scholarly journals Transient Analysis of a Semi-infinite Crack Subjected to Dynamic Concentrated Forces

1992 ◽  
Vol 59 (4) ◽  
pp. 804-811 ◽  
Author(s):  
Chwan-Huei Tsai ◽  
Chien-Ching Ma
Keyword(s):  
Laplace Transform ◽  
Fundamental Problem ◽  
Closed Form Solution ◽  
Crack Tip ◽  
Time History ◽  
Dynamic Crack ◽  
Transform Domain ◽  
Concentrated Force ◽  
Crack Problems ◽  
The Laplace Transform

An exact transient closed-form solution for a semi-infinite crack subjected to a timedependent concentrated force is obtained in this study. The total wave field is due to the effect of this point source and the scattering of the incident waves by the crack tip. An alternative methodology for constructing the reflected and diffracted field is proposed, which proves both powerful and efficient in solving complicated dynamic crack problems. An exponentially distributed loading at the crack surfaces in the Laplace transform domain is used as the fundamental problem. The waves reflected by the traction-free crack surface and diffracted from the crack tip can be constructed by superimposing this fundamental solution. The superposition is performed in the Laplace transform domain. Numerical results for the time history of stresses and stress intensity factors during the transient process are obtained and compared with the corresponding static values. It is shown that the field solution will approach the static value after the last diffracted wave has passed.

scholarly journals Transient Analysis of Dynamic Crack Propagation With Boundary Effect

1995 ◽  
Vol 62 (4) ◽  
pp. 1029-1038 ◽  
Author(s):  
Chien-Ching Ma ◽  
Yi-Shyong Ing
Keyword(s):  
Fundamental Solution ◽  
Crack Propagation ◽  
Laplace Transform ◽  
Fundamental Problem ◽  
Boundary Effect ◽  
Dynamic Crack Propagation ◽  
Dynamic Crack ◽  
Transform Domain ◽  
Propagating Crack ◽  
The Laplace Transform

In this study, a dynamic antiplane crack propagation with constant velocity in a configuration with boundary is investigated in detail. The reflected cylindrical waves which are generated from the free boundary will interact with the propagating crack and make the problem extremely difficult to analyze. A useful fundamental solution is proposed in this study and the solution is determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The Cagniard’s method for Laplace inversion is used to obtain the transient solution in time domain. Numerical results of dynamic stress intensity factors for the propagation crack are evaluated in detail.

Dynamic Crack Propagation in Piezoelectric Materials Subjected to Dynamic Body Forces for Vacuum Boundary

2007 ◽  
Vol 23 (3) ◽  
pp. 229-238 ◽  
Author(s):  
X.-H. Chen ◽  
C.-C. Ma ◽  
Y.-S. Ing
Keyword(s):  
Intensity Factor ◽  
Fundamental Solution ◽  
Laplace Transform ◽  
Piezoelectric Material ◽  
Electric Displacement ◽  
Dynamic Crack ◽  
Transform Domain ◽  
Electric Displacement Intensity Factor ◽  
Propagating Crack ◽  
The Laplace Transform

AbstractThe problem of a semi-infinite propagating crack in the piezoelectric material subjected to a dynamic anti-plane concentrated body force is investigated in the present study. It is assumed that between the growing crack surfaces there is a permeable vacuum free space, in which the electrostatic potential is nonzero. It is noted that this problem has characteristic lengths and a direct attempt towards solving this problem by transform and Wiener-Hopf techniques [1] is not applicable. This paper proposes a new fundamental solution for propagating crack in the piezoelectric material and the transient response of the propagating crack is determined by superposition of the fundamental solution in the Laplace transform domain. The fundamental solution represents the responses of applying exponentially distributed loadings in the Laplace transform domain on the propagating crack surface. Exact analytical transient solutions for the dynamic stress intensity factor and the dynamic electric displacement intensity factor are obtained by using the Cagniard-de Hoop method [2,3] of Laplace inversion and are expressed in explicit forms. Finally, numerical results based on analytical solutions are calculated and are discussed in detail.

Stability and Controllability of Euler-Bernoulli Beams With Intelligent Constrained Layer Treatments

1996 ◽  
Vol 118 (1) ◽  
pp. 70-77 ◽  
Author(s):  
I. Y. Shen
Keyword(s):  
Laplace Transform ◽  
Closed Form ◽  
Characteristic Equation ◽  
Matrix Equation ◽  
Homogeneous Equation ◽  
Transform Domain ◽  
Threshold Control ◽  
Control Gain ◽  
The Laplace Transform ◽  
The Stability

This paper studies the stability and controllability of Euler-Bernoulli beams whose bending vibration is controlled through intelligent constrained layer (ICL) damping treatments proposed by Baz (1993) and Shen (1993, 1994). First of all, the homogeneous equation of motion is transformed into a first order matrix equation in the Laplace transform domain. According to the transfer function approach by Yang and Tan (1992), existence of nontrivial solutions of the matrix equation leads to a closed-form characteristic equation relating the control gain and closed-loop poles of the system. Evaluating the closed-form characteristic equation along the imaginary axis in the Laplace transform domain predicts a threshold control gain above which the system becomes unstable. In addition, the characteristic equation leads to a controllability criterion for ICL beams. Moreover, the mathematical structure of the characteristic equation facilitates a numerical algorithm to determine root loci of the system. Finally, the stability and controllability of Euler-Bernoulli beams with ICL are illustrated on three cantilever beams with displacement or slope feedback at the free end.

