• 대한기계학회논문집A
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• 제26권6호
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• pp.1169-1177
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• 2002

A study of fee vibration of circular Mindlin plates is presented. The analysis is based on the pseudospctral method, which uses Chebyshev polynomials and Fourier series as basis functions. It Is demonstrated that rapid convergence and accuracy as well as the conceptual simplicity could be achieved when the pseudospectral method was apt)lied to the solution of eigenvalue problems. Numerical examples of circular Mindlin plates with clamped and simply supported boundary conditions are provided for various thickness-to-radius ratios.

• 대한조선학회지
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• 제18권2호
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• pp.1-6
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• 1981

The buckling of stiffened plates is considered using a finite element method. In this paper stiffened plates are treated as orthotropic plates and by appling Mindlin's plate theory the effects of shear deformation to buckling loads are considered. In general, it is found that for moderately thick plates Mindlin's plate theory gives lower buckling load than those obtained using classical thin plate theory.

• 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.

• 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.

• Smart Structures and Systems
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• 제22권3호
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• pp.249-257
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• 2018

This study contributes to evaluate multiphase topology optimization design of plate-like elastic structures with constant thickness and Reissner-Mindlin plate theory. Stiffness and adjoint sensitivity formulations linked to Reissner-Mindlin plate potential energy of bending and shear are derived in terms of multiphase design variables. Multiphase optimization problem is solved through alternative active-phase algorithm with Gauss-Seidel version as an optimization model of optimality criteria. Numerical examples verify efficiency and diversity of the present topology optimization method of Reissner-Mindlin elastic plates depending on multiphase and Poisson's ratio.

• 한국전산구조공학회:학술대회논문집
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• 한국전산구조공학회 2004년도 봄 학술발표회 논문집
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• pp.25-32
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• 2004

In this proposed work new finite element model for multi-delaminated plates is proposed. In the current analysis procedures of multi-delaminated plates, plate element based on Mindlin plate theory is used in order to obtain accurate results of out-of-plane displacement of thick plate. And for delaminated region, plate element based on Kirchhoff plate theory is considered. To satisfy the displacement continuity conditions, displacement vector based on Kirchhoff theory is transformed to displacement of transition element. The numerical results show that the effect of delaminations on the modal parameters of delaminated composites plates is dependent not only on the size, the location and the number of the delaminations but also on the mode number and boundary conditions. Kirchhoff based model have higher natural frequency than Mindlin based model and natural frequency of the presented model is closed to Mindlin based model.

• 전산구조공학
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• 제5권2호
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• pp.105-118
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• 1992

Static performance was compared for the triangular plate elements through some numerical experiments. Four Kirchhoff elements and six Mindlin elements were selected for the comparison. Numerical tests were executed for the problems of rectangular plates with regular and distorted meshes, rhombic plates, circular plates and cantilever plates. Among the Kirchhoff 9 DOF elements, the discrete Kirchhoff theory element was the best. Element distortion and the aspect ratio were shown to have negligible effects on the displacement behaviour. The Specht's element resulted in better results than the Bergan's but it was sensitive to the aspect ratio. The element based on the hybrid stress method also resulted in good results but it assumed to be less reliable. Among the linear Mindlin elements, the discrete shear triangle was the best in view of reliability, accuracy and convergence. Since the thin plate behaviour of it was as good as the DKT element, it can be used effectively in the finite element code regardless of the thickness. As a quadratic Mindlin element, the MITC7 element resulted in best results in almost all cases considered. The results were at least as good as those of doubly refined meshes of linear elements.

• 한국구조물진단유지관리공학회 논문집
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• 제2권4호
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• pp.209-216
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• 1998

본 논문에서는 부채꼴형 Mindlin 평판의 엄밀한 휨진동해를 제시하였다. 진동변위의 두 가지 적합 함수식, 즉 대수삼각다항식과 Mindlin 모서리함수를 Ritz방법에 적용하였다. 모서리함수는 부채꼴형 평판의 둔각 정점부에 존재하는 모멘트와 전단력의 특이도를 동시에 고려하고 있다. 이러한 모서리함수는 진동수의 수렴속도를 가속화한다. 본 연구에서는 부채꼴형 각도의 범위와 두께 비에 따른 엄밀한 진동수 및 수직진동 변위의 전형적인 등고선을 제시하였다.

• 한국산학기술학회논문지
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• 제4권2호
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• pp.76-80
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• 2003

본 연구에서는 직교이방성 박판 및 후판의 휨문제에 대한 해석결과를 제시하였다. 수치해석방법으로는 유한요소법을 사용하였으며, 직교이방성판 휨문제에 대한 지배방정식은 Kirchhoff가정에 의한 박판이론과 Mindlin 가정에 의한 후판이론을 이용하여 유도하였으며 판의 폭-두께비의 변화에 따른 해석결과를 비교 검토하였다.