• Title/Summary/Keyword: 응력 텐서

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Fracture and Hygrothermal Effects in Composite Materials (복합재의 파괴와 hygrothermal 효과에 관한 연구)

  • Kook-Chan Ahn;Nam-Kyung Kim
    • Journal of the Korean Society of Safety
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    • v.11 no.4
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    • pp.143-150
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    • 1996
  • This is an explicit-Implicit, finite element analysis for linear as well as nonlinear hygrothermal stress problems. Additional features, such as moisture diffusion equation, crack element and virtual crack extension(VCE ) method for evaluating J-integral are implemented in this program. The Linear Elastic Fracture Mechanics(LEFM) Theory is employed to estimate the crack driving force under the transient condition for and existing crack. Pores in materials are assumed to be saturated with moisture in the liquid form at the room temperature, which may vaporize as the temperature increases. The vaporization effects on the crack driving force are also studied. The Ideal gas equation is employed to estimate the thermodynamic pressure due to vaporization at each time step after solving basic nodal values. A set of field equations governing the time dependent response of porous media are derived from balance laws based on the mixture theory Darcy's law Is assumed for the fluid flow through the porous media. Perzyna's viscoplastic model incorporating the Von-Mises yield criterion are implemented. The Green-Naghdi stress rate is used for the invariant of stress tensor under superposed rigid body motion. Isotropic elements are used for the spatial discretization and an iterative scheme based on the full newton-Raphson method is used for solving the nonlinear governing equations.

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H-refined Shape Design Sensitivity Analysis of Elastic Structures using Multi-Resolution Approach (다중 조밀도를 이용한 탄성 구조의 h-세분화 아이소-지오메트릭 설계민감도 해석)

  • Lee, Taeho;Yoon, Minho;Cho, Seonho;Koo, Bonyong
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.31 no.3
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    • pp.155-163
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    • 2018
  • One of the major disadvantages of isogeometric analysis(IGA) is that local refinement is nearly impossible in a conventional manner because of the tensor product nature in NURBS. In this research, we investigate a local refinement scheme for isogeometric analysis, named multi-resolution approach where different resolutions are employed at each subdomain, using h-refinement relation to endow displacement compatibility on an interface of subdomains. Then, we develop shape sensitivity analysis possessing same compatibility condition as in the analysis. Numerical examples are shown to demonstrate the computational efficiency of the method in analysis especially stress concentration problem and accurate sensitivity results which is also compatible on the interface.

A Study on Comparison and Application of Numerical Models to Experiments in Discontinuous Rock Mass (불연속성 암반에서의 수치모델 검토 및 시험과의 비교.적용에 대한 연구)

  • 정교철
    • The Journal of Engineering Geology
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    • v.7 no.2
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    • pp.91-99
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    • 1997
  • In general, there are various approaches available in literature to model discontinuous rock masses and engineers are often confused which one to use for designing structures in rock masses. Modelling rock masses can be classified mainly into two approaches. One is discrete modelling of intact rock and discontinuities and the other is the equivalent continuum modelling. In this study five models are selected ;(1) Crack tensor model, (2) Equivalent volume defect model, (3) Damage model, (4) Micro - structure model (Parallel model and Series model), and (5) Homogenization model. Most of these models are mainly concerned with how to define additional strain due to discontinuities over the representative elementary volume (REV) and how to relate the stress field of discontinuities to that acting on the REV. The characteristics of these models are clarified by comparing with results of some laboratory tests.

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Direct-Current Dielectrophoretic Motions of a Pair of Particles due to Interactions with a Nearby Nonconducting Wall (비전도성 벽과의 상호작용에 따른 한 쌍 입자의 직류 유전영동 운동)

  • Kang, Sangmo
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.39 no.10
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    • pp.805-815
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    • 2015
  • The present study numerically investigated two-dimensional dielectrophoretic motions of a pair of particles suspended freely in a viscous fluid, interacting with a nearby nonconducting planar wall, under an external uniform electric field. The results show that the motions depend strongly on the set of two electric conductivity signs and the particles-wall separation gap. When both particles have the same sign, they revolve and finally align parallel to the electric field. In contrast, with different signs, they revolve in the opposite direction and finally align perpendicular to the field. Simultaneously, they are repelled to move farther away from the wall regardless of their conductivity set. With further separation from the wall, the particles-wall interaction effect diminishes and tthe particle-particle effect dominates.

Isogeometric Topological Shape Optimization of Structures using Heaviside Enrichment (헤비사이드 강화를 이용한 구조물의 아이소-지오메트릭 위상 최적설계)

  • Ahn, Seung-Ho;Cho, Seonho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.26 no.1
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    • pp.79-87
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    • 2013
  • An isogeometric topological shape optimization method is developed using the level sets and Heaviside enrichments. In the level set method, the initial domain is kept fixed and its boundary is represented by an implicit moving boundary embedded in the level set functions, which facilitates to handle complicated topological shape changes. The Heaviside enrichment improves the isogeometric analysis by adding some enrichment functions to model the internal boundaries. The proposed topological shape optimization method has several benefits: exact geometric models can be obtained using the isogeometric approach and the limitation of tensor-product patches can be overcome using the Heaviside enrichments to represent the internal voids. Even in a single patch, discontinuous displacement fields as well as smooth stress field can be obtained. Since the level sets offer the implicit moving boundary inside the domain, it is easy to represent the topological shape variations in the isogeometric analysis using Heaviside enrichments.

