• Title/Summary/Keyword: 이방성 판

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The Determination of Group Velocity of Lamb Wave So Mode in Composite Plates with Anisotropy (이방성 복합재료 판에서 램파 $S_0$ 모드의 군속도 결정)

  • Rhee, Sang-Ho;Lee, Jeong-Ki;Lee, Jung-Ju
    • Journal of the Korean Society for Nondestructive Testing
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    • v.26 no.4
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    • pp.239-245
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    • 2006
  • Experimentally measured Lamb wave group velocities in composite materials with anisotropic characteristics are not accorded with the theoretical group velocities as calculated with the Lamb wave dispersion equation. This discrepancy arises from the fact that the angle between the group velocity direction and the phase velocity direction in anisotropic materials exists. Wave propagation in a composite material with anisotropic characteristics should be considered with respect to magnitude in addition to direction. In this study, $S_0$ mode phase velocity dispersion corves are depicted with the variation of degree with respect to the fiber direction using a Lamb wave dispersion relation in the unidirectional, bidirectional, and quasi-isotropic composite plates. Slowness surface is sketched by the reciprocal value of the phase velocity curves. The magnitude and direction of the group velocity are calculated from the slowness surface. The theoretically determined group velocity, which is calculated from the slowness surface, Is compared with experimentally measured group velocities. The proposed method shows good agreements with theoretical and experimental results.

Effect of viscous interfaces on bending of orthotropic rectangular laminate (직교 이방성 적층판의 굽힘에 대한 점성 경계면의 영향)

  • Kim, Geun-Woo;Lee, Kang-Yong;Chen, W.Q.
    • Proceedings of the KSME Conference
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    • 2004.04a
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    • pp.180-185
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    • 2004
  • This paper investigates asimply supported orthotropic rectangular laminate with viscous interfaces subjected to bending. Additional mathematical difficulty is involved due to the presence of viscous interfaces because the behavior of the laminate depends on time. A step-by-step state-space approach is suggested, which is directly based on the threedimensional theory of elasticity. In particular, Taylor's expansion theorem is employed to model the variations of field variables with time. The proposed method is suitable for analyzing laminated plate of arbitrary thickness. Numerical calculations are performed and it is shown that the viscous interfaces have a significant fluence on the response.

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Strengthening Capacity of Bridge Deck Strengthened with Carbon Fiber Rod and Polymer Mortar (고강도 폴리머 모르타르 및 탄소섬유 봉(Rod)으로 보강된 교량 바닥판의 보강성능)

  • Sim Jongsung;Moon Do-Young;Ju Mm-Kwan
    • Journal of the Korea Concrete Institute
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    • v.16 no.2 s.80
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    • pp.213-220
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    • 2004
  • This paper deals with an enhanced structural capacity of reinforced concrete bridge deck strengthened with carbon fiber rod (CFR) which is subjected to monotonic and cyclic loads. Strengthening variables considered in this test were evenly and unevenly strengthening type. To evaluate strengthening capacity for these two strengthening types, load-carrying capacity and crack and failure pattern from the failure test were analyzed and fatigue response were examined. According to the test results, all the strengthened specimens showed punching shear failure as a result of premature failure of bonding interface between mortar and concrete. In the case of strengthening capacity, it was observed that the strengthened specimens was more effective in strength, stiffness and fatigue endurance limit than the unstrengthened specimen. In addition, the unevenly strengthening method (CR-UE) was more effective than the evenly strengthening method (CR-E).

Vibration Analysis of [$\alpha/\beta/\beta/\gamma/\alpha/\alpha/\beta$]r type Composite Laminated Plates by the Simple Method of Analysis for Preliminary Design for Civil Construction (건설용 적층복합재료판의 예비설계를 위한 간편해석법을 사용한 [$\alpha/\beta/\beta/\gamma/\alpha/\alpha/\beta$r 형 적층판의 진동해석)

