• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.35 no.9
• /
• pp.1051-1061
• /
• 2011

The influences of density variation on stress and displacement fields at a propagating Mode-III crack tip in orthotropic functionally graded materials (OFGMs) are studied. The crack propagates dynamically at a right angle to the gradient of physical properties. Three kinds of elasticity and density gradients are analyzed in this study. They are as follows: (1) the density varies without elasticity variation, (2) the directions of the density and elasticity gradients are opposite to each other, and (3) same. For these cases, the stress and displacement fields at the crack tip are developed and the dynamic stress intensity factors for propagating cracks are also studied. When the crack speed is low, the influence of density variation on the stresses and displacement is low. However, when the crack speed is high, this influence is very high.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.2
• /
• pp.331-341
• /
• 1993

The propagating crack problems under dynamic antiplane mode in orthotropic material is studied in this paper. To analyze the dynamic fracture problems by theoretical method or experimental method in orthotropic material, it is important to know the dynamic stress intensity factor in the vicinity of crack tip. Therefore the dynamic stress field and dynamic displacement field with dynamic stress intensity factor of orthotropic material in mode III were derived. When the crack propagation speed approachs to zero, the dynamic stress components and dynamic displacement components derived in this paper are identical to the those of static state. In addition, the relationships between dynamic stress intensity factor and dynamic energy release rate are determined by using the concept of crack closure energy with the dynamic stresses and dynamic displacements derived in this paper. Finally, the characteristics of crack propagation are studied with the properties of orthotropic material and crack speed. The variation of angle .alpha. between fiber direction and crack propagating direction and crack propagation speed fairly effect on stress component and displacement component in crack tip. The influence of crack propagation speed on the speed on the stress and displacement is greater in the case of .alpha.=90.deg. than in the case of .alpha.=0.deg. and the faster the crack propagation speed, the greater the stress value and displacement value.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.39 no.2
• /
• pp.143-156
• /
• 2015

The stress and displacement fields at the crack tip were studied during the unsteady propagation of a mode III crack in a direction that was different from the property graduation direction in functionally graded materials (FGMs). The property graduation in FGMs was assumed based on the linearly varying shear modulus under a constant density and the exponentially varying shear modulus and density. To obtain the solution of the harmonic function, the general partial differential equation of the dynamic equilibrium equation was transformed into a Laplace equation. Based on the Laplace equation, the stress and displacement fields, which depended on the time rates of change in the crack tip speed and stress intensity factor, were obtained through an asymptotic analysis. Using the stress and displacement fields, the effects of the angled property variation on the stresses, displacements, and stress intensity factors are discussed.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.19 no.2 s.72
• /
• pp.151-160
• /
• 2006

In this study, we propose a new efficient 2-noded hybrid-mixed element for curved beam vibrationshaving a uniform and non-uniform cross section. The present element considering transverse shear strain is based on Hellinger-Reissner variational principle and introduces additional nodeless degrees for displacement field interpolation in order to enhance the numerical performance. The stress parameters are eliminated by the stationary condition and then the nodeless degrees are condensed out by the Guyan reduction. In the performance evaluation process of the present field-consistent higher-order element, we carefully examine the effects of field consistency and the role of higher-order interpolation functions on the hybrid-mixed formulation. Several benchmark tests confirm e superior behavior of the present hybrid-mixed element for curved beam vibrations.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.17 no.2
• /
• pp.313-330
• /
• 1993

The propagating crack problems under dynamic plane mode in orthotropic material is studied in this paper. To analyze the dynamic fracture problems in orthortropic material, it is important to know the dynamic stress components and dynamic displacement components around the crack tip. Therefore the dynamic stress components of dynamic stress field and dynamic displacement components of dynamic displacement field in the crack tip of orthotropic material under the dynamic load and the steady state in crack propagation were derived. When the crack propagation speed approachs to zero, the dynamic stress component and dynamic displacement components derived in this study are identical to the those of static state. In addition, the relationships between dynamic stress intensity factor and dynamic energy release rate are determinded by using the concept of crack closure closure energy with the dynamic stresses and represented according to physical properties of the orthotrophic material and crack speeds. The faster the crack velocity, the greater the stress value of stress components in crack tip. The stress value of the stress component of crack tip is greater when fiber direction coincides with the crack propagation than when fider direction is normal to the crack propagation.

