• Structural Engineering and Mechanics
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• v.86 no.4
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• pp.535-546
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• 2023

In the present paper, multiple interface cracks between a functionally graded orthotropic coating and an orthotropic half-plane substrate under concentrated loading are considered by means of the distribution dislocation technique (DDT). With the use of integration of Fourier transform the problem is reduced to a system of Cauchy-type singular integral equations which are solved numerically to compute the dislocation density on the surfaces of the cracks. The distribution dislocation is a powerful method to calculate accurate solutions to plane crack problems, especially this method is very good to find SIFs for multiple unequal cracks located at the interface. Hence this technique allows considering any number of interface cracks. The primary objective of this paper is to investigate the effects of the interaction of multiple interface cracks, load location, material orthotropy, nonhomogeneity parameters and geometry parameters on the modes I and II SIFs. Numerical results show that modes I/II SIFs decrease with increasing the nonhomogeneity parameter and the highest magnitude of SIF occurs where distances between the load location and crack tips are minimal.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2007.11a
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• pp.81-82
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• 2007

• Transactions of the Korean Society of Mechanical Engineers A
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• v.32 no.12
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• pp.1072-1087
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• 2008

A mixed volume and boundary integral equation method (Mixed VIEM-BIEM) is used to calculate the plane elastostatic field in an isotropic elastic half-plane containing an isotropic or anisotropic inclusion and a void subject to remote loading parallel to the traction-free boundary. A detailed analysis of stress field at the interface between the isotropic matrix and the isotropic or orthotropic inclusion is carried out for different values of the distance between the center of the inclusion and the traction-free surface boundary in an isotropic elastic half-plane containing three different geometries of an isotropic or orthotropic inclusion and a void. The method is shown to be very accurate and effective for investigating the local stresses in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions and multiple voids.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.12
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• pp.95-103
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• 2001

The buckling of an orthotropic layer bonded to an orthotropic half-space with an interface crack subjected to compressive load under plane strain is analyzed. General solution to the stability equations describing the buckling behavior of both the layer and the half-space is expressed in terms of displacement functions. The displacement functions are represented by the solution of Cauchy-type singular integral equations, which are numerically solved. Numerical results of the critical buckling loads are presented fur various geometric parameters and material properties of both the layer and half-space.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.815-818
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• 2001

The buckling of an orthotropic layer bonded to an isotropic half-space with an interface crack subjected to compressive load under plane strain is considered. Basic stability equations derived from the mathematical theory of elasticity are applied to describe the buckling behavior. A system of homogeneous Cauchy-type singular integral equations of the second kind is solved numerically by utilizing Gauss-Chebyshev integral formulae. Numerical results for the buckling load are presented for various delamination geometries and material properties of both the layer and half-space.

• Earthquakes and Structures
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• v.18 no.6
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• pp.743-752
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• 2020

The phenomenon of reflection and transmission of plane waves at an interface between fluid half space and orthotropic piezothermoelastic solid half-space with two-temperature has been investigated. Energy ratios of various reflected and transmitted waves are computed with the use of amplitude ratios. The law of conservation of energy across the interface has been justified. It is found that the energy ratios are the functions of angle of incidence, frequency of independent wave and depend on the different piezothermoelastic material. A piezothermoelastic material has been considered which is in welded contact with water. Variations of energy ratios corresponding to the reflected waves and transmitted waves are computed and shown graphically for the two different models. A particular reduced case of interest is also discussed.

• Structural Engineering and Mechanics
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• v.72 no.4
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• pp.455-468
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• 2019

The present article is aimed at studying the reflection phenomena of plane waves in a homogeneous, orthotropic, initially stressed magneto-thermoelastic rotating medium with diffusion. The enuciation is applied to generalized thermoelasticity based on Lord-Shulman theory. There exist four coupled waves, namely, quasi-longitudinal P-wave (qP), quasi-longitudinal thermal wave (qT), quasi-longitudinal mass diffusive wave (qMD) and quasi-transverse wave (qSV) in the medium. The amplitude and energy ratios for these reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programming. The effects of rotation, initial stress, magnetic and diffusion parameters on the amplitude ratios are depicted graphically. The expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence. Effect of anisotropy is also depicted on velocities of various reflected waves.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.5 no.3
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• pp.95-105
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• 1985

This dissertation presents an exact solution for the normal and shearing stresses of an orthotropic plane body loaded by a moment load. The solution satisfies the conditions of equilibrium compatibility equations concurrently and is governing for the body being in the elasto-plastic state. An Airy stress function is introduced to solve the problem related to an orthotropic half-infinite plane under a moment load. All the equations for orthotropy must be degenerated into the expressions for isotropy when orthotropic constants are replaced by isotropic ones. The author has evaluated all the equations of orthotropy and succeeded in obtaining exactly identical expressions to the equations of isotropy which were derived independently by of L'hosptials rule. The analytical results of isotropy are compared with the simple results of other investigator. Since moment Load under the elastic state and plastic state only is a particular case of moment load under the elasto-plastic state. All the equations of elasto-plastic state case are degenerated into the expressions for the each case. The formal solution is expressed in terms of closed form. The orthotropic constants are evaluated for two kinds and two different orientations of the grain of wood and two kinds of structures. The numerical results for orthotropy are evaluated for one kind and two different orientations of three-layered ply wood. The distribution of normal and shearing stresses are shown in figures. It is noted that the distribution of stresses of orthotropic materials depends on the type of materials and orientations of the grain and stiffening.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.1
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• pp.1-10
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• 1984

This dissertation presents an exact solution for the shearing and normal stresses of an orthotropic plane body loaded by a pairtial-uniform shear load. The solution satisfies the equilibrium and compatibility equations concurrently. An Airy stress function is introduced to solve the problem related to an orthotropic half-infinite plane under a partial-uniform shear load. All the equations for orthotropy must be degenerated into the expressions for isotropy when orthotropic constants are replaced by isotropic ones. The author has evaluated all the equations of orthotropy and succeeded in obtaining exactly identical expressions to the equations of isotropy which were derived independently by means of L'hospital's rule. The analytical results of, isotropy ate compared with the simple results of other investigator. Since a concentrated shear load is a particular case of partial-uniform shear load, all the equations of partial-uniform shear load case are degenerated into the expressions for concentrated load case of isotropy and orthotropy. The formal solution is expressed in terms of closed form. The numerical results for orthotropy are evaluated for two kinds and two different orientations of the grain of wood. The type of wood considered are three-layered plywood and laminated delta wood. The distribution of normal and shearing stresses are shown in figures. It is noted that the distribution of stresses of orthctropic materials dependson the type of materials and orientations of the grain.