  • 김덕현;이정호;이남주
    • Proceedings of the Korean Society For Composite Materials Conference
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    • 1999.11a
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    • pp.22-27
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    • 1999
  • 고급복합재료(advanced composite material)는 여러 가지 훌륭한 장점에도 불구하고 건설기술자에게는 그 이론이 너무 복잡하여 건설구조에 대한 응용이 지연되고 있다. [$\alpha/\beta/\beta/\gamma/\alpha/\alpha/\beta$]r, $\alpha$=-$\beta$, $\gamma$=0$^{\circ}$ 또는 90$^{\circ}$ 와 같은 몇 가지 배향각을 갖은 적층판은, r이 증가함에 따라, $B_{i,j}$강성이 0으로 접근한다(1995). 건설구조물은 그 치수가 커서 r이 증가해도 지간 대 두께비가 충분히 커서, 횡방향 변형율(${\varepsilon}_{xz}$,${\varepsilon}_{yz}$)의 영향이 무시될 수 있다. 이 경우 판의 지배방정식은 간단한 특별직교이방성판의 식으로 변화된다. 김덕현은 토목구조물에 흔히 적용될 수 있는 이러한 배향각을 가진 적층판의 지배방정식을 취급이 간단한 특별직교 이방성 판의 경우로 변경시킨 다음 해석을 더 간단히 진행할 수 있도록 기술자들이 유사 등방성 상수(quasi-isotropic constant)를 사용하여 낮익은 등방성판의 방정식을 사용하여 답을 구한 다음 그가 개발한 "수정계수(correction factor)"를 사용하여 "정확한"해를 구하는 방법을 발표한바 있다(1991).는 방법을 발표한바 있다(1991).

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Strength Analysis for the Plate System of the Mark III Cargo Containment (Mark III 방열 판 구조물의 파손 강도 평가에 관한 연구)

  • Jeong, Han-Koo;Yang, Young-Soon
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.27 no.6
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    • pp.625-633
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    • 2014
  • Mark III CCS plate is considered in this paper to perform its strength assessment. Mark III CCS plate is designed and constructed by stacking various non-metallic engineering materials such as plywood, triplex and reinforced PU foam that are supported by series of mastic upon inner steel hull structure. From the viewpoint of structural analysis, this plated structure is treated as a laminated anisotropic structure. Commercially available general purpose finite element analysis programs such as MSC PATRAN and MARC are used to develop the finite element (FE) model of the Mark III CCS plate. Because of the characteristics of LNG cargo that the Mark III CCS plate deals with, it is subjected to a wide range of temperature variations, i.e. about $-163^{\circ}C$ to $20^{\circ}C$. Different material properties of the Mark III CCS plate at these temperature levels are considered in the FE model. Using the developed FE model, strength assessment procedure is developed incorporating various anisotropic failure criteria such as Hashin, Hill, Hoffman, Maximum stress and Tsai-Wu. The strength assessment is performed within the initial failure state of the Mark III CCS plate and, as a result, failure details such as failure locations and loads are identified.

The Effect of the Loading Size on Displacements of Stiffened Plates with Open Ribs (재하 크기가 개단면 리브 보강판의 처짐에 미치는 영향)

  • Chu, Seok Beom
    • Journal of Korean Society of Steel Construction
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    • v.18 no.5
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    • pp.563-574
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    • 2006
  • The objective of this study is to determine the effect of the loading size on displacements of stiffened plates with open ribs using the orthotropic rigidity ratio as the parameter. To analyze the displacement behavior of stiffened plates according to the loading size, a concentrated load and three types of uniform distributed loads were applied on the rib at the center of some plates. The results of the analysis of various stiffened plates show that the central displacement ratio of the distributed load to the concentrated load increased according to the decrease in the loading size, and that the ratio can be expressed as a function of the rigidity ratio for each rib space. The maximum displacement of the stiffened plate subjected to the distributed load did not appear at the center of the plate due to the local behavior, and the increasing ratio of the maximum displacement to the central displacement can be expressed as a function of the rigidity ratio for each rib space. Orthotropic plate analysis can achieve more accurate results using the proposed functions, and the application of the functions to examples of a different aspect ratio and support condition shows good accuracy. Therefore, using the functions proposed in this study, the central and maximum displacements can easily be achieved in the orthotropic plate analysis of stiffened plates subjected to the distributed load.

