Bending of orthotropic super-elliptical plates on intermediate point supports

Altekin, Murat

doi:10.1016/j.oceaneng.2010.03.015

Cited by 12 publications

(7 citation statements)

References 43 publications

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“…(2009) analyzed transverse vibration of a clamped elliptical plate carrying a concentrated mass at an arbitrary position using the Ritz method. Bending of orthotropic super-elliptical plates on intermediate point supports has been studied by Altekin (2010) using the Ritz method.…”

Section: Platesmentioning

confidence: 99%

The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review

Kumar¹

2017

Journal of Vibration and Control

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The Rayleigh–Ritz method is a classical method that has been widely used to investigate dynamic, static and buckling behavior, i.e., the natural frequencies, mode shapes, moments, stresses, critical buckling loads of vibrating structures and to solve boundary value problems. Different developments in the method have taken place from time to time. This paper presents a comprehensive literature review on the application of the Rayleigh–Ritz method to analyze vibration, static and buckling characteristics of beams, shells and plates using different theories.

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Section: Platesmentioning

confidence: 99%

The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review

Kumar¹

2017

Journal of Vibration and Control

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“…which is then substituted into the remaining equilibrium equation (6), leading to a single governing equation for the introduced function F…”

Section: Formulation Of the Problemmentioning

confidence: 99%

“…4,5 For orthotropic super-elliptical plates, Altekin utilized the Ritz method to analyze optimization of the support location. 6 The optimum radius of an internal elastic ring support for maximum buckling load was also determined for elastic buckling of circular plates with internal elastic ring support and elastically restrained edge against rotation and translation. 7 For composite columns, parameter optimization against buckling was made using the integral equation method.…”

Section: Introductionmentioning

confidence: 99%

Optimal location of ring support for heavy Mindlin plates under axisymmetric loading

Xie

2017

Proceedings of the Institution of Mechanical Engineers, Part C:

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Bending of an annular thick plate resting on a ring support is analyzed under the action of power-law axisymmetric loading. A single governing differential equation for the Mindlin plate theory is derived. By solving associated boundary value problem, the optimal support location is determined to achieve minimizing the maximum deflection of a moderately thick circular or annular plate. The minimum sag of a heavy solid circular plate with or without the center support under self-weight is also analyzed. In addition to applied loading and the restraint of plate's rims, the optimal location of the ring support is also related to Poisson's ratio and the ratio of inner-to-outer radius. Auxetic plates with negative Poisson's ratio require larger ring support's radius, and conventional plates require smaller ring support's radius. Usually, the optimal support location is closer to the outer rim and far to the inner rim for a plate of self-weight. The obtained results are useful in safety design of circular or annular plates under complicated loading.

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“…Super elliptical plates which are defined by shapes between an ellipse and a rectangle have a wide range of use in engineering applications. Some studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] for linear behaviors of super elliptical plates are available in the literature. Wang et al [1] presented accurate frequency and buckling factors for super elliptical plates with either simply supported or clamped edges by using Rayleigh-Ritz method.…”

Section: Introductionmentioning

confidence: 99%

“…Zhou et al [5] analysed three-dimensional free vibration of super elliptical plates based on linear elasticity theory using Chebyshev-Ritz method. Altekin [6] gave out free linear vibration and buckling of super-elliptical plates resting on symmetrically distributed point-supports, Altekin and Altay [7] calculated static analysis of point-supported super-elliptical plates, then Altekin [8,9] discussed free vibration and bending of orthotropic super elliptical plates on intermediate supports. Çeribaşı et al [10] gave out static linear analysis of super elliptical clamped plates based on the classical plate theory by Galerkin's method, Çeribaşı and Altay [11] investigated free vibration of super elliptical plates with constant and variable thickness by Ritz method, then Çeribaşı [12] investigated static and dynamic linear analyses of thin uniformly loaded super elliptical clamped functionally graded plates.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Bending and Thermal Post-buckling Analysis of FGM Super Elliptical Thin Plates

Zhang¹

2017

Res. Rev. J Mat. Sci

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Bending of orthotropic super-elliptical plates on intermediate point supports

Cited by 12 publications

References 43 publications

The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review

The Rayleigh–Ritz method for linear dynamic, static and buckling behavior of beams, shells and plates: A literature review

Optimal location of ring support for heavy Mindlin plates under axisymmetric loading

Nonlinear Bending and Thermal Post-buckling Analysis of FGM Super Elliptical Thin Plates

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