• 제목/요약/키워드: simply supported edge

검색결과 54건 처리시간 0.024초

Edge stresses analysis in thick composite panels subjected to axial loading using layerwise formulation

  • Ahmadi, Isa
    • Structural Engineering and Mechanics
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    • 제57권4호
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    • pp.733-762
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    • 2016
  • Based on a reduced displacement field, a layer-wise (LW) formulation is developed for analysis of thick shell panels which is subjected to axial tension. Employing the principle of minimum total potential energy, the local governing equations of thick panel which is subjected to axial extension are obtained. An analytical method is developed for solution of the governing equations for various edge conditions. The governing equations are solved for free and simply supported edge conditions. The interlaminar stresses in the panel are investigated by means of Hooke's law and also by means of integration of the equilibrium equations of elasticity. Dependency of the result upon the number of numerical layers in the layerwise theory (LWT) is studied. The accuracy of the numerical results is validated by comparison with the results of the finite element method and with other available results in the open literature and good agreement is seen between the results. Numerical results are then presented for the distribution of interlaminar normal and shear stresses within the symmetric and un-symmetric cross-ply thick panels with free and simply supported boundaries. The effects of the geometrical parameters such as radius to thickness and width to thickness ratio are investigated on the distribution of the interlaminar stresses in thick panels.

Flexural Vibration of Clamped and Simplv Supported Sectorial Plates with Combinations of Simply Supported and Free Radial Edges

  • Han, Bong-Ko;Kim, Joo-Woo
    • Nuclear Engineering and Technology
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    • 제31권2호
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    • pp.214-225
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    • 1999
  • An accurate method is presented for flexural vibrations of sectorial plates having simply supported-free and free-free radial edges, when the circular edge is either clamped or simply supported. The classical Ritz method is employed with two sets of admissible functions assumed for the transverse vibratory displacements. These sets consist of : (1) mathematically complete algebraic-trigonometric polynomials which gurantee convergence to exact frequencies as sufficient terms are retained, and (2) comer functions which account for the bending moment singularities at re-entrant comer of the radial edges having arbitrary edge conditions. Accurate (at least four significant figures) frequencies and normalized contours of the transverse vibratory displacement are presented for the spectra of corner angles [90$^{\circ}$, 180$^{\circ}$(semi-circular), 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 355$^{\circ}$, 360$^{\circ}$ (complete circular)] causing a re-entrant comer of the radial edges. Future solutions drawn from alternative numerical procedures and finite element techniques may be compared with these accurate results.

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다양한 경계조건을 갖는 링보강 복합재료 원통셸의 진동특성해석 (Vibration Characteristics of Ring-Stiffened Composite Cylindrical Shells with Various Edge Boundary Conditions)

  • 이영신;김영완;최명환;류충현;신도섭
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 1998년도 춘계학술대회논문집; 용평리조트 타워콘도, 21-22 May 1998
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    • pp.359-364
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    • 1998
  • The effects of boundary conditions on natural frequencies for the ring stiffened composite cylindrical shells are investigated by theoretical method. The Love's thin shell theory and the discrete stiffener theory with beam functions in the Ritz procedure are used to derive the frequency equation. Five different boundary conditions such as clamped-clamped, simply supported-simply supported, free-free, clamped-free, clamped-simply supported are considered in this study. Also, the experimental investigation is presented to validate the theoretical results.

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단순 지지 경계 조건을 가진 임의 형상 평판의 고정밀도 자유 진동 해석을 위한 NDIF법 개발 (Development of NDIF Method for Highly Accurate Free Vibration Analysis of Arbitrarily Shaped Plates with Simply Supported Boundary Condition)

  • 강상욱;우윤환
    • 한국소음진동공학회논문집
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    • 제21권2호
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    • pp.186-193
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    • 2011
  • The NDIF method(non-dimensional dynamic influence function method) for free vibration analysis of arbitrarily shaped plates with the simply supported edge is newly developed in the paper. In order to extract the system matrix that gives the natural frequencies and natural modes of the plate of interest, the difficulty of measuring higher differential terms involved in the simply supported boundary condition is successfully overcome. Finally, the excellence of the characteristics of convergence and accuracy of the proposed method is shown through two verification examples, which indicate that natural frequencies and natural modes obtained by the proposed method are very accurate and swiftly converged even though a small number of nodes are used compared with FEM.

단순지지된 Steel 및 복합재료 원통셸의 진동에 대한 실험적 고찰 (An Experimental Study on the Free Vibration of the Steel and Composite Cylindrical Shells with Simply Supported Edge Conditions)

  • 이영신;최명환;길기남;송근영
    • 한국소음진동공학회:학술대회논문집
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    • 한국소음진동공학회 1998년도 춘계학술대회논문집; 용평리조트 타워콘도, 21-22 May 1998
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    • pp.334-339
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    • 1998
  • The free vibration analysis of the simply supported steel and composite cylindrical shells are investigated. The natural frequencies and mode shapes of the shell are experimentally obtained by impact testing using an impact hammer and an accelerometer. The effects of the material and geometry on the vibrational characteristics of the shell are examined. The experimental results are compared with the analytical and a finite element results. They showed good agreement with each other.

