• Structural Engineering and Mechanics
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• 제85권2호
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• pp.147-161
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• 2023

Based on the ideas of variational differential quadrature (VDQ) and finite element method (FEM), a numerical approach named as VDQFEM is applied herein to study the large deformations of plate-type structures under static loading with arbitrary shape hole made of functionally graded graphene platelet-reinforced composite (FG-GPLRC) in the context of higher-order shear deformation theory (HSDT). The material properties of composite are approximated based upon the modified Halpin-Tsai model and rule of mixture. Furthermore, various FG distribution patterns are considered along the thickness direction of plate for GPLs. Using novel vector/matrix relations, the governing equations are derived through a variational approach. The matricized formulation can be efficiently employed in the coding process of numerical methods. In VDQFEM, the space domain of structure is first transformed into a number of finite elements. Then, the VDQ discretization technique is implemented within each element. As the last step, the assemblage procedure is performed to derive the set of governing equations which is solved via the pseudo arc-length continuation algorithm. Also, since HSDT is used herein, the mixed formulation approach is proposed to accommodate the continuity of first-order derivatives on the common boundaries of elements. Rectangular and circular plates under various boundary conditions with circular/rectangular/elliptical cutout are selected to generate the numerical results. In the numerical examples, the effects of geometrical properties and reinforcement with GPL on the nonlinear maximum deflection-transverse load amplitude curve are studied.

• 대한조선학회지
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• 제21권1호
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• pp.21-34
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• 1984

This paper is concerned with the experimental investigation of transverse vibration characteristics in water of rectangular plates having an inner free cutout. Systematic experiments are carried out to investigate effects of the surrounding water on the added mass and the natural frequency of the plates due to the changes of the aspect ratio, hole size and eccentricity. The main subject is the clamped rectangular plate with a circular hole. For the purpose of comparative evaluations, some other common-type boundary conditions and hole shapes such as ellipses and rectangles are also investigated. Some of the results obtain are as follows; 1) For each given aspect ratio of the plate, there is a hole area ratio which gives a minimum value of the nondimensional frequency parameter for each mode. The hole area ratio increases as the order number of the mode increases. 2) The nondimensinal mass-increment parameter decreases as the aspect ration or the order number of the mode increases. For each given aspect ratio, the parameter the fundamental mode decreases monotonically as the hole area ratio increase. In cases of the second and higher order modes, however, each mode has a hole area ratio which gives a maximum value of the parameter for each aspect ratio more then 2/3. 3) Comparing elliptic holes with rectangular ones with same hole area ratio, nondimensional frequency parameters are almost same for each given ratio of the shorter axises to the longer one. 4) The influences of difference in boundary condion on nondimensional frequency parameters in water are similar to those in air.

• 대한조선학회지
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• 제24권3호
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• pp.35-42
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• 1987

For the analysis of natural vibrations of a rectangular stiffened plate with inner cutouts, an application of the Rayleigh-Ritz method is investigated. In construction of the trial function for the Rayleigh quotient, only the outer boundary conditions are satisfied with combination of Euler beam functions. As to the modeling of stiffened plates for the energy calculations, a lumping stiffener-effects method and the orthotropic plate analogy are considered for the purpose of comparison. Some numerical results obtained by the Rayleigh-Ritz method are compared with results by experiments and the finite element method. The following are major conclusions; (1) With the lumping stiffener-effects modeling the Rayleigh-Ritz method gives good results of both natural frequencies and mode shapes. The orthotropic plate analogy in cases of regularly stiffened plates is of restrictive use i.e. acceptable for a small cutout. (2) The natural frequency of a stiffened plate with inner cutouts between stiffeners is higher than that of without cutouts and increase as the hole area ratio increases as long as there are no discontinuous stiffeners due to the cutout.

• Structural Engineering and Mechanics
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• 제34권2호
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• pp.159-174
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• 2010

Elastic buckling load of perforated steel plates is typically predicted using the finite element or conjugate load/displacement methods. In this paper an artificial neural network (ANN)-based formula is presented for the prediction of the elastic buckling load of rectangular plates having a circular cutout. By using this formula, the elastic buckling load of perforated plates can be calculated easily without setting up an ANN platform. In this study, the center of a circular cutout was chosen at different locations along the longitudinal x-axis of plates subjected to linearly varying loading. The results of the finite element method (FEM) produced by the commercial software package ANSYS are used to train and test the network. The accuracy of the proposed formula based on the trained ANN model is evaluated by comparing with the results of different researchers. The results show that the presented ANN-based formula is practical in predicting the elastic buckling load of perforated plates without the need of an ANN platform.

