• Journal of Welding and Joining
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• v.19 no.4
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• pp.406-412
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• 2001

This study is focussed on the numerical prediction of the thermal fatigue life of a ${\mu}BGA$(Micro Ball Grid Array) solder joint. Numerical method is used to perform three-dimensional finite element analysis for Sn-37mass%Pb. Sn-3.5mass%Ag solder alloys during the given thermal cycling. Strain values, along with the result of mechanical fatigue tests for solder alloys were then used to predict the solder joint fatigue life using the Coffin-Manson equation. In this study, a practical correlation for the prediction of the thermal fatigue life is suggested by using the dimensionless variable $\gamma$. As a result. it could be found that Sn-3.5mass%Ag has longer fatigue life than Sn-37mass%Pb in low cycle fatigue. In addition. the result with ${\gamm}ashow$a good agreement with the FEA results.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.9 s.102
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• pp.1053-1059
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• 2005

Dynamic stability of an axially accelerating beam structure is investigated in this paper. The equations of motion of a fixed-free beam are derived using the hybrid deformation variable method and the assumed mode method. Unstable regions due to periodical acceleration are obtained by using the Floquet's theory. Stability diagrams are presented to illustrate the influence of the dimensionless acceleration, amplitude, and frequency. Also, buckling occurs when the acceleration exceeds a certain value. It is found that relatively large unstable regions exist around the first bending natural frequency, twice the first bending natural frequency, and twice the second bending natural frequency. The validity of the stability diagram is confirmed by direct numerical integration of the equations of motion.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.13 no.12
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• pp.1230-1235
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• 2001

The laminar convection heat transfer in a ventilated space with various horizontal partitions was studied numerically and experimentally. The experimental results by holographic interferometer showed good agreements with the numerical results. For the numerical study, the governing equations were solved by using a finite volume method for $46.6\leqRe\leq1332,\;1460\leqGr\leql1585$, Pr=0.71 and the variations of partition lengths. The isotherms and velocity vectors have been represented for various parameters. As the length of partition increases, the convection heat transfer decreases. Based on the numerical data, a correlation was obtained for the dimensionless mean Nusselt number in terms of $Gr/Re^2$. In the region of $Gr/Re^2$<1, the mean Nusselt number was very small, but in the region of $Gr/Re^2\geq1$, the mean Nusselt number was constant.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1997.04a
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• pp.139-146
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• 1997

The main purpose of this paper is to investigate the near-optimal parameters of continuous beam subject to a moving load. The computer-aided optimization technique is used to obtain the near-optimal parameters. The computer program is developed to obtain the natural frequency parameters and the forced vibration responses to a transit point load for the continuous beam with variable support spacing, mass and stiffness. The optimization function to describe the design efficiency is defined as a linear combination of four dimensionless span characteristics: the maximum dynamic stress; the stress difference between span segments; the rms deflection under the transit point load; and the total span mass. Studies of three span beams show that the beam with near-optimal parameters can improve design efficiency by 12 to 24 percent when compared to a reference configuration beams of the same total span length.

• Journal of Welding and Joining
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• v.20 no.1
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• pp.83-90
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• 2002

Metal Transfer in gas metal arc (GMA) welding is a complex phenomenon affected by many parameters of the welding conditions and material properties. In this research, the correlation equation between the welding condition and detaching droplet size and detaching velocity in GMA welding was studied via recession analysis on the results of numerical analysis using the volume-of-fluid (VOF) method. Welding parameters and material properties were grouped into three dimensionless numbers and detaching droplet size was expressed as the function of them. Second order and exponential multi-variable correlation forms were assumed, and the coefficients of these equations were calculated for globular and spray modes as well as entire transfer modes. Applying correlation equation into available experimental data, it shows good agreement.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.573-585
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• 2018

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

• Advances in nano research
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• v.5 no.4
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• pp.281-301
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• 2017

