Three-Dimensional Wave Propagation in a Cracked Elastic Solid

1978 ◽  
Vol 45 (4) ◽  
pp. 807-811 ◽  
Author(s):  
S. Itou
Keyword(s):  
Dynamic Stress ◽  
Dynamic Stress Intensity Factor ◽  
Three Dimensional ◽  
Elastic Solid ◽  
Expansion Method ◽  
The Self ◽  
Finite Width ◽  
Infinite Length ◽  
Dimensional Wave ◽  
Series Expansion Method

The three-dimensional dynamic problem is presented for an infinite elastic medium weakened by a plane crack of infinite length and finite width. On the surfaces of the crack, the self-equilibrated system of a load varies harmonically in time and is distributed arbitrarily on those surfaces. The Fourier transformations are utilized to reduce the problem to a solution of two simultaneous integral equations which can be solved by using the series expansion method. The dynamic stress-intensity factor is computed numerically for some applied loads.

scholarly journals The effect of couple-stresses on the stress concentration around a moving crack

1981 ◽  
Vol 4 (1) ◽  
pp. 165-180 ◽  
Author(s):  
S. Itou
Keyword(s):  
Dynamic Stress ◽  
Couple Stress Theory ◽  
Dynamic Stress Intensity Factor ◽  
Expansion Method ◽  
Infinite Medium ◽  
Dual Integral Equations ◽  
Moving Crack ◽  
Stress Theory ◽  
Finite Crack ◽  
Series Expansion Method

The problem of a uniformly propagating finite crack in an infinite medium is solved within the linearized couple-stress theory. The self-equilibrated system of pressure is applied to the crack surfaces. The problem is reduced to dual integral equations and solved by a series-expansion method. The dynamic stress-intensity factor is computed numerically.

ELASTODYNAMIC STRESS INTENSITY FACTOR FOR A FINITE CRACK IN ELASTIC SOLID UNDER 3D TRANSIENT LOADING OF MODE I

2013 ◽  
Vol 05 (04) ◽  
pp. 1350044
Author(s):  
XIANHONG MENG ◽  
ZHAOYU BAI ◽  
MING LI
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Integral Transform ◽  
Elastic Solid ◽  
Scattered Wave ◽  
Mode I ◽  
Finite Width ◽  
Infinite Length ◽  
Distance Ratio

In this paper, the three-dimensional dynamic problem for an infinite elastic medium weakened by a crack of infinite length and finite width is analyzed, while the crack surfaces are subjected to mode I transient linear tractions. The integral transform approach is applied to reduce the governing differential equations to a pair of coupled singular integral equations, whose solutions can be obtained with the typical iteration method. The analytical solution of the stress intensity factor when the first wave and the first scattered wave reach the investigated crack tip is obtained. Numerical results are presented for different values of the width-to-longitudinal distance ratio z/l. It is found that the stress intensity factor decreases with the arrival of the first scattered longitudinal wave and increases with the arrival of the first scattered Rayleigh wave and tends to be stable. The static value considering both the first scattered wave and the first wave is about 50% greater than that considering only the first wave, and then the effect of the reflected wave is remarkable and deserves further study.

Surface Waves Guided by a Slit in an Elastic Solid

1972 ◽  
Vol 39 (4) ◽  
pp. 1027-1032 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Surface Waves ◽  
Crack Surface ◽  
Body Wave ◽  
Elastic Solid ◽  
Dispersion Relations ◽  
Finite Width ◽  
Infinite Length ◽  
Open Crack ◽  
Oblique Reflection ◽  
Rate Of Decay

Wave propagation in an isotropic elastic solid containing a slit is studied. The slit is viewed as an open crack of finite width and infinite length. In particular, the propagation of surface waves on the faces of the slit is considered. Making use of a reflection law for the oblique reflection of a Rayleigh wave from the tip of an open half-plane crack, surface waves are superimposed to form guided surface waves in the slit. In order to carry out the construction of dispersion relations, an assumption on the rate of decay of body wave modes localized in the vicinity of the edges of the guide is made, and the range of validity of the assumption is discussed. The dispersion relations are obtained by geometrical construction, and representative dispersion curves are shown.

Three-Dimensional Analysis for the Free Vibration of Finite-Length Orthotropic Piezoelectric Circular Cylindrical Shells

1998 ◽  
Vol 120 (1) ◽  
pp. 194-198 ◽  
Author(s):  
Chang-Qing Chen ◽  
Ya-Peng Shen
Keyword(s):  
Free Vibration ◽  
Smart Materials ◽  
Piezoelectric Materials ◽  
Three Dimensional ◽  
Power Series Expansion ◽  
Expansion Method ◽  
Simply Supported ◽  
Piezoelectric Effects ◽  
Circular Cylindrical Shells ◽  
Series Expansion Method

An exact elasticity study of the free vibration of a simply-supported cross-ply cylindrical shell containing a piezoelectric layer is presented. The solution of the derived governing differential equations is obtained through the power series expansion method. Both the direct and inverse piezoelectric effects are investigated. Results presented here provide an understand of the behavior of piezoelectric materials when acted as smart materials and can be used to assess various numerical results obtained from approximate shell theories.

Numerical Simulation of Transient Temperature Fields in Solids Irradiated by Moving Gaussian and Donut Sources

2011 ◽  
Vol 312-315 ◽  
pp. 959-964
Author(s):  
Oronzio Manca ◽  
Sergio Nardini ◽  
Daniele Ricci ◽  
Salvatore Tamburrino
Keyword(s):  
Power Distribution ◽  
Three Dimensional ◽  
Axial Direction ◽  
Temperature Fields ◽  
Transient Temperature ◽  
Transfer Model ◽  
Finite Width ◽  
Infinite Length ◽  
Laser Material Processing ◽  
Motion Direction

This work presents a three-dimensional heat transfer model developed for laser material processing with a moving Gaussian and donut heat sources, using Comsol Multhiphysics 3.5 code. The laser beam, having a defined power distribution, strikes the surface of an opaque substrate of semi infinite length but finite width and depth moving with a uniform velocity in the positive axial direction. The solid dimension along the motion direction is assumed to be infinite or semi-infinite, while a finite width and thickness are considered. Thermal properties are considered temperature dependent. Surface heat losses toward the ambient are taken into account. The results are presented in terms of temperature profiles and thermal fields are given for some Biot and material thicknesses at a constant Peclet number.

A Method for Aerodynamic Design of Blades in Quasi-Three-Dimensional Calculation of Turbomachines

1988 ◽  
Vol 110 (2) ◽  
pp. 181-186 ◽  
Author(s):  
Zhengming Wang
Keyword(s):  
Inverse Problem ◽  
Turbine Blade ◽  
Series Expansion ◽  
Thickness Distribution ◽  
Three Dimensional ◽  
Expansion Method ◽  
Aerodynamic Design ◽  
Blade Profile ◽  
The Mean ◽  
Series Expansion Method

A special inverse problem is formulated in which the shape of the mean streamline and the circumferential thickness distribution of the profile are given. On the basis of the series expansion method on a selected streamline, in quasi-three-dimensional aerodynamic design, the blade profile thickness is automatically fulfilled by computer. Six radial sections of a turbine blade are designed by this method.

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