• 한국의학물리학회지:의학물리
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• 제13권1호
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• pp.27-31
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• 2002

6MeV 전자선의 output 인자를 결정하기 위해 간편하게 output 인자를 예측하는 수단인 1D(Dimension) 방법을 이용하였으며 그리고 1D 방법으로 결정된 output 인자를 개별적 beam cutout 하에서 직접 측정한 output 인자와 비교하여 1D 방법의 정확성을 분석하였다. 1D 방법은 정방형 field의 한 변과 항상 동일한 한 변을 갖는 사각형 field의 output 인자로서 규정되며, 임의의 사각형 field (X,Y)의 output은 1D output 인자의 곱으로 주어진다. 6MeV 전자선의 대단히 큰 정방형 field의 output은 1D 방법을 사용하면 실제보다 높은 값을 나타내지만 교정인자 CF=C.[(X-10)(Y-10)/$\mid$(X-10)(Y-10)$\mid^{1/2}]$를 적용하면 개별적 cutout하에 직접 측정된 output 인자와 잘 일치하였으며 그 오차 범위는 1% 이내였다.

• 소음진동
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• 제8권3호
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• pp.467-476
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• 1998

The free vibration analysis and design optimization of the rotating composite cylindrical shells with a rectangular cutout are investigated by theoretical method. The Love's thin shell theory is used to derive the frequency equation. The theoretical results are obtained by application of the energy method employing the Rayleigh-Ritz procedure. The used circumferential vibration modes are trigonometric functions, the axial modes are the beam modal functions chosen to satisfy the prescribed boundary conditions. To check the validity, the theoretical results are compared with experimental, FEM and other theoretical results.

• 한국소음진동공학회논문집
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• 제17권9호
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• pp.881-887
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• 2007

This paper is concerned with the vibration analysis of a rectangular plate with multiple rectangular holes. Even though there have been many methods developed for the addressed problem, they suffer from computational time. In this paper, we applied the Independent Coordinate Coupling Method(ICCM) to the addressed problem, which was developed to compute natural vibration characteristics of the rectangular plate with a rectangular hole and proven to be computationally effective. The ICCM is based on Rayleigh-Ritz method but utilizes independent coordinates for each hole domain. By matching the deflection conditions for each hole imposed on the expressions, we can easily derive the reduced mass and stiffness matrices. The resulting equation is then used for the calculation of the eigenvalue problem. The numerical results show the efficacy of the Independent Coordinate Coupling Method.

• 한국소음진동공학회논문집
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• 제17권11호
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• pp.1086-1092
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• 2007

This paper is concerned with the vibration analysis of a rectangular plate with multiple circular holes. On the contrary to the case of rectangular plate with multiple rectangular holes, it is very difficult to perform qualitative analysis on natural vibration characteristics because of geometrical inconsistency. In this paper, we applied the Independent Coordinate Coupling Method(ICCM) to the addressed problem, which was developed to compute natural vibration characteristics of the rectangular plate with a circular hole and proven to be computationally effective. The ICCM is based on Rayleigh-Ritz method but utilizes independent coordinates for each hole domain. By matching the deflection conditions for each hole imposed on the expressions, we can easily derive the reduced mass and stiffness matrices. The resulting equation is then used for the calculation of the eigenvalue problem. The numerical results show the efficacy of the Independent Coordinate Coupling Method.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2006년도 춘계학술대회논문집
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• pp.1229-1234
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• 2006

This paper is concerned with the dynamic modeling and controller design for a cylindrical shell equipped with MFC actuators. The dynamic model was derived by using Ravleigh-Ritz method based on Donnel-Mushtari shell theory. The boundary conditions at both ends were assumed to be shear diaphragm. To verify the theoretical results, a cylindrical shell structure made of aluminum was built ana tested by using impact hammer. Experimental results show that there are little discrepancies compared to theoretical results because of the boundary conditions at both ends. The MFC actuators were glued to the cylindrical shell in longitudinal and circumferential directions. The PPF controller were designed for lowest two modes and applied to the MFC actuators. The experimental results show that vibrations can be successfully suppressed.

• 한국구조물진단유지관리공학회 논문집
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• 제9권4호
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• pp.109-118
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• 2005

철근콘크리트조 고층아파트의 경우 흔히 전단벽식 구조시스템을 채택하게 된다. 이때에는 작업자의 이동과 재료나 장비의 수평 운반 편의상 세대간의 내력벽에 직 4각형 형태의 개구부를 설치할 때가 많다. 이와 같은 개구부는 화재등의 재난시에 신속한 대피용 통로로 이용하도록 하는 경우도 있다. 전단벽의 개구부는 구조체의 안전이나 안정을 위협하는 중요한 요소로 될 수 있으므로 설계시나 안전검토에서 반드시 검토해야할 사항이다. 이번 연구는 개구부를 갖는 직 4각형 전단벽의 탄성안정에 관한 것이다. 연구에서는 유한 요소법을 이용하였고 수치해석의 중요 변수는 개구부의 위치와 크기이다. 또한 연직 하중에 의한 균등 압축응력은 물론 휨 모멘트에 의한 응력 및 수평 전단력이 판의 임계응력에 미치는 영향도 검토하였다. 끝으로 비재하면의 구속이 전단벽의 안정성에 미치는 영향도 검토하였다.