• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.1 s.256
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• pp.89-96
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• 2007

A volume integral equation method (VIEM) is applied for the effective analysis of plane elastostatic problems in unbounded solids containing single isotropic inclusion of two different shapes considering composite fiber volume fraction. Single cylindrical inclusion and single square cylindrical inclusion are considered in the composites with six different fiber volume fractions (0.25, 0.30, 0.35, 0.40, 0.45, 0.50). Using the rule of mixtures, the effective material properties are calculated according to the corresponding composite fiber volume fraction. The analysis of plane elastostatic problems in the unbounded effective material containing single fiber that covers an area corresponding to the composite fiber volume fraction in the bounded matrix material are carried out. Thus, single fiber, matrix material with a finite region, and the unbounded effective material are used in the VIEM models for the plane elastostatic analysis. A detailed analysis of stress field at the interface between the matrix and the inclusion is carried out for single cylindrical or square cylindrical inclusion. Next, the stress field is compared to that at the interface between the matrix and the single inclusion in unbounded isotropic matrix with single isotropic cylindrical or square cylindrical inclusion. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of inclusions. Through the analysis of plane elastostatic problems, it will be established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing inclusions considering composite fiber volume fraction.

• Proceedings of the KSME Conference
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• 2001.11a
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• pp.341-348
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• 2001

A Mixed Volume and Boundary Integral Equation Method is applied for the effective analysis of plane elastostatic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids or isotropic inclusions. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids or isotropic inclusions, it will be established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.23 no.11 s.170
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• pp.1993-2006
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• 1999

A Volume Integral Equation Method (VIEM) is applied for the effective analysis of elastic wave scattering problems and plane elastostatic problems in unbounded solids containing general anisotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids. Through the analysis of plane elastodynamic and elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids, it will be established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions and voids.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.4
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• pp.775-786
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• 2002

A Mixed Volume and Boundary Integral Equation Method is applied for the effective analysis of elastic wave scattering problems and plane elastostatic problems in unbounded solids containing general anisotropic inclusions and voids or isotropic inclusions. It should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. This new method can also be applied to general two-dimensional elastodynamic and elastostatic problems with arbitrary shapes and number of anisotropic inclusions and voids or isotropic inclusions. In the formulation of this method, the continuity condition at each interface is automatically satisfied, and in contrast to finite element methods, where the full domain needs to be discretized, this method requires discretization of the inclusions only. Finally, this method takes full advantage of the pre- and post-processing capabilities developed in FEM and BIEM. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with orthotropic inclusions and voids or isotropic inclusions, and the analysis of plane wave scattering problems in unbounded isotropic matrix with isotropic inclusions and voids, it will be established that this new method is very accurate and effective for solving plane wave scattering problems and plane elastic problems in unbounded solids containing general anisotropic inclusions and voids/cracks or isotropic inclusions.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.515-536
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• 2012

This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is first established to obtain the moment stability but without almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while existing Razumikhin-type theorems aim at only the moment stability. By virtue of the $M$-matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.7
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• pp.1120-1131
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• 2003

A recently developed numerical method based on a mixed volume and boundary integral equation method is applied to calculate the accurate stress intensity factors at the crack tips in unbounded isotropic solids in the presence of multiple anisotropic inclusions and cracks subject to external loads. Firstly, it should be noted that this newly developed numerical method does not require the Green's function for anisotropic inclusions to solve this class of problems since only Green's function for the unbounded isotropic matrix is involved in their formulation for the analysis. Secondly, this method takes full advantage of the capabilities developed in FEM and BIEM. In this paper, a detailed analysis of the stress intensity factors are carried out for an unbounded isotropic matrix containing an orthotropic cylindrical inclusion and a crack. The accuracy and effectiveness of the new method are examined through comparison with results obtained from analytical method and volume integral equation method. It is demonstrated that this new method is very accurate and effective for solving plane elastostatic problems in unbounded solids containing anisotropic inclusions and cracks.

• Earthquakes and Structures
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• v.3 no.3_4
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• pp.383-411
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• 2012

The objective of the present paper is to review and implement the most recent developments in the Spectral Element Method (SEM), as well as improve aspects of its implementation in the study of wave propagation by numerical simulation in elastic unbounded domains. The classical formulation of the method is reviewed, and the construction of the mass matrix, stiffness matrix and the external force vector is expressed in terms of matrix operations that are familiar to earthquake engineers. To account for the radiation condition at the external boundaries of the domain, a new absorbing boundary condition, based on the Perfectly Matched Layer (PML) is proposed and implemented. The new formulation, referred to as the Multi-Axial Perfectly Matched Layer (M-PML), results from generalizing the classical Perfectly Matched Layer to a medium in which damping profiles are specified in more than one direction.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.9
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• pp.1284-1296
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• 2004

In order to investigate effects of anisotropic fiber packing on stresses in composites, a Volume Integral Equation Method is applied to calculate the elastostatic field in an unbounded isotropic elastic medium containing multiple orthotropic inclusions subject to remote loading, and a Mixed Volume and Boundary Integral Equation Method is introduced for the solution of elastostatic problems in unbounded isotropic materials containing multiple anisotropic inclusions as well as one void under uniform remote loading. A detailed analysis of stress fields at the interface between the isotropic matrix and the central orthotropic inclusion is carried out for square, hexagonal and random packing of orthotropic cylindrical inclusions, respectively. Also, an analysis of stress fields at the interface between the isotropic matrix and the central orthotropic inclusion is carried out, when it is assumed that a void is replaced with one inclusion adjacent to the central inclusion of square, hexagonal and random packing of orthotropic cylindrical inclusions, respectively, due to manufacturing and/or service induced defects. The effects of random orthotropic fiber packing on stresses at the interface between the isotropic matrix and the central orthotropic inclusion are compared with the influences of square and hexagonal orthotropic fiber packing on stresses. Through the analysis of plane elastostatic problems in unbounded isotropic matrix with multiple orthotropic inclusions and one void, it will be established that these new methods are very accurate and effective for investigating effects of general anisotropic fiber packing on stresses in composites.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1999.04a
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• pp.276-286
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• 1999

A recently developed numerical method based on a volume integral formulation is developed for the effective accurate calculation of the stress intensity factors at the crack tips in unbounded isotropic solids in the presence of multiple anisotropic inclusions and cracks and subjected to external loads. In this paper, a detailed analysis of the stress intensity factors are carried out for an unbounded isotropic matrix containing an orthotropic cylindrical inclusion and a crack. The accuracy and effectiveness of the new method are examined through comparison with results obtained from analytical method and finite element method using ANSYS. It is demonstrated that this new method is very accurate and effective for solving plane elastostatic problems in unbounded solids containing anisotropic inclusions and cracks.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.04a
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• pp.41-52
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• 1998

A volume integral equation method and a mixed volume and boundary integral equation method are presented for the solution of plane elastostatic problems in solids containing orthotropic inclusions and voids. The detailed analysis of the displacement and stress fields are developed for orthotropic cylindrical and elliptic-cylindrical inclusions and voids. The accuracy and effectiveness of the new methods are examined through comparison with results obtained from analytical and boundary integral equation methods. Through the analysis of plane elastostatic problems in unbounded isotropic matrix containing orthotropic inclusions and voids, it is established that these new methods are very accurate and effective for solving plane elastostatic and elastodynamic problems in unbounded solids containing general anisotropic inclusions and voids or cracks.