In this disquisition, an exact solution method is developed for analyzing the vibration characteristics of magneto-electro-elastic functionally graded (MEE-FG) beams by considering porosity distribution and various boundary conditions via a four-variable shear deformation refined beam theory for the first time. Magneto-electroelastic properties of porous FG beam are supposed to vary through the thickness direction and are modeled via modified power-law rule which is formulated using the concept of even and uneven porosity distributions. Porosities possibly occurring inside functionally graded materials (FGMs) during fabrication because of technical problem that lead to creation micro-voids in FG materials. So, it is necessary to consider the effect of porosities on the vibration behavior of MEE-FG beam in the present study. The governing differential equations and related boundary conditions of porous MEE-FG beam subjected to physical field are derived by Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factor. An analytical solution procedure is used to achieve the natural frequencies of porous-FG beam supposed to magneto-electrical field which satisfies various boundary conditions. A parametric study is led to carry out the effects of material graduation exponent, porosity parameter, external magnetic potential, external electric voltage, slenderness ratio and various boundary conditions on dimensionless frequencies of porous MEE-FG beam. It is concluded that these parameters play noticeable roles on the vibration behavior of MEE-FG beam with porosities. Presented numerical results can be applied as benchmarks for future design of MEE-FG structures with porosity phases.

• Structural Engineering and Mechanics
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• v.63 no.1
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• pp.65-76
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• 2017

This research investigated the vibration frequency of sandwich plate made of piezoelectric fiber reinforced composite core (PFRC) and face sheets of piezomagnetic materials. The effective electroelastic constants for PFRC materials are obtained by the micromechanical approach. The resting medium of sandwich plate is modeled by Pasternak foundation including normal and shear modulus. Besides, sandwich plate is subjected to linearly varying normal stresses that change by load factor. The coupled equations of motion are derived using first order shear deformation theory (FSDT) and energy method. These equations are solved by differential quadrature method (DQM) for simply supported boundary condition. A detailed numerical study is carried out based on piezoelectricity theory to indicate the significant effect of load factor, volume fraction of fibers, modulus of elastic foundation, core-to-face sheet thickness ratio and composite materials on dimensionless frequency of sandwich plate. These findings can be used to aerospace, building and automotive industries.

• Journal of Welding and Joining
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• v.21 no.3
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• pp.92-98
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• 2003

This paper describes the numerical prediction of the thermal fatigue life of a $\mu$BGA(Micro Ball Grid Array) solder joint. Finite element analysis(FEA) was employed to simulate thermal cycling loading for solder joint reliability. Strain values, along with the result of mechanical fatigue tests for solder alloys were then used to predict the solder joint fatigue life using the Coffin-Manson equation. The results show that Sn-3.5mass%Ag solder had the longest thermal fatigue life in low cycle fatigue. Also a practical correlation for the prediction of the thermal fatigue life was suggested by using the dimensionless variable ${\gamma}$, which was possible to use several lead free solder alloys for prediction of thermal fatigue life. Furthermore, when the contact angle of the ball and chip has 50 degrees, solder joint has longest fatigue life.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.3
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• pp.267-279
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• 1998

A numerical study was made of flow behind a circular cylinder in a uniform flow, where the cylinder was rotationally oscillated in time. The temporal behavior of vortex formation was scrutinized over broad ranges of the two externally specified parameters, i.e., the dimensionless rotary oscillating frequency (.110.leq. $S_{f}$.leq..220) and the maximum angular amplitude of rotation (.theta.$_{max}$=15 deg., 30 deg. and 60 deg.). The Reynolds number (Re= $U_{{\inf}D}$.nu.) was fixed at Re=110. A fractional-step method was utilized to solve the Navier-Stokes equations with a generalized coordinate system. The main emphasis was placed on the initial vortex formations by varying $S_{f}$ and .theta.$_{max}$. Instantaneous streamlines and pressure distributions were displayed to show the vortex formation patterns. The vortex formation modes and relevant phase changes were characterized by measuring the lift coefficient ( $C_{L}$) and the time of negative maximum $C_{L}$( $t_{-C}$$_{Lmax}$) with variable forcing conditions.s.tions.s.s.s.