• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.9
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• pp.1408-1414
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• 2004

The use of flip-chip technology has many advantages over other approaches for high-density electronic packaging. ACF (anisotropic conductive film) is one of the major flip-chip technologies, which has short chip-to-chip interconnection length, high productivity, and miniaturization of package. In this study, thermal fatigue lift of ACF bonding flip-chip package has been predicted. Elastic and thermal properties of ACF were measured by using DMA and TMA. Temperature dependent nonlinear hi-thermal analysis was conducted and the result was compared with Moire interferometer experiment. Calculated displacement field was well matched with experimental result. Thermal fatigue analysis was also conducted. The maximum shear strain occurs at the outmost located bump. Shear stress-strain curve was obtained to calculate fatigue life. Fatigue model for electronic adhesives was used to predict thermal fatigue life of ACF bonding flip-chip packaging. DOE (Design of Experiment) technique was used to find important design factors. The results show that PCB CTE (Coefficient of Thermal Expansion) and elastic modulus of ACF material are important material parameters. And as important design parameters, chip width, bump pitch and bump width were chose. 2$^{nd}$ DOE was conducted to obtain RSM equation far the choose 3 design parameter. The coefficient of determination ($R^2$) for the calculated RSM equation is 0.99934. Optimum design is conducted using the RSM equation. MMFD (Modified Method for feasible Direction) algorithm is used to optimum design. The optimum value for chip width, bump pitch and bump width were 7.87mm, 430$\mu$m, and 78$\mu$m, respectively. Approximately, 1400 cycles have been expected under optimum conditions. Reliability analysis was conducted to find out guideline for control range of design parameter. Sigma value was calculated with changing standard deviation of design variable. To acquire 6 sigma level thermal fatigue reliability, the Std. Deviation of design parameter should be controlled within 3% of average value.

• Structural Engineering and Mechanics
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• v.56 no.1
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• pp.137-156
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• 2015

In this paper, an analytical solution of displacement, strain and stress field for rotating thick-walled cylinder made of functionally graded material subjected to the uniform external magnetic field and thermal field in plane strain state has been studied. Stress, strain and displacement field as a function of radial coordinates considering magneto-thermo-elasticity are derived analytically. According to the Maxwell electro-dynamic equations, Lorentz force in term of displacement is obtained in cylindrical coordinates. Also, symmetric temperature distribution along the thickness of hollow cylinder is obtained by solving Fourier heat transfer equation in cylindrical coordinates. Using equation of equilibrium and thermo-mechanical constitutive equations associated with Lorentz force, a second-order inhomogeneous differential equation in term of displacement is obtained and will be solved analytically. Except Poisson's ratio, other mechanical properties such as elasticity modulus, density, magnetic permeability coefficient, heat conduction coefficient and thermal expansion coefficient are assumed to vary through the thickness according to a power law. In results analysis, non-homogeneity parameter has been chosen arbitrary and inner and outer surface of cylinder are assumed to be rich metal and rich ceramic, respectively. The effect of rotation, thermal, magnetic field and non-homogeneity parameter of functionally graded material which indicates percentages of cylinder's constituents are studied on displacement, Von Mises equivalent stress and Von Mises equivalent strain fields.

• Proceedings of the Korea Concrete Institute Conference
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• 2008.11a
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• pp.201-204
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• 2008

The proposed method, capable of predicting various stress-strain responses in axially loaded concrete confined with FRP (Fiber Reinforced Polymers) composites in a rational manner, is based on the fact that the volumetric expansion due to progressive microcracking in mechanically loaded concrete is an important measure of the extent of damage in the material microstructure. The elastic modulus expressed as a function of area strain and concrete porosity, the energy-balance equation relating the dilating concrete to the confining device interactively, the varying confining pressure, and an incremental calculation algorithm are included in the solution procedure. This procedure enables the evaluation of lateral strains consecutively according to the related mechanical model and the energy-balance equation, rather than using an empirically derived equation for Poisson's ratio or dilation rate as in other analytical methods.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.16 no.7 s.112
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• pp.690-696
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• 2006

Thickness of damping layer in sandwich plate needs to be optimized in order to make modal loss factor of the sandwich plate maximum. Since previous studies were interested in noise reductions over high frequency range, the modal properties were derived based on simply supported boundaries. This conventional formula is approximately applicable to other boundary conditions over high frequency range only. The purpose of this study is to propose a method to determine optimum damping layer thickness of sandwich plate for maximum modal damping in low frequency range when the boundary condition is not a simple support. The conventional RKU equation based on simply supported boundary is modified to reflect other boundary conditions and the modified RKU equation is subsequently applied to determine the optimum damping layer thickness for arbitrary conditions. In order to reflect frequency-dependent characteristics of elastic modulus of the damping layer, an iteration method is proposed in determining the modal properties. Test results on sandwich plates for optimum damping layer thickness are compared with predictions by the proposed method and conventional method.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.2
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• pp.127-136
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• 2007

In this paper, the equations of the scaled boundary finite element method are derived for non-homogeneous half plane and analyzed numerically In the scaled boundary finite element method, partial differential equations are weaken in the circumferential direction by approximation scheme such as the finite element method, and the radial direction of equations remain in analytical form. The scaled boundary equations of non-homogeneous half plane, its elastic modulus varies as power function, are newly derived by the virtual work theory. It is shown that the governing equation of this problem is the Euler-Cauchy equation, therefore, the logarithm mode used in the half plane problem is not valid in this problem. Two numerical examples are analysed for the verification and the feasibility.

