Jungki Lee

A volume integral equation technique for multiple inclusion and crack interaction problems

A volume integral equation method is introduced for the solution of elastostatic problems in heterogeneous solids containing interacting multiple inclusions, voids, and cracks. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions and cracks. The influence of interface layers on the interfacial stress field is investigated. The stress intensity factors for microcracks in the presence of interacting inclusions or voids are also calculated for a variety of model geometries. The accuracy and efficiency of the method are examined through comparison with results obtained from analytical and boundary integral methods.

Stress analysis of an unbounded elastic solid with orthotropic inclusions and voids using a new integral equation technique

A recently developed numerical method based on a volume integral formulation is applied to calculate the elastostatic field in an unbounded isotropic elastic medium containing orthotropic inclusions subject to remote loading. A modified form of the method in which the integral equations involve volumes of the inclusions and boundaries of voids or cracks is used to deal with the presence of both types of inhomogeneity. A detailed analysis of displacement and stress fields is carried out for orthotropic cylindrical and elliptic cylindrical inclusions as well as voids. The accuracy and effectiveness of the new methods are examined through comparison with results obtained from analytical and boundary integral equation methods.

A volume integral equation technique for multiple scattering problems in elastodynamics

Abstract A volume integral equation method is introduced as a new numerical scheme for the solution of certain elastodynamic problems in unbounded solids containing multiple inclusions. The effectiveness of the method is compared with the boundary integral equation method for different problem geometries. For the single inclusion problem, both methods are found to work equally well. For multiple inclusions, the volume integral equation method is shown to be much more convenient for numerical formulation and to give very accurate results.

A mixed volume and boundary integral equation technique for elastic wave field calculations in heterogeneous materials

Abstract An integral equation method is applied for the calculation of elastic wave fields in unbounded solids containing general anisotropic inclusions and voids. The domain of the integral equation involves the volume of the inclusions as well as the surface of the voids. In contrast to the conventional boundary integral equation method (BIEM), where the infinite medium Green’s functions for both the matrix material and the inclusion material are needed, the present method does not require the latter. Since the elastodynamic Green’s functions for anisotropic media are extremely difficult to calculate, the present method offers a definite advantage over methods based on boundary integral equation (BIE) alone. The newly developed mixed method takes full advantage of the volume integral equation method that is effective for problems with anisotropic inclusions and the BIEM that is effective for problems involving voids and cracks. In this paper, the mixed method is used to calculate the interaction of plane, time-harmonic elastic waves with an isotropic and an orthotropic cylindrical inclusion in absence or presence of a parallel cylindrical void in its vicinity, for waves incident normal to the cylinder axis. Numerical results are presented for the displacement and stress fields at the interfaces of the inclusions in a broad frequency range of practical interest. The new method is shown to be very accurate and efficient for solving this class of problems.

Stress analysis of multiple anisotropic elliptical inclusions in composites

A volume integral equation method is introduced for the solution of elastostatic problems in an unbounded isotropic elastic solid containing interacting multiple anisotropic elliptical inclusions subject to uniform remote tension or remote in-plane shear. This method is applied to two-dimensional problems involving long parallel elliptical cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central elliptical inclusion is carried out for square and hexagonal packing of anisotropic inclusions. The effects of the number of anisotropic inclusions and various inclusion volume fractions on the stress field at the interface between the isotropic matrix and the central elliptical cylindrical inclusion are investigated in detail. The stress field at the interface between the isotropic matrix and the central elliptical inclusion is also compared with that between the isotropic matrix and the central circular inclusion.

SH Wave Scattering Problems for Multiple Orthotropic Elliptical Inclusions

A volume integral equation method (VIEM) is applied for the effective analysis of elastic wave scattering problems in unbounded solids containing general anisotropic inclusions. It should be noted that this numerical method does not require use of Greens function for anisotropic inclusions to solve this class of problems since only Greens function for the unbounded isotropic matrix is necessary for the analysis. This new method can also be applied to general two-dimensional elastodynamic problems involving arbitrary shapes and numbers of anisotropic inclusions. A detailed analysis of SH wave scattering problems is developed for an unbounded isotropic matrix containing multiple orthotropic elliptical inclusions. Numerical results are presented for the displacement fields at the interfaces of the inclusions in a broad frequency range of practical interest. Through the analysis of plane elastodynamic problems in an unbounded isotropic matrix with multiple orthotropic elliptical inclusions, it is established that this new method is very accurate and effective for solving plane elastic problems in unbounded solids containing general anisotropic inclusions of arbitrary shapes.

