• Journal of Mechanical Science and Technology
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• 제17권10호
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• pp.1458-1465
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• 2003

An eigenvalue analysis of the circular Mindlin plates with free boundary conditions is presented. The analysis is based on the Chebyshev-Fourier pseudospectral method. Even though the eigenvalues of lower vibration modes tend to convergence more slowly than those of higher vibration modes, the eigenvalues converge for sufficiently fine pseudospectral grid resolutions. The eigenvalues of the axisymmetric modes are computed separately. Numerical results are provided for different grid resolutions and for different thickness-to-radius ratios.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 1992년도 가을 학술발표회 논문집
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• pp.39-44
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• 1992

This paper is concerned with formulations of the hierarchical $C^{o}$-plate element on the basis of Reissner-Mindlin plate theory. On reason for the development of the aforementioned element is that it is still difficult to construct elements based on h-version concepts which are accurate and stable against the shear locking effects. An adaptive mesh refinement and selective p-distribution of the polynomial degree using hp-version of the finite element method we proposed to verify the superior convergence and algorithmic efficiency with the help of the clamped L-shaped plate problems.s.

• Structural Engineering and Mechanics
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• 제11권1호
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• pp.89-104
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• 2001

This paper reviews the author's work on the development of relationships between solutions of the Kirchhoff (classical thin) plate theory and the Mindlin (first order shear deformation) thick plate theory. The relationships for deflections, stress-resultants, buckling loads and natural frequencies enable one to obtain the Mindlin plate solutions from the well-known Kirchhoff plate solutions for the same problem without much tedious mathematics. Sample thick plate solutions, deduced from the relationships, are presented as benchmark solutions for researchers to use in checking their numerical thick plate solutions.

• Structural Engineering and Mechanics
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• 제3권1호
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• pp.35-48
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• 1995

This paper presents new frequency results for elliptical and semi-elliptical Mindlin plates of various aspect ratios, thicknesses and boundary conditions. The results were obtained using the recently developed computerized Rayleigh-Ritz method for thick plate analysis. For simply supported elliptical plates, it is proposed that the penalty function method be used to enforce the condition of zero rotation of the midplane normal in the tangent plane to the plate boundary.

• Structural Engineering and Mechanics
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• 제19권2호
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• pp.199-215
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• 2005

An assumed stress quadrilateral thin/moderately thick plate element HQP4 based on the Mindlin/Reissner plate theory is proposed. The formulation is based on Hellinger-Reissner variational principle. Static and free vibration analyses of plates are carried out. Numerical examples are presented to show that the validity and efficiency of the present element for static and free vibration analysis of plates. Satisfactory accuracy for thin and moderately thick plates is obtained and it is free from shear locking for thin plate analysis.

• Structural Engineering and Mechanics
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• 제48권1호
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• pp.77-91
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• 2013

The paper presents the formulation of 3-nodal line semi-analytical Mindlin-Reissner finite strip in the buckling analysis of thin-walled members, which are subjected to arbitrary loads. The finite strip is simply supported in two opposite edges. The general loading and in-plane rotation techniques are used to develop this finite strip. The linear stiffness matrix and the geometric stiffness matrix of the finite strip are given in explicit forms. To validate the proposed model and study its performance, numerical examples of some thin-walled sections have been performed and the results obtained have been compared with finite element models and the published ones.

• Structural Engineering and Mechanics
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• 제49권5호
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• pp.661-672
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• 2014

Laminated Rectangular plates embedded in elastic foundations are used in many mechanical structures. This study presents an analytical approach for transverse bending analysis of an embedded symmetric laminated rectangular plate using Mindlin plate theory. The surrounding elastic medium is simulated using Pasternak foundation. Adopting the Mindlin plate theory, the governing equations are derived based on strain-displacement relation, energy method and Hamilton's principle. The exact analysis is performed for this case when all four ends are simply supported. The effects of the plate length, elastic medium and applied force on the plate transverse bending are shown. Results indicate that the maximum deflection of the laminated plate decreases when considering an elastic medium. In addition, the deflection of the laminated plate increases with increasing the plate width and length.

• Steel and Composite Structures
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• 제27권1호
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• pp.27-33
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• 2018

In this study, a mixed-interpolated tensorial component 4 nodes method (MITC4) is treated as a numerical analysis model for topology optimization using multiple materials assigned within Reissner-Mindlin plates. Multi-material optimal topology and shape are produced as alternative plate retrofit designs to provide reasonable material assignments based on stress distributions. Element density distribution contours of mixing multiple material densities are linked to Solid Isotropic Material with Penalization (SIMP) as a design model. Mathematical formulation of multi-material topology optimization problem solving minimum compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples illustrate the reliability and accuracy of the present design method for multi-material topology optimization with Reissner-Mindlin plates using MITC4 elements and steel materials.

• Steel and Composite Structures
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• 제9권1호
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• pp.59-75
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• 2009

In this study, a simple approach for bending analysis of Reissner-Mindlin plates is presented using the four-node quadrilateral domain transformation based on discrete singular convolution. In the proposed approach, irregular physical domain is transformed into a rectangular domain by using the geometric coordinate transformation. The DSC procedures are then applied to discrete the governing equations and boundary conditions. The accuracy of the proposed method is verified by comparison with known solutions obtained by other numerical or analytical methods. Results for Reissner-Mindlin plates show a satisfactory agreement with the analytical and numerical solutions.

• 전산구조공학
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• 제1권2호
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• pp.83-90
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• 1988

본 연구에서는 평판 구조물의 해석을 위한 개선된 유한요소를 제시하였다. 이 요소는 Mindlin 평판이론에 의하여 수식화되었으며, 'Heterosis'평판요소의 변위장에 비적합변위형을 추가함으로써 유도되었다. 본 연구에서 제시한 평판요소는 요소의 강체운동과 관련된 Zero Eigenvalue만을 갖고 있으므로 Spurious Zero Energy Mode를 보이지 않는다. 대표적인 문제에 대한 수치해석을 해 본 결과 본 연구에서 제시한 평판요소는 우수한 수렴도를 보여 주었으며, 아주 얇은 평판문제에서도 요소의 형상에 관계없이 Shear Locking현상을 극복하였다.