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다양한 경계조건을 갖는 링보강 복합재료 원통셸의 진동특성 (Vibration Characteristics of Ring-Stiffened Composite Cylindrical Shells with Various Edge Boundary Conditions)

  • 김영완;이영신
    • 소음진동
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    • 제9권3호
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    • pp.485-492
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    • 1999
  • The effects of boundary conditions on vibration characteristics for the ring stiffered composite cylindrical shells are investigated by theoretical and experimental method. In the theoretical procedure, the Love's thin shell theory combined with the discrete stiffener theory to consider the ring stiffening effect are adopted to derive the frequency equation. In experiment, the impact exciting method is used to obtain the vibraton results. Five different boundary conditions: clamped-clamped, simply supported-simply supported, free-free, clamped-free, clamped-simply supported are considered in this study.

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직사각형 후판의 면외 진동인텐시티 해석 (Out-of-plane Structural Intensity Analysis of Rectangular Thick Plate)

  • 김국현;조대승
    • 한국해양공학회지
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    • 제26권4호
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    • pp.42-49
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    • 2012
  • A numerical method is presented for an out-of-plane structural intensity analysis of rectangular thick plates with arbitrary elastic edge constraints. The method adapts an assumed mode method based on Timoshenko beam functions to obtain the velocities and internal forces needed for a structural intensity analysis. To verify the presented method, the structural intensity of a square thick plate under harmonic force excitation, for which four edges are simply supported, is analyzed, and the result is compared with existing solutions using the assumed mode method based on trigonometric functions. In addition, numerical analyses are carried out for a rectangular-shaped thick plate under harmonic force excitations, of which three edges are simply supported and one edge utilizes an arbitrary elastic edge constraint. These numerical examples show the good accuracy and applicability of the presented method for rectangular thick plates with arbitrary edge constraints.

Simply supported boundary condition for bifurcation analysis of functionally graded material: Thickness control by exponential fraction law

  • Shadi Alghaffari;Muzamal Hussain;Mohamed A. Khadimallah;Faisal Al Thobiani;Hussain Talat Sulaimani
    • Advances in nano research
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    • 제14권4호
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    • pp.303-312
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    • 2023
  • In this study, the bifurcation analysis of functionally graded material is done using exponential volume fraction law. Shell theory of Love is used for vibration of shell. The Galerkin's method is applied for the formation of three equations in eigen value form. This eigen form gives the frequencies using the computer software MATLAB. The variations of natural frequencies (Hz) for Type-I and Type-II functionally graded cylindrical shells are plotted for exponential volume fraction law. The behavior of exponent of volume fraction law is seen for three different values. Moreover, the frequency variations of Type-I and -II clamped simply supported FG cylindrical shell with different positions of ring supports against the circumferential wave number are investigated. The procedure adopted here enables to study vibration for any boundary condition but for brevity, numerical results for a cylindrical shell with clamped simply supported edge condition are obtained and their analysis with regard various physical parameters is done.

다양한 방사연단 조건을 갖는 고정 및 단순지지 부채꼴형 평판 진동에 대한 경계응력특이도의 영향 (Influence of Boundary Stress Singularities on the Vibration of Clamped and Simply Supported Sectorial Plates With Various Radial Edge Conditions)

  • 김주우
    • 한국강구조학회 논문집
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    • 제10권4호통권37호
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    • pp.601-613
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    • 1998
  • 본 논문은 부채꼴형 평판의 원형연단이 고정되어 있거나 또는 단순지지 되어 있을 때 요각 모서리의 응력 특이도를 고려하여 자유 진동해를 최초로 구한 연구이다. Ritz방법을 이용하여 수직진동변위를 두가지 적합함수식으로 가정하였다. 본 연구에서는 부채꼴형 각도의 범위에 따른 엄밀한 진동수 및 수직진동 변위의 전형적인 등고선을 제시하였다.

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Free Vibrations and Buckling of Rectangular Plates with Linearly Varying In-Plane Loading

  • 장경호;심현주;강재훈
    • 한국공간구조학회논문집
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    • 제4권4호
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    • pp.99-111
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    • 2004
  • An exact solution procedure is formulated for the free vibration and buckling analysis of rectangular plates having two opposite edges simply supported when these edges are subjected to linearly varying normal stresses. The other two edges may be clamped, simply supported or free, or they may be elastically supported. The transverse displacement (w) is assumed as sinusoidal in the direction of loading (x), and a power series is assumed in the lateral (y) direction (i.e., the method of Frobenius). Applying the boundary conditions yields the eigenvalue problem of finding the roots of a fourth order characteristic determinant. Care must be exercised to obtain adequate convergence for accurate vibration frequencies and buckling loads, as is demonstrated by two convergence tables. Some interesting and useful results for vibration frequencies and buckling loads, and their mode shapes, are presented for a variety of edge conditions and in-plane loadings, especially pure in-plane moments.

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