Volume Integral Equation Method for Multiple Isotropic Inclusion Problems in an Infinite Solid Under Uniaxial Tension

A volume integral equation method (VIEM) is introduced for solving the elastostatic problems related to an unbounded isotropic elastic solid; this solid is subjected to remote uniaxial tension, and it contains multiple interacting isotropic inclusions. The method is applied to two-dimensional problems involving long parallel cylindrical inclusions. A detailed analysis of the stress field at the interface between the matrix and the central inclusion is carried out; square and hexagonal packing of the inclusions are considered. The effects of the number of isotropic inclusions and different fiber volume fractions on the stress field at the interface between the matrix and the central inclusion are also investigated in detail. The accuracy and efficiency of the method are clarified by comparing the results obtained by analytical and finite element methods. The VIEM is shown to be very accurate and effective for investigating the local stresses in composites containing isotropic fibers.

Elastic Analysis of a Half-Plane Containing Multiple Inclusions Using Volume Integral Equation Method

A volume integral equation method (VIEM) is used to calculate the plane elastostatic field in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions subject to remote loading. A detailed analysis of stress field at the interface between the matrix and the central inclusion in the first column of square packing is carried out for different values of the distance between the center of the central inclusion in the first column of square packing of inclusions and the traction-free surface boundary in an isotropic elastic half-plane containing multiple isotropic or anisotropic inclusions. 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.

A Study on Performance Improvement of Whirling Machines

In order to meet the increasing competitive pressures coupled with higher demands for component quality, whirling machines have been at the cutting edge of the automobile industry for more than 25 years. The hard whirling process can save on machining time and operation elimination. Hard whirling is done dry, without coolant. The chips carry away nearly all of the heat during cutting, leaving the workpiece cool and minimizing any thermal geometry variations. The surface finish and profile accuracy are close to grinding quality. Whirling machines usually consist of four major parts; 1) loading system that requires the necessary axial speeds, 2) head stock that needs high precision clamping and positioning system at the chuck and tailstock, 3) whirling unit that demands the high cutting speeds and cutting power fer cutting deep thread profiles and 4) unloading system that requires an easy workpiece unloading. Also, capabilities of the whirling machine can be improved by attaching a vision system to the machine. Most of whirling machines in Korean automobile industry are imported from the Leistritz company, Germany and the Hasegawa company, Japan. Tn this paper, a basic research will be performed to improve and enhance the existing whirling machines. Finally, a new Korean whirling machine will be proposed and developed.

Near and far field scattering of SH waves by multiple multilayered anisotropic circular inclusions using parallel volume integral equation method

Purpose The purpose of this paper is to calculate near field and far field scattering of SH waves by multiple multilayered anisotropic circular inclusions using parallel volume integral equation method (PVIEM) quantitatively. Design/methodology/approach The PVIEM is applied for the analysis of elastic wave scattering problems in an unbounded solid containing multiple multilayered anisotropic circular inclusions. It should be noted that this numerical method does not require the use of the Green’s function for the inclusion – only the Green’s function for the unbounded isotropic matrix is needed. This method can also be applied to solve general elastodynamic problems involving inhomogeneous and/or anisotropic inclusions whose shape and number are arbitrary. Findings A detailed analysis of the SH wave scattering problem is presented for multiple multilayered orthotropic circular inclusions. Numerical results are presented for the displacement fields at the interfaces and the far field scattering patterns for square and hexagonal packing arrays of multilayered circular inclusions in a broad frequency range of practical interest. Originality/value To the best of the authors’ knowledge, the solution for scattering of SH waves by multiple multilayered anisotropic circular inclusions in an unbounded isotropic matrix is not currently available in the literature. However, in this paper, calculation of displacements on interfaces and far field scattering patterns of multiple multilayered anisotropic circular inclusions using PVIEM as a pioneer of numerical modeling enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), the multilayer’s geometry, isotropy/anisotropy and softness/hardness.