Contimuum Damage Model of Concrete using Hypothesis of Equivalent Elastic Energy (등가탄성에너지법에 의한 콘크리트의 연속체 손상모델)

  • 이기성;변근주;송하원
    • Magazine of the Korea Concrete Institute
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    • v.7 no.5
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    • pp.172-178
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    • 1995
  • Concrete contains numerous microcracks at initially poured. The growth and propagation of nicrockacsk are believed tc finally incur the faiure of concrete. These processings are understood as a damage. Damage IS represented as a second-order tensor and crack is treated as a con tinuum phenomenon. In this paper, damage is characterized through the effective stress concept together with the hypothesis of elastic energy equivalence, and damage evolution law and constitutive equation of a damage model are derived by using the Helmholtz frte eriergy and the dissipation potential by means of the thermodynamic principles. The constitutive equation of the model includes the effects of elasticity, anisotropic damage and plasticity of concrete. There are two effective tangent stiffness tensors in this model : one is for elastic-darnage and the other for plastic damage. For the verification of the model, finite element analysis was performed for the analysis of concrete subjec:t to uniaxial and biaxial loading and the results obtained were compared with test results.

Isogeometric Analysis of Electrostatic Adhesive Forces in Two-Dimensional Curved Electrodes (2차원 곡면형 전극에서 정전기 흡착력의 아이소-지오메트릭 해석)

  • Oh, Myung-Hoon;Kim, Jae-Hyun;Kim, Hyun-Seok;Cho, Seonho
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.34 no.4
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    • pp.199-204
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    • 2021
  • In this study, an isogoemetric analysis (IGA) method that uses NURBS (Non-Uniform Rational B-Spline) basis functions in computer-aided design (CAD) systems is employed to account for the geometric exactness of curved electrodes constituting an electro-adhesive pad in electrostatic problems. The IGA is advantageous for obtaining precise normal vectors when computing the electro-adhesive forces on curved surfaces. By performing parametric studies using numerical examples, we demonstrate the superior performance of the curved electrodes, which is attributed to the increase in the normal component of the electro-adhesive forces. In addition, concave curved electrodes exhibit better performance than their convex counterparts.

A Numerical Study on the Effect of Initial Shape on Inelastic Deformation of Solder Balls under Various Mechanical Loading Conditions (다양한 기계적 하중조건에서 초기 형상이 솔더볼의 비탄성 변형에 미치는 영향에 관한 수치적 연구)

  • Da-Hun Lee;Jae-Hyuk Lim;Eun-Ho Lee
    • Journal of the Microelectronics and Packaging Society
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    • v.30 no.4
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    • pp.50-60
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    • 2023
  • Ball Grid Array (BGA) is a widely used package type due to its high pin density and good heat dissipation. In BGA, solder balls play an important role in electrically connecting the package to the PCB. Therefore, understanding the inelastic deformation of solder balls under various mechanical loads is essential for the robust design of semiconductor packages. In this study, the geometrical effect on the inelastic deformation and fracture of solder balls were analyzed by finite element analysis. The results showed that fracture occurred in both tilted and hourglass shapes under shear loading, and no fracture occurred in all cases under compressive loading. However, when bending was applied, only the tilted shape failed. When shear and bending loads were combined with compression, the stress triaxiality was maintained at a value less than zero and failure was suppressed. Furthermore, a comparison using the Lagrangian-Green strain tensor of the critical element showed that even under the same loading conditions, there was a significant difference in deformation depending on the shape of the solder ball.

Multi-scale Progressive Fatigue Damage Model for Unidirectional Laminates with the Effect of Interfacial Debonding (경계면 손상을 고려한 적층복합재료에 대한 멀티스케일 피로 손상 모델)

  • Dongwon Ha;Jeong Hwan Kim;Taeri Kim;Young Sik Joo;Gun Jin Yun
    • Composites Research
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    • v.36 no.1
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    • pp.16-24
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    • 2023
  • This paper presents a multi-scale progressive fatigue damage model incorporating the model for interfacial debonding between fibers and matrix. The micromechanics model for the progressive interface debonding was adopted, which defined the four different interface phases: (1) perfectly bonded fibers; (2) mild imperfect interface; (3) severe imperfect interface; and (4) completely debonded fibers. As the number of cycles increases, the progressive transition from the perfectly bonded state to the completely debonded fiber state occurs. Eshelby's tensor for each imperfect state is calculated by the linear spring model for a damaged interface, and effective elastic properties are obtained using the multi-phase homogenization method. The fatigue damage evolution formulas for fiber, matrix and interface were proposed to demonstrate the fatigue behavior of CFRP laminates under cyclic loading. The material parameters for the fiber/matrix fatigue damage were characterized using the chaotic firefly algorithm. The model was implemented into the UMAT subroutine of ABAQUS, and successfully validated with flat-bar UD laminate specimens ([0]8,[90]8, [30]16) of AS4/3501-6 graphite/epoxy composite.