• Structural Engineering and Mechanics
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• 제23권2호
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• pp.115-127
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• 2006

The axisymmetric free vibrations of transversely isotropic magnetoelectroelastic laminated circular plates are studied. Based on the three-dimensional governing equations of magnetoelectroelastic medium, the state space equations of laminated circular plates are obtained. By using the finite Hankel transform and rendering the free terms left by the transform in terms of the boundary quantities, the solutions of the state space equations are given for two kinds of boundary conditions. The frequency equations of the free vibration are derived using the propagator matrix method and the boundary conditions at top and bottom surfaces. By virtue of the inverse Hankel transform, the mode shapes are also determined. Since the solutions strictly satisfy the governing equations in the region and the boundary conditions at the edges, they are the three-dimensionally exact. Finally, the natural frequencies of such plates are tabulated and compared with those of the piezoelectric and elastic plates in the numerical example.

• Steel and Composite Structures
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• 제34권1호
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• pp.141-154
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• 2020

In the present paper, free vibration analysis of angle-ply laminated composite annular and circular plates is performed by numerical methods. First-order shear deformation plate theory is used for kinematic relations. The related governing equations of motion are discretized via differential quadrature and discrete singular convolution methods. Frequency values are obtained for different lamina scheme, thickness-to-radius ratio, and mode numbers. The advantages and accuracy of these two methods are also tested in detail.

• Steel and Composite Structures
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• 제29권6호
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• pp.759-770
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• 2018

In the present investigation, by using the two numerical methods, free vibration analysis of laminated annular and annular sector plates have been studied. In order to obtain the main equations two different shell theories such as Love's shell theory and first-order shear deformation theory (FSDT) have been used for modeling. After obtaining the fundamental equations in briefly, the methods of harmonic differential quadrature (HDQ) and discrete singular convolution (DSC) are used to solve the equation of motion. Accuracy, convergence and reliability of the present HDQ and DSC methods were tested by comparing the existing results obtained by different methods in the literature. The effects of some geometric and material properties of the plates are investigated via these two methods. The advantages and accuracy of the HDQ and DSC methods have also been examined with different grid numbers and shell theory. Some results for laminated annular plates and laminated circular plates were also been supplied.

• Structural Engineering and Mechanics
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• 제10권5호
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• pp.441-449
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• 2000

In this study, the state equation for axisymmetric bending of laminated transversely isotropic circular plates on elastic foundation is established on the basis of three-dimensional elasticity. By using the expansions of Bessel functions, an analytical solution of the problem is presented. As a result, all the fundamental equations of three-dimensional elasticity can be satisfied exactly and all the independent elastic constants can be fully taken into account. Furthermore, the continuity conditions at the interfaces of plies can also be satisfied.

• Structural Engineering and Mechanics
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• 제7권1호
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• pp.19-33
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• 1999

The critical buckling loads of unsymmetrically laminated rectangular plates with a given material system and subjected to combined lateral and inplane loads are maximized with respect to fiber orientations by using a sequential linear programming method together with a simple move-limit strategy. Significant influence of plate aspect ratios, central circular cutouts, lateral loads and end conditions on the optimal fiber orientations and the associated optimal buckling loads of unsymmetrically laminated plates has been shown through this investigation.

• 한국복합재료학회:학술대회논문집
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• 한국복합재료학회 1999년도 추계학술발표대회 논문집
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• pp.223-226
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• 1999

This paper presents the theoretical analysis method to determine the stress concentrations around the circular cutouts with various geometrical parameters. The purposes of this study are to investigate on the stress distribution around the circular cutouts due to interaction between two circular cutouts and to develop the design method in composite plates. The composite laminated plate with 2 equal collinear circular cutouts under inplane loads is treated as an quasi-isotropic, symmetric, finite, square, multiply connected and thin plate. The effects of cutout sizes, distances between two circular cutouts and inplane load conditions on stress distribution are studied in detail.

• Steel and Composite Structures
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• 제17권1호
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• pp.1-19
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• 2014

Buckling and vibration characteristics of circular laminated plates under in-plane edge loads and resting on Winkler-type foundation are solved by the Ritz method. Inclusive numerical data are presented for the first three eigen-frequencies as a function of in-plane load for different classical edge conditions. Moreover, the effects of fiber orientation on the natural frequencies and critical buckling loads of laminated angle-ply plates with stacking sequence of $[({\beta}/-{\beta}/{\beta}/-{\beta})]_s$, are studied. Also, selected deformation mode shapes are illustrated. The correctness of results is established using finite element software as well as by comparison with the existing results in the literature.

• 한국재난정보학회 논문집
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• 제12권1호
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• pp.62-68
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• 2016

본 연구에서는 충격 문제를 거론하며 Mindlin 판 이론을 확장한 1차 전단 변형 이론에 근거하여 충격 하중을 받는 적층판의 응답 특성의 해석을 목적으로 아이소파라메트릭요소에 의한 정식화를 시도한다. 유한요소법을 이용하여 역대칭 Angle-Ply 적층판의 사각판과 원형판의 수치해석을 통해 정적해석과 동적해석의 결과를 도출하여 각 변위에 대한 분석결과를 비교한다.

• Structural Engineering and Mechanics
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• 제56권5호
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• pp.835-854
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• 2015

In this paper, the modified form of shear deformation plate theories is proposed. First, the displacement field geometry of classical and the first order shear deformation theories are compared with each other. Using this comparison shows that there is a kinematic relation among independent variables of the first order shear deformation theory. So, the modified forms of rotation functions in shear deformation theories are proposed. Governing equations for rectangular and circular thick laminated plates, having been analyzed numerically so far, are solved by method of separation of variables. Natural frequencies and mode shapes of the plate are determined. The results of the present method are compared with those of previously published papers with good agreement obtained. Efficiency, simplicity and excellent results of this method are extensible to a wide range of similar problems. Accurate solution for governing equations of thick composite plates has been made possible for the first time.

• Structural Engineering and Mechanics
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• 제77권2호
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• pp.245-259
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• 2021

In this research, the influence of the laminate stacking sequence on thermal stress distribution in symmetric composite plates with a quasi-square cutout subjected to uniform heat flux is examined analytically using the complex variable technique. The analytical solution is obtained based on the thermo-elastic theory and the Lekhnitskii's method. Furthermore, by employing a suitable mapping function, the solution of symmetric laminates containing a circular cutout is extended to the quasi-square cutout. The effect of important parameters including the stacking sequence of laminates, the angular position, the bluntness, the aspect ratio of cutout, the flux angle and the composite material are examined on the thermal stress distribution. It is found out that the circular shape for cutout may not necessarily be the optimum geometry for all stacking sequences. The finite element analysis results are used to validate the analytical solution.