• 대한전기학회논문지
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• 제34권10호
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• pp.379-383
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• 1985

A method employing infinite elements is described for the magnetic field computations of the magnetic circuits with permanent magnet. The system stiffness matrix is derived by a variational approach, while the interfacial boundary conditions between the finite element regions and the infinite element regions are dealt with using collocation method. The proposed method is applied to a simple linear problems, and the numerical results are compared with those of the standard finite element method and the analytic solutions. It is observed that the proposed method gives more accurate results than those of the standard finite element method under the same computing efforts.

• Structural Engineering and Mechanics
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• 제42권5호
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• pp.729-745
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• 2012

This study presents dynamic analysis of laminated beams traversed by moving loads using a multilayered beam element based on the first-order shear deformation theory. The present element consists of N layers with different thickness and material property, and has (3N + 7) degrees of freedom corresponding three axial, four transversal, and 3N rotational displacements. Delamination and interfacial slip are not allowed. Comparisons with analytical and/or numerical results available in literature for some illustrative examples are made. Numerical results for natural frequencies, deflections and stresses of laminated beams are given to explain the effect of load speed, lamina layup, and boundary conditions.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 1997년도 추계학술발표회논문집(1)
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• pp.617-624
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• 1997

This Paper Presents an effective and simple procedure for the simulation of the motion of the solid-liquid interfacial boundary and the transient temperature field during phase change process. To accomplish this purpose, an iterative implicit solution algorithm has been developed by employing the dual reciprocity boundary element method. The dual reciprocity boundary element approach provided in this paper is much simpler than the usual boundary element method applying a reciprocity principle and an available technique for dealing with domain integral of boundary element formulation simultaneously. The effectiveness of the present analysis method have been illustrated through comparisons of the calculation results of an example with its semi-analytical or other numerical solutions where available.

• 소성∙가공
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• 제9권6호
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• pp.590-597
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• 2000

A finite element formulation lot the simulation of axisymmetric sheet hydroforming is proposed, and an implicit program is coded. In order to describe normal anisotropy of steel sheet, Hill's non-quadratic yield function (Hill, 1979) is employed. Frictional contacts among sheet surface, rigid tool surface, and flexible hydrostatic pressure are considered using mesh normal vectors based on finite element of the sheet. Applied hydraulic pressure is also considered as a function of forming rate and time and treated as an external loading. The complete set of the governing relations comprising equilibrium and interfacial equations is approximately linearized for Newton-Raphson algorithm. In order to verify the validity of the developed finite element formulation, the axisymmetric bulge test is simulated. Simulation results are compared with other FEM results and experimental measurements and showed good agreements. In axisymmetric hydroforming processes of a disk cover, formability changes are observed according to the hydraulic pressure curve changes.

• 마이크로전자및패키징학회지
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• 제29권3호
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• pp.37-42
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• 2022

최근 반도체 패키지 구조는 점점 더 얇아지고 복잡해지고 있다. 두께가 얇아짐에 이종 계면에서 물성차이에 의한 박리는 심화될 수 있으며 따라서 계면의 신뢰성이 패키징 설계에 중요한 요소라 할 수 있다. 특히, 반도체 패키징에 많이 사용되는 폴리머는 온도와 수분에 영향을 크게 받기 때문에 환경에 따른 물성 변화 고려가 필수적이다. 따라서, 본 연구에서는 다양한 온도조건에서 수분의 흡습과 탈습을 모두 고려한 패키지 구조의 계면 박리 예측을 유한 요소 해석을 통해 수행하였다. 확산계수와 포화 수분 함량과 같은 재료의 물성은 흡습 실험을 통해 확보하였으며, 흡습 이후 TMA 와 TGA 를 통하여 각 재료의 수분 팽창 계수를 확보하였다. 각 계면의 접합 강도 평가를 위해 수분의 영향을 고려하여 다양한 온도 조건에서 마이크로 전단 실험을 수행하였다. 이러한 물성을 바탕으로 온도와 수분에 의해 발생하는 변형을 모두 고려한 패키지 박리 예측 해석을 수행하였으며, 결과적으로 리플로우 공정 동안의 실시간 수분 탈습 거동을 고려한 계면 박리 예측을 성공적으로 수행하였다.