Vibration Analysis of Special Orthotropic Plates on Elastic Foundation with Arbitrary Boundaries (자유경계를 갖고 탄성기초에 놓인 특별직교이방성 적층복합판의 진동해석)

  • 김덕현;이정호;홍창우;심도식
    • Composites Research
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    • v.12 no.4
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    • pp.25-32
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    • 1999
  • A method of calculating the natural frequency corresponding to the first mode of vibration of beams and tower structures, with irregular cross sections and with arbitrary boundary conditions was developed and reported by Kim, D. H. in 1974. In this paper, the result of application of this method to the special orthotropic plates on elastic foundation with free boundaries is presented. Such plates represent the concrete highway slab and hybrid composite pavement on bridges. Any method may be used to obtain the deflection influence surfaces needed for this vibration analysis. Finite difference method is used for this purpose, in this paper. The influence of the modulus of the foundation and the aspect ratio of the plate on the natural frequency is thoroughly studied. The effect of neglecting the mass of the plates on the natural frequency, as the ratio of the point mass/masses to the plate mass increases, is also studied, in deep.

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Three-Dimensional Vibration Analysis of Cantilevered Laminated Composite Plates (캔틸레버 복합 적층판의 3차원 진동해석)

  • 김주우;정희영
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.14 no.3
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    • pp.299-308
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    • 2001
  • This paper presents the three-dimensional (3-D) study of the natural vibration of cantilevered laminated composite plates. The Ritz method is used to obtain stationary values of the associated Lagrangian functional with displacements approximated by mathematically complete polynomials satisfying the boundary conditions at the clamped edge exactly. The accuracy of the 3-D model is established through a convergence study of non-dimensional frequencies followed by a comparison of the converged 3-D solutions with analytical and experimental findings in the existing literature. A wide scope of 3-D frequency results explain the influence of a number of geometrical and material parameters for cantilevered laminated plates, namely aspect ratio (a/b), width-to-thickness ratio (a/h), orthotropy of material, number of plies (NP), fiber orientation angle(θ), and stacking sequence.

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Vibration Analysis of Special Orthotropic Plate with Non-uniform Cross-Section and with Arbitrary Boundary Condition (변단면과 경계조건에 따른 특별직교이방성판의 진동해석)

  • 김덕현;원치문;이정호;홍창우
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.12 no.4
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    • pp.563-571
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    • 1999
  • 변단 면과 다양한 경계조건을 갖는 보와 타워구조물의 제1모드에서의 고유진동수를 구하는 정확한 해는 1974년에 Kim에 의해 발표되었다. 최근 이 방법은 복합재료 적층 판을 포함하는 2차원 문제의 제 1모드 진동해석에 확장되었으며, 다양한 경계조건과 불규칙 단면을 갖는 판에 매우 효과적이다. 이 논문에서는 변단 면과 경계조건에 따른 특별직교 이방성 판에 대한, Kim에 의해 개발된 간편한 진동해석 방법의 응용결과가 주어진다. 또한 집중하중들에 대한 영향이 연구되었다.

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Vibration Analysis of Special Orthotropic Laminated Composite Plates under Axial Loadings (축방향 하중을 받는 특별직교이방성 적층복합판의 진동해석)

  • Won, Chi Moon
    • Journal of Korean Society of Steel Construction
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    • v.18 no.1
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    • pp.93-100
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    • 2006
  • A simple but precise method of calculating the natural vibration frequencies of composite laminated plates with all-simple support and under axial loadings is presented herein. This method uses deflection influence surfaces, which can be obtained by any method for vibration analysis and member due to the inertia force under resonance condition. Beginning with an initially guessed mode shape, the exact mode shape is obtained by the process similar to iteration. In this paper, equations are given for the case of special orthotropic laminates. The same equations, however, can be used for any laminate as long as ${B_1_6}$, ${B_2_6}$, ${D_1_6}$, and ${D_2_6}$ are negligible as the number of plies increases. Some laminates that possess such properties are presented in the paper.