering problem of a semi-circular canyon, and have shown its applicability by computing the synthetic seismograms for several selected irregular multi-layered media cases. Finally, applying our algorithm to the Whittier-Narrows earthquake of 1987, we have successfully interpreted the observed records.

scholarly journals A modified truncation singular value decomposition method for solving ill-posed problems

2018 ◽  
Vol 13 ◽  
pp. 174830181881360 ◽  
Author(s):  
Zhenyu Zhao ◽  
Riguang Lin ◽  
Zehong Meng ◽  
Guoqiang He ◽  
Lei You ◽  
...  
Keyword(s):  
Singular Value Decomposition ◽  
Decomposition Method ◽  
Singular Value ◽  
Numerical Results ◽  
New Method ◽  
Truncated Singular Value Decomposition ◽  
Singular Value Decomposition Method ◽  
Ill Posed ◽  
Value Decomposition

A modified truncated singular value decomposition method for solving ill-posed problems is presented in this paper, in which the solution has a slightly different form. Both theoretical and numerical results show that the limitations of the classical TSVD method have been overcome by the new method and very few additive computations are needed.

A NEW INTERFACE CEMENT EQUILIBRATED MORTAR (NICEM) METHOD WITH ROBIN INTERFACE CONDITIONS: THE P1 FINITE ELEMENT CASE

2013 ◽  
Vol 23 (12) ◽  
pp. 2253-2292 ◽  
Author(s):  
CAROLINE JAPHET ◽  
YVON MADAY ◽  
FREDERIC NATAF
Keyword(s):  
Finite Element ◽  
Error Analysis ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Numerical Results ◽  
New Method ◽  
Interface Conditions ◽  
Well Posed

We design and analyze a new non-conforming domain decomposition method, named the NICEM method, based on Schwarz-type approaches that allows for the use of Robin interface conditions on non-conforming grids. The method is proven to be well posed. The error analysis is performed in 2D and in 3D for P1 elements. Numerical results in 2D illustrate the new method.

scholarly journals ESTIMATION OF WATER PARTICLE VELOCITIES OF SHALLOW WATER WAVES BY A MODIFIED TRANSFER FUNCTION METHOD

1986 ◽  
Vol 1 (20) ◽  
pp. 33 ◽  
Author(s):  
Hirofumi Koyama ◽  
Koichiro Iwata
Keyword(s):  
Transfer Function ◽  
Shallow Water ◽  
Approximate Method ◽  
Stream Function ◽  
Water Waves ◽  
Function Method ◽  
Finite Amplitude ◽  
Water Particle ◽  
Irregular Wave ◽  
Particle Velocities

This paper Is intended to propose a simple, yet highly reliable approximate method which uses a modified transfer function in order to evaluate the water particle velocity of finite amplitude waves at shallow water depth in regular and irregular wave environments. Using Dean's stream function theory, the linear function is modified so as to include the nonlinear effect of finite amplitude wave. The approximate method proposed here employs the modified transfer function. Laboratory experiments have been carried out to examine the validity of the proposed method. The approximate method is shown to estimate well the experimental values, as accurately as Dean's stream function method, although its calculation procedure is much simpler than that of Dean's method.

Transient Response of an Interface-Crack in a Layered Plate

1986 ◽  
Vol 53 (3) ◽  
pp. 579-586 ◽  
Author(s):  
T. Kundu
Keyword(s):  
Stress Field ◽  
Interface Crack ◽  
Transient Response ◽  
Singular Integrals ◽  
Fortran Program ◽  
Numerical Results ◽  
New Method ◽  
Layered Plate ◽  
Improved Method ◽  
Sample Problem

In this paper, the transient response of an interface crack, in a two layered plate subjected to an antiplane stress field, is analytically computed. The problem is formulated in terms of semi-infinite integrals following the technique developed by Neerhoff (1979). It has been shown that the major steps of Neerhoff’s technique, which was originally developed for layered half-spaces, can also be applied to layered plate problems. An improved method for manipulation of semi-infinite singular integrals is also presented here. Finally, the new method is coded in FORTRAN program and numerical results for a sample problem are presented.

scholarly journals Validation of the stream function method used for reconstruction of experimental ionospheric convection patterns

2000 ◽  
Vol 18 (4) ◽  
pp. 454-460
Author(s):  
P.L. Israelevich ◽  
V. O. Papitashvili ◽  
A. I. Ershkovich
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Stream Function ◽  
Electric Fields ◽  
Electric Potential ◽  
Potential Distribution ◽  
Function Method ◽  
Polar Cap ◽  
Ionospheric Convection ◽  
Convection Patterns

Abstract. In this study we test a stream function method suggested by Israelevich and Ershkovich for instantaneous reconstruction of global, high-latitude ionospheric convection patterns from a limited set of experimental observations, namely, from the electric field or ion drift velocity vector measurements taken along two polar satellite orbits only. These two satellite passes subdivide the polar cap into several adjacent areas. Measured electric fields or ion drifts can be considered as boundary conditions (together with the zero electric potential condition at the low-latitude boundary) for those areas, and the entire ionospheric convection pattern can be reconstructed as a solution of the boundary value problem for the stream function without any preliminary information on ionospheric conductivities. In order to validate the stream function method, we utilized the IZMIRAN electrodynamic model (IZMEM) recently calibrated by the DMSP ionospheric electrostatic potential observations. For the sake of simplicity, we took the modeled electric fields along the noon-midnight and dawn-dusk meridians as the boundary conditions. Then, the solution(s) of the boundary value problem (i.e., a reconstructed potential distribution over the entire polar region) is compared with the original IZMEM/DMSP electric potential distribution(s), as well as with the various cross cuts of the polar cap. It is found that reconstructed convection patterns are in good agreement with the original modelled patterns in both the northern and southern polar caps. The analysis is carried out for the winter and summer conditions, as well as for a number of configurations of the interplanetary magnetic field.Key words: Ionosphere (electric fields and currents; plasma convection; modelling and forecasting)

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