• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.2 s.173
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• pp.496-505
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• 2000

A semi-infinite parallel crack propagated with constant velocity in two bonded anisotropic strip under anti-plane clamped displacement is analyzed. Using Fourier integral transform a Wiener-Hopf equation is derived. By solving this equation the asymptotic stress and displacement fields near the crack tip are determined, where the results give the more general expression applicable to the extent of the anisotropic material having one plane of elastic symmetry for the parallel crack. The dynamic stress intensity factor and energy release rate are also obtained as a closed form, which are the results applicable to the problem both of dynamic and static crack under the same geometry as this study. The stress intensity factor approaches zero at the critical crack velocity which is less than the shear wave velocity, but in typical case of isotropic or orthotropic material agrees with the velocity of shear wave. Also a circular shear stress around crack tip is considered, from which the stress is shown to be approximately symmetric about the horizontal axis. Referring to the maximum stress criteria, it could be shown that a brenched crack is formed by crack growth as crack velocity increases.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.6
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• pp.949-958
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• 2001

A semi-infinite interfacial crack propagated with constant velocity in two bonded anisotropic strips under out-of-plane clamped displacements is analyzed. Using Fourier integral transform the problem is formulated and the Wiener-Hopf equation is derived. By solving this equation the asymptotic stress and displacement fields near the crack tip are obtained, where the results get more general expressions applicable not only to isotropic/orthotropic materials but also to the extent of the anisotropic material having one plane of elastic symmetry for the interfacial crack. The dynamic stress intensity factor is obtained as a closed form, which is decreased as the velocity of crack propagation increases. The critical velocity where the stress intensity factor comes to zero is obtained, which agrees with the lower value between the critical values of parallel crack merged in the material 1 and 2 adjacent to the interface. Using the near tip fields of stresses and displacements, the dynamic energy release rate is also obtained as a form of the stress intensiy factor.

• Journal of KSNVE
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• v.8 no.1
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• pp.146-156
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• 1998

To mitigate excessive noise from highways, and high speed rail road, it is often necessary to construct a noise barrier. Absorptive barroer attenuation solution is obtained for the problem of diffration of a plane wave sound source by a semi-infinite plane. A finite region in the vicinity of the edge has an highly absorbing boundary condition ; the remaining portion of the half plane is rigid. The problem which is solved is a mathematical model for a hard barrier with an absorbing edge. If the wavelength of the sound is much smaller than the length scale associated with the barrier, the diffraction process is governed to all intents and purpose by the solution to a standard problem of diffraction by a semi-infinite hard plane with an absorbent edge. It is concluded that the absorbing material that comprises the edge need only be of the order of a wavelength long to have approximately the same effect, on the sound attenuation in the shadow side of the barrier. Traffic noise is composed of thousands of sources with varying frequency content. To simplify noise predictions when barriers are present, an effective frequency of 550Hz may be used to represent all vehicles. The wavelength of sound at f=550Hz for traffic noise is about 2 feet. According to the above conclusion, an absorptive highway noise barrier is only needed to cover to cover approximately a 2 foot length of absorbing material. It would be more economical to cover only the region in the immediate vicinity of the edge with highly sound obsorbent material.

• Tunnel and Underground Space
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• v.12 no.3
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• pp.171-178
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• 2002

A dynamic analysis of a horseshoe_shaped tunnel near to cavity was performed to study the effect of the cavity on the dynamic behavior of the tunnel. In order to obtain the dynamic response of the tunnel embedded in a semi-infinite domain, a hybrid numerical technique was primarily developed. A dynamic fundamental solution in frequency domain for multi-layered half planes was derived and subsequently incorporated in the boundary element method. Coupling of the boundary element method for the far field with the finite element method for the near field is made by imposing compatibility condition of a displacement at the interface. The boundary element method is then coupled with the finite element method, which is utilized to model the near field including the tunnel and the cavity. In order to demonstrate the validity of the proposed technique, dynamic responses of single and multiply-layered semi-infinite structural systems are obtained by using the Kicker waveform and investigated in the limestone layer to find how the being and the location of the cavity affect the dynamic characteristics of the system.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.3
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• pp.624-635
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• 1990

Analytical study based on linear fracture mechanics was conducted on propagation behavior of inclined surface crack in semi-infinite elastic body. The analytical model was assumed to be inclined surface crack under plane strain condition upon which Hertzian stress was superimposed. Supposing continuous distribution of dislocation and applying Erdogan-Gupta's method to this crack problem, the stress intensity factors $K_{I}$ and $K_{II}$) at the crack-tip were obtained for various Hertzian contact positions. Analytic results have shown that driving force for crack growth is $K_{I}$ for non-lubricated condition and $K_{II}$ for fluid and boundary lubricated condition. The coefficient of friction at the hertzian contact and crack surfaces plays an important role in predicting the direction of crack propagation. It is also found that the maximum effective stress intensity factor exists at cracks of a certain specific length depending on lubricated condition.ion.n.

