Static analysis of superelliptical clamped plates by Galerkin's method

Çeribaşı, Seyit; Altay, Gülay; Dökmeci, M. Cengiz

doi:10.1016/j.tws.2007.08.015

Cited by 12 publications

(6 citation statements)

References 9 publications

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“…Developed program was validated with the analytical results for free vibration of circular and annular FGM plates in Hashemi et al article [22].…”

Section: Equation Of Motionmentioning

confidence: 99%

“…Since commercial FEM codes do not allow directly inputting FGM properties, a FEM computer code was developed to implement finite element method and solve frequency equation. Developed program was validated with the analytical results for free vibration of circular and annular FGM plates in Hashemi et al article [22].…”

Section: Virtual Work Of Inertial Forces Is Expressed Asmentioning

confidence: 99%

“…Zhang D-G. [21] investigated non-linear bending analysis for super elliptical thin plates with Ritz method. Ceribasi et al [22] investigated static behavior of clamped superelliptical plates with Galerkin's method. Nie et al [23] investigated free and forced vibration of functionally graded annular sectorial plates using a semi-analytical approach.…”

Section: Introductionmentioning

confidence: 99%

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Shape Effect on Free Vibration of Functionally Graded Plates

Kurtaran

2014

International Journal of Engineering &Amp; Applied Sciences

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“…Developed program was validated with the analytical results for free vibration of circular and annular FGM plates in Hashemi et al article [22].…”

Section: Equation Of Motionmentioning

confidence: 99%

Section: Virtual Work Of Inertial Forces Is Expressed Asmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Shape Effect on Free Vibration of Functionally Graded Plates

Kurtaran

2014

International Journal of Engineering &Amp; Applied Sciences

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“…and Altay [7] conducted static analysis of point-supported super-elliptical plates of uniform thickness subjected to uniformly distributed load, and authors noted: "Studies on rectangular plates with rounded corners are rather scarce, although they are used extensively in industrial applications as structural and machine elements". Static analysis of super-elliptical clamped plates was dealt with by Çeribaşı et al [8], by the Bubnov-Galerkin method. Zhang [9] analyzed nonlinear bending of super-elliptical thin plates.…”

Section: Introductionmentioning

confidence: 99%

Generalization of the super ellipsoid concept and its application in mechanics

Elishakoff

Jiang

et al. 2016

Applied Mathematical Modelling

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In this paper, we generalize the concept of super ellipsoid that was proposed by the French mathematician and mechanician Gabriel Lamé in 1818. Super ellipsoid itself represents a generalization of the ellipsoid, namely when the power n appearing in super ellipsoid equals 2, the conventional ellipsoid is obtained. In this paper the notion of super ellipsoid is further extended by introducing as many generally different powers, as is dictated by the dimensionality and the physics of the problem. Specifically, two different power parameters are introduced for the generalized super ellipse. Likewise, three generally different powers are adopted for the three-dimensional super ellipsoid etc. An applied mechanics problem is considered to demonstrate the efficiency of the notion of generalized super ellipsoids, namely we study the static behavior of an engine's crankshaft. Two to five geometric parameters specifying the crankshaft are treated as belonging to a generalized super ellipsoid set.

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“…However, the numerous studies have been mainly focused on rectangular, circular, and elliptical plates, which are special cases of the super-elliptical plates. Considering the lack of contribution in the static behavior of this kind of plate shape, Çeribaşı et al [15] used Galerkin's method to analyze the static behavior of super-elliptical clamped plates, and the detailed results were arranged in tabular form. That study was carried out for a wide range of super-elliptical plates, and the presented results were very useful for practical applications of these sorts of plates.…”

Section: Introductionmentioning

confidence: 99%

Application of new double side approach method to the solution of super-elliptical plate problems

2011

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The new double side approach method combining the mathematical programming and the subdomain method in the method of weighted residual is presented in this article. Under the validation of maximum principle, and up on the subdomain method, the differential equation can be transferred into a bilateral inequality problem. Applying the genetic algorithms helps to find optimal solutions of upper and lower bounds which satisfy the inequalities. Here, the method is first verified by analyzing the deflection of elliptical clamped plate problem under various aspect ratios and further apply it to analyze the clamped super-elliptical plates problem. By using this method, the good approximate solution can be obtained accurately.

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Static analysis of superelliptical clamped plates by Galerkin's method

Cited by 12 publications

References 9 publications

Shape Effect on Free Vibration of Functionally Graded Plates

Shape Effect on Free Vibration of Functionally Graded Plates

Generalization of the super ellipsoid concept and its application in mechanics

Application of new double side approach method to the solution of super-elliptical plate problems

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