• 대한기계학회:학술대회논문집
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• 대한기계학회 2005년도 창립60주년 기념 추계 학술대회
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• pp.153.2-153.2
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• 2005

• 대한치과기공학회지
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• 제23권1호
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• pp.31-43
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• 2001

This study was performed to observe the micro-structure change of surface, behavior of oxide change of element, the component transformation of the alloy and the bonding strength between the porcelain interface in order to investigate effects of indium, tin on interfacial properties of porcelain fused to low gold alloy. Hardness of castings was measured with a micro-Vicker's hardness tester. The compositional change of the surface of heat-treated specimen was analyzed with an EDS and an EPMA. The interfacial shear bonding strength between alloy specimen and fused porcelain was measured with a mechanical testing system(MTS 858.20). The results were as follows: 1) The hardness value of alloy increased as increasing amount of indium addition. 2) The formation of oxidation increased as increasing indium and tin contents after heat treatment. 3) Diffusion of indium and tin elements increased as increasing indium and tin contents in metal-porcelain surface after porcelain fused to metal firing. 4) The most interfacial shear bonding strength was increased as increasing a composition of adding elements, and a heat-treatment time, and an oxygen partial pressure. From the results of this study it was found that the addition of alloying elements such as indium and tin increase hardness of as-cast alloy, produce surface oxide layer of adding elements by heat-treatment which may improve interfacial bonding strength between alloy and porcelain.

• Composites Research
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• 제12권2호
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• pp.10-25
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• 1999

Fragmentation 시험법에 의한 섬유상 복합재료의 계면적 특성에 대한 새로운 평가방법이, 순차적으로 섬유간의 간격이 변하게 된 단계적 다섬유 복합재료를 사용하여 제시되었다. 섬유간의 간격이 증가함에 따라, 부서진 섬유들의 형상비는 감소하였으며, 섬유와 기지간의 계면전단강도는 증가함을 보여주었다. 섬유간 거리의 역수를 취했을 때에, 형상비와 계면전단강도 모두가 포화되는 값을 보여주었다. 이것은 단계적 다섬유 복합재료가 형상비에서의 상한값을 나타내고, 계면전단강도에서 하한값을 보여준다는 것을 의미한다. 이 fragmentation 시험법은 복합재료의 평가에 새로운 방법이 될 수 있다. 왜냐하면, 이 두 한계값의 차이를 줄이는 것이 복합재료의 강화에 효과적이기 때문이다. 또한, 섬유 파괴점 부근에서의 섬유응력 분포와 위의 결과를 관련시키기 위해 탄송-소성 유한요소 해석이 행해졌다. 단계적 다섬유 복합재료 시험에서 얻어진 한계값은 그룹형태의 다 섬유 파괴에 의해 야기된 응력집중과 밀접하게 관련되어 있다는 것이 입증되었다.

• Interaction and multiscale mechanics
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• 제1권2호
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• pp.279-301
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• 2008

This paper develops a 3D homogenization based continuum damage mechanics (HCDM) model for fiber reinforced composites undergoing micromechanical damage under monotonic and cyclic loading. Micromechanical damage in a representative volume element (RVE) of the material occurs by fiber-matrix interfacial debonding, which is incorporated in the model through a hysteretic bilinear cohesive zone model. The proposed model expresses a damage evolution surface in the strain space in the principal damage coordinate system or PDCS. PDCS enables the model to account for the effect of non-proportional load history. The loading/unloading criterion during cyclic loading is based on the scalar product of the strain increment and the normal to the damage surface in strain space. The material constitutive law involves a fourth order orthotropic tensor with stiffness characterized as a macroscopic internal variable. Three dimensional damage in composites is accounted for through functional forms of the fourth order damage tensor in terms of components of macroscopic strain and elastic stiffness tensors. The HCDM model parameters are calibrated from homogenization of micromechanical solutions of the RVE for a few representative strain histories. The proposed model is validated by comparing results of the HCDM model with pure micromechanical analysis results followed by homogenization. Finally, the potential of HCDM model as a design tool is demonstrated through macro-micro analysis of monotonic and cyclic damage progression in composite structures.

• 한국정밀공학회지
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• 제20권10호
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• pp.183-190
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• 2003

Major device failures such as die cracking, interfacial delamination and warpage in flip chip packages are due to excessive heat and thermal gradients- There have been significant researches toward understanding the thermal performance of electronic packages, but the majority of these studies do not take into account the combined effects of thermo-mechanical interactions of the different package constituents. This paper investigates the thermo-mechanical performance of flip chip package constituents based on the finite element method with thermo-mechanically coupled elements. Delaminations with different lengths between the silicon die and underfill resin interfaces were introduced to simulate the defects induced during the assembly processes. The temperature gradient fields and the corresponding stress distributions were analyzed and the results were compared with isothermal case. Parametric studies have been conducted with varying thermal conductivities of the package components, substrate board configurations. Compared with the uniform temperature distribution model, the model considering the temperature gradients provided more accurate stress profiles in the solder interconnections and underfill fillet. The packages with prescribed delaminations resulted in significant changes in stress in the solder. From the parametric study, the coefficients of thermal expansion and the package configurations played significant roles in determining the stress level over the entire package, although they showed little influence on stresses profile within the individual components. These observations have been implemented to the multi-board layer chip scale packages (CSP), and its results are discussed.