• Journal of Korean Society of Steel Construction
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• v.9 no.4 s.33
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• pp.523-533
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• 1997

Current limit state design method for encased composite columns contains irrational and uncertain design equations in defining section and material properties of composite members. Through investigating previous research used in formulating the design equation, this paper explores the irrationality and uncertainty such as 1) transformation of yield stress and elastic modulus for composite section, 2) an equation influencing buckling strength in terms of area rather than moment of inertia, and 3) selection of larger radius of gyration between steel and concrete sections. Improving the design equations this paper proposes two design methods which can be directly used in practical design.

• Journal of the Korean Geotechnical Society
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• v.19 no.4
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• pp.145-153
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• 2003

The resonant column testing determines the shear modulus and material damping factor dependent on the shear strain magnitude, based on the wave-propagation theory. The determination of the dynamic soil properties requires the theoretical formulation of the dynamic behavior of the resonant column testing system. One of the theoretical formulations is the use of the wave equation for the soil specimen in the resonant column testing device. Wood, Richart and Hall derived the wave equation by assuming the linear elastic soil, and didn't take the material damping into consideration. Hardin incorporated the viscoelastic damping of soil in the wave equation, but he had to assume the material damping factor for the determination of the shear modulus. For the better theoretical formulation of the resonant column testing, this study derived a new wave equation to include the viscosity of soil, and proposed an approach for the solution. Also, in this study, the equation of motion for the testing system, which is another approach of the theoretical formulation of the resonant column testing, was also derived. The equation of motion leads to the better understanding of the resonant column testing, which includes the dynamic magnification factor and the phase angle of the response. For the verification of the proposed equation of motion for the resonant column testing, the finite element analysis was performed for the resonant column testing. The comparison of the dynamic magnification factors and the phase angles far the system response were performed.

• Tunnel and Underground Space
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• v.26 no.5
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• pp.363-374
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• 2016

All five independent elastic constants of a transversely isotropic rock sometimes need to be determined from a single specimen. Saint-Venant approximation has been widely used for a long time in the analysis of single specimen test. This paper has proven how this empirical equation can be mathematically transformed into a form of the apparent Young's modulus based on theory of elasticity. The transformed equation is a monotonous function on anisotropic angle and can be useful in the analysis of the in-situ stress measurement in an anisotropic rock mass. The estimations of data in literatures have shown that the measured values of $G^2$ are uniform on anisotropic angles and smaller than that of Saint-Venant's case. This decrement may be caused by sliding of the interface of strata and the decrement rate is inferred to relate well with the combination of bonding condition of strata and strength of rock material. Accumulation of these kinds of studies in the future enables to define the decrement and to determine elastic constants of a transversely isotropic rock from a single specimen from modifying Saint-Venant approximation.

• Proceedings of the Korea Concrete Institute Conference
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• 2002.10a
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• pp.227-232
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• 2002

To evaluate the practical application of oyster shells as construction materials, an experimental study was performed. More specifically, the long-term mechanical properties and durability of concrete blended with oyster shells were investigated. Test results indicate that long-term strength of concrete blended with 10% oyster shells is almost identical to that of normal concrete. However, the long-term strength of concrete blended with 20% oyster shells Is appreciably lower than that of normal concrete. 1'hereby, concrete with higher oyster shell has the possibility giving a bad influence on the concrete long-term strength. Elastic modulus of concrete blended with crushed oyster shells decreases as the blending mixture ratio increases. Namely, the modulus is reduced by approximately 10∼15% when oyster shells are blended up to 20% replacing the fine aggregate. The drying shrinkage strain increases as the blending ratio increases. In addition, the existing model code of drying shrinkage does not coincide with the test results of this study. An adequate prediction equation needs to be developed. The utilization of oyster shells as the fine aggregate in concrete has an insignificant effect on freezing and thawing resistance, carbonation and sulfuric acid attack of concrete recycling. However, water permeability is considerably improved.

• Journal of the Korean Geotechnical Society
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• v.18 no.5
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• pp.237-249
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• 2002

Nonlinearity and anisotropy of soil should be considered for the exact prediction of deformation before the failure state. In this study, a new constitutive model is developed in which the nonlinearity of soil is formulated by Ramberg-Osgood equation and the soil anisotropy is implemented by the cross-anisotropic elasticity. Nonlinear anisotropic model and other models for comparison are used to analyze the simple boundary value problems and the circular footing problem. In the results, the anisotropic ratio of elastic modulus is a key value for the bulk modulus of soil, the coeffcient of earth pressure at rest, and the slope of effective stress paths. Furthermore, it is found that the nonlinearity of soil considering the in-situ stresses has the great influence on the magnitude of settlements.