Propagation of Discontinuities in Coupled Thermoelastic Problems

1968 ◽  
Vol 35 (3) ◽  
pp. 489-494 ◽  
Author(s):  
B. A. Boley ◽  
R. B. Hetnarski
Keyword(s):  
Heat Flux ◽  
Boundary Conditions ◽  
Laplace Transform ◽  
Applied Strain ◽  
Transform Domain ◽  
Arbitrary Boundary ◽  
One Dimensional ◽  
The Laplace Transform ◽  
Thermoelastic Problems

The character and magnitude of traveling discontinuities in one-dimensional coupled transient thermoelastic problems are studied. For this purpose, 16 different fundamental problems are considered in detail, by examination of the nature of the solutions in the Laplace-transform domain. These problems correspond to various combinations of applied strain or stress as mechanical variables, and of applied temperature or heat flux as thermal variables. A system of classification of discontinuities is devised, which permits the results of the 16 problems to be extended to some general conclusions as to the character of the discontinuities in cases of arbitrary boundary conditions.

Thermodiffusion with two time delays and Kernel functions

2016 ◽  
Vol 23 (2) ◽  
pp. 195-208 ◽  
Author(s):  
Ahmed S El-Karamany ◽  
Magdy A Ezzat ◽  
Alaa A El-Bary
Keyword(s):  
Laplace Transform ◽  
Kernel Functions ◽  
Transform Domain ◽  
Thermoelastic Diffusion ◽  
One Dimensional ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Isotropic Elastic Medium ◽  
Time Variations ◽  
With Memory

The present work is concerned with the investigation of disturbances in a homogeneous, isotropic elastic medium with memory-dependent derivatives (MDDs). A one-dimensional problem is considered for a half-space whose surface is traction free and subjected to the effects of thermodiffusion. For treatment of time variations, the Laplace-transform technique is utilized. The theories of coupled and of generalized thermoelastic diffusion with one relaxation time follow as limit cases. A direct approach is introduced to obtain the solutions in the Laplace transform domain for different forms of kernel functions and time delay of MDDs, which can be arbitrarily chosen. Numerical inversion is carried out to obtain the distributions of the considered variables in the physical domain and illustrated graphically. Some comparisons are made and shown in figures to estimate the effects of MDD parameters on all studied fields.

Diffraction of elastic waves by a rigid 90° wedge Part I

1968 ◽  
Vol 58 (3) ◽  
pp. 1083-1096 ◽  
Author(s):  
Edgar A. Kraut
Keyword(s):  
Laplace Transform ◽  
Elastic Wave ◽  
Elastic Waves ◽  
Closed Form Solution ◽  
Compressional Wave ◽  
Form Solution ◽  
Complex Variables ◽  
Quarter Plane ◽  
The Laplace Transform ◽  
Diffraction Of Elastic Waves

abstract The problem of calculating the reflected and diffracted elastic waves generated when a plane compressional wave strikes a rigid quarter plane is formulated as a Wiener-Hopf problem in two complex variables. It is shown how a closed form solution of this two variable Wiener-Hopf problem can be obtained provided that the Laplace transform of the elastic wave Green's function can be factorized into factors having suitable analytic properties.

scholarly journals Dynamic Crack Propagation in a Layered Medium Under Antiplane Shear

1997 ◽  
Vol 64 (1) ◽  
pp. 66-72 ◽  
Author(s):  
Chien-Ching Ma ◽  
Yi-Shyong Ing
Keyword(s):  
Stress Intensity ◽  
Fundamental Solution ◽  
Laplace Transform ◽  
Dynamic Stress ◽  
Layered Medium ◽  
Transform Domain ◽  
Intensity Factors ◽  
Dynamic Stress Intensity Factors ◽  
Propagating Crack ◽  
The Laplace Transform

In this study, the transient analysis of dynamic antiplane crack propagation with a constant velocity in a layered medium is investigated. The individual layers are isotropic and homogeneous. Infinite numbers of reflected cylindrical waves, which are generated from the interface of the layered medium, will interact with the propagating crack and make the problem extremely difficult to analyze. A useful fundamental solution is proposed in this study, and the solution can be determined by superposition of the fundamental solution in the Laplace transform domain. The proposed fundamental problem is the problem of applying exponentially distributed traction (in the Laplace transform domain) on the propagating crack faces. The Cagniard’s method for Laplace inversion is used to obtain the transient solution in time domain. The exact closed-form transient solutions of dynamic stress intensity factors are expressed in compact formulations. These solutions are valid for an infinite length of time and have accounted for contributions from all the incident and reflected waves interaction with the moving crack tip. Numerical results of dynamic stress intensity factors for the propagation crack in layered medium are evaluated and discussed in detail.

The laplace transform DBEM for mixed-mode dynamic crack analysis

1996 ◽  
Vol 59 (6) ◽  
pp. 1021-1031 ◽  
Author(s):  
P. Fedelinski ◽  
M.H. Aliabadi ◽  
D.P. Rooke
Keyword(s):  
Laplace Transform ◽  
Mixed Mode ◽  
Dynamic Crack ◽  
Crack Analysis ◽  
The Laplace Transform
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