• Journal of the Earthquake Engineering Society of Korea
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• v.1 no.4
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• pp.59-68
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• 1997

In analysis of underground structures, the effects of artificial boundary conditions are considered as one of the major reasons for differences from experimental results. These phenomena can be overcome by using the boundary elements which satisfy the multi-layered half space conditions. The fundamental solutions of multi-layered half-space for boundary element method is formulated satisfying the transmission and reflection of waves at each layer interface and radiation conditions at bottom layer. The governing equations can be obtained from the displacements at each layer which are expressed in terms of harmonic functions. All types of waves can be included using the complete response from semi-infinite integrals with respect to horizontal wavenumbers using expansion of Fourier series and Hankel transformation. Two dimensional Green's functions are derived from cylindrical Navier equations and potentials performing infinite integration in y-direction. In this case, it is effective to transform into two dimensional problem using semi-analytical integration and sinusoidal Bessel function. Some verifications are given to show the accuracy and efficiency of the developed method, and numerical examples to demonstrate the dynamic behavior of underground with various properties.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.6
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• pp.665-672
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• 2012

Interfacial cracks bonded with dissimilar transversely isotropic piezoelectric media that are subjected to combined anti-plane mechanical and in-plane electrical loading are analyzed. The problem is formulated using complex function theory, from which the Hilbert problem is derived. By solving the Hilbert problem, the general form solution is obtained. Using this solution, closed-form solutions for one or two finite cracks as well as a semi-infinite crack are obtained, for the problem in which one concentrated mechanical and electrical load is imposed on the crack surface. This solution could be used as a Green's function to generate solutions to other problems with the same geometry but different loading conditions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.4
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• pp.1275-1289
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• 1996

The plane elasticity problem of collinear cracks in a layered medium is investigated. The medium is modeled as bonded structure constituted from a surface layer and a semi-infinite substrate. Along the bond line between the two dissimilar homegeneous constituents, it is assumed that as interfacial zone having the functionally graded, nonhomogeneous elastic modulus exists. The layered medium contains three collinear cracks, one in each constituent material oriented perpendicular to the nominal interfaces. The stiffness matrix formulation is utilized and a set of homogeneous conditions relevant to the given problem is readily satisfied. The proposed mixed boundary value problem is then represented in the form of a system of integral equations with Cauchy-type singular kernels. The stress intensity factors are defined from the crack-tip stress fields possessing the standard square-root singular behavior. The resulting values of stress intensity factors mainly address the interactions among the cracks for various crack sizes and material combinations.

• Structural Engineering and Mechanics
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• v.78 no.2
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• pp.135-143
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• 2021

In this study, continuous contact problem in the functionally graded (FG) layer loaded with a FG flat punch resting on the elastic semi-infinite plane was analyzed by the finite element method (FEM). It was assumed that the shear modulus and density of the layer and punch varied according to exponentially throughout their depth. FG layer's weight was included to the problem and additionally all surfaces were considered as frictionless. Analysis of FG materials was performed with a special macro which was added to the ANSYS program. Firstly, the shear modulus of the punch was considered to be very rigid and the results of initial separation load (λcr) and distance (xcr) were compared with the analytical solution. Afterwards, results obtained from the contact analysis made according to the inhomogeneity parameters (β, γ) between FG punch-FG layer which had been unprecedented in the literature were discussed. As a result, FG punch's stress values at the punch edges where stress accumulations occurred were found to be smaller than the rigid punch. The security of the structure, longer life of the material and ease of production are directly related to the reduction of the stress values. The results obtained in this study are important in this respect. Also this work is the first study that investigates the effect of FG punch on the FG layer.

• Tribology and Lubricants
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• v.20 no.5
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• pp.252-258
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• 2004

In this study, using high cycle fatigue (HCF) criteria, the simulation of rolling contact fatigue is conducted under elliptical contact. The HCF criteria fall into three categories: the critical plane approach, the stress invariant approach and the approach based on the mesoscopic scale. The accurate calculation of contact stresses and subsurface stresses is essential to the prediction of crack initiation life. Contact stresses are obtained by contact analysis of a semi-infinite solid based on the use of influence functions and the subsurface stress field is obtained using rectangular patch solutions. The simulation results show that the critical load is decreasing rapidly and the site of crack initiation also moves rapidly to the surface from the subsurface when the friction coefficient exceeds a specific value for all of three fatigue criteria.