• Journal of the Korean Geotechnical Society
• /
• v.32 no.11
• /
• pp.73-81
• /
• 2016

Recently, the construction of onshore waste landfill sites has been studied due to the increase of waste and geosynthetics are widely utilized to enforce and protect waste landfill. Geosynthetics comprises the interface with soil and the seismic behavior and stability mostly depend on the dynamic shear behavior of the geosynthetic-soil interface. Therefore, the understanding of dynamic shear behavior and dynamic relative displacement of the interface is critical. The dynamic shear behavior of the interface is affected by surrounding conditions and loading and shows very complicated response, and, it is difficult to study theoretically. In this study, laboratory test to investigate dynamic relative displacement is performed under chemical condition. Dynamic interface apparatus is utilized and cyclic simple shear tests are conducted under short term (60 days of submerging period) and long term (840 days of submerging period) conditions. Consequently, relative displacement of the interface shows the largest values under acid condition, which means more severe damage of the interface.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.34 no.7
• /
• pp.851-858
• /
• 2010

A generalized elastic solution for a transient mode III crack propagating along the gradient in functionally graded materials (FGMs) is obtained through an asymptotic analysis. The shear modulus and density of the FGMs are assumed to vary exponentially along the gradient. The stress and displacement fields near the crack tip are obtained in terms of powers of radial coordinates, and the coefficients depend on the time rates of the change of the crack tip speed and stress intensity factors. The influence of nonhomogeneity and transients on the higher order terms of the stress and displacement fields is discussed.

• Journal of the Korean Geotechnical Society
• /
• v.19 no.1
• /
• pp.173-180
• /
• 2003

In spite of its potential importance in the assessment of geosynthetic-related dynamic problems, no serious attempt has yet been made to investigate a probable dependence of dynamic friction resistance of the geosynthetic interface on shear displacement rate. Hence, an experimental study of geosynthetics was carried out on a shaking table, and the relationship between dynamic friction resistance and shear displacement rate of geosynthetic interfaces was investigated. A cyclic, displacement rate-controlled experimental setup was used. The subsequent multiple rate tests showed that interfaces that involve geotextiles have such unique shearing characteristics that shear strengths tend to increase with displacement rate. In contrast, once submerged with water, the shear strength appears to be no longer dependent on the displacement rate, partly due to lubrication effect of water trapped inside the interface. The results of the experimental study can be used in the seismic safety assessment of a landfill cover and slope where the geosynthetic materials are exposed to a relatively low normal stress.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.1
• /
• pp.87-98
• /
• 1995

When the crack in orthotropic material is propagating under dynamic model I load, influences of anisotropic property ratio $E_{L}$/ $E_{T}$ on stress and displacement around propagating crack tip are studied in this paper. When M<0.55 and .alpha.=90.deg.(.alpha.; the angle of fiber direction with crack propagating direction, M; crack propagation velocity/shear stress wave velocity), the influence of $E_{L}$/ $E_{T}$ on stress .sigma.$_{x}$, .sigma.$_{y}$, .tau.$_{xy}$ and .sigma.$_{\theta}$ is the greast on .sigma.$_{y}$. Except M<0.55 and .alpha.=90.deg., it is the greast on .sigma.$_{x}$ in any situation. Increasing $E_{L}$/ $E_{T}$, stress components are increased or decreased. When maximum stress is based, the stress .sigma.$_{x}$(.alpha.=90.deg.), .sigma.$_{y}$(.alpha.=0.deg.) and .tau.$_{xy}$ (.alpha.=90.deg.) are decreased with increment of $E_{L}$/ $E_{T}$ in M=0. any stresses except .sigma.$_{*}$x/(.alpha.=0.deg.) are decreased with increment of $E_{L}$/ $E_{T}$ in M=0.9. When .alpha.=90.deg., the influence of $E_{L}$/ $E_{T}$ on displacement U and V is V>U in any velocities of crack propagation, when .alpha.=0.deg., it is VU in M>0.75 and when $E_{L}$/ $E_{T}$ is increased, U and V are decreased in any conditions.sed in any conditions.tions.tions.tions.