Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory

Mantari, J.L.; Soares, C. Guedes

doi:10.1016/j.compstruct.2012.01.005

Cited by 110 publications

(56 citation statements)

References 38 publications

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“…It should be noted that the quasi-3D solutions [33][34] are derived based on a trigonometric variation of both in-plane and transverse displacements, while the quasi-3D solutions [28] are computed based on a cubic variation of in-plane displacements and a parabolic variation of transverse displacement across the thickness. In addition, the results of HSDT [35] are also provided to show the importance of including the thickness stretching effect.…”

Section: Results For Bending Analysismentioning

confidence: 99%

“…Since the present quasi-3D theory and other quasi-3D theories include the thickness stretching effect, their solutions are very close to each other. Meanwhile, the HSDT [35], which omits this effect, gives inaccurate prediction and slightly overestimates the deflection especially for very thick plates (i.e., / 2 a h = , see Tables 1 and 3). The errors in the HSDT are reduced with increasing the thickness ratio / a h .…”

Section: Results For Bending Analysismentioning

confidence: 99%

“…In general, the present quasi-3D theory is highly accurate and comparable to 3D solution even in the case of very thick plates, e.g., / 2 a h = . It is worth noting that the developed theory consists of five unknowns, while the number of unknowns in the HSDT [35] and other quasi-3D theories [28,[33][34] is five and six, respectively. Consequently, it may be concluded that the present quasi-3D theory is not only more accurate than the HSDT having the same five unknowns, but also comparable with the quasi-3D theories having more number of unknowns.…”

Section: Results For Bending Analysismentioning

confidence: 99%

“…The HSDT solution [35] is computed based on a trigonometric variation of in-plane displacements and a constant transverse displacement across the thickness (i.e., thickness stretching effect is omitted, 0 z e = ).…”

Section: Results For Bending Analysismentioning

confidence: 99%

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A quasi-3D hyperbolic shear deformation theory for functionally graded plates

Thai

Bui

et al. 2013

Acta Mech

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Section: Results For Bending Analysismentioning

confidence: 99%

Section: Results For Bending Analysismentioning

confidence: 99%

Section: Results For Bending Analysismentioning

confidence: 99%

Section: Results For Bending Analysismentioning

confidence: 99%

See 2 more Smart Citations

A quasi-3D hyperbolic shear deformation theory for functionally graded plates

Thai

Bui

et al. 2013

Acta Mech

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“…Some authors have tried to solve the problem relating to correction factors by introducing shear deformation shape functions [5][6][7][8][9][10][11][12][13][14][15][16]. This paper considers the problem of free vibrations of simply supported laminate plates by applying high-order shear deformation theories (HSDT) based on selected shape functions.…”

Section: Introductionmentioning

confidence: 99%

Free Vibrations Analysis of Composite Laminate Plates Used in Automotive Industry

Radaković¹,

Milosavljević²,

Bogdanović³

et al. 2017

MVM

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ABSTRACT:The paper describes the process of applying mathematical methods for obtaining analytic solutions in dynamic problems of free vibrations of composite laminate materials which are used in automotive industry. For selected high-order deformation theories the paper presents mathematical method for analytic solving of partial differential equations of motion. The procedure of obtaining results by combining symbolic and numerical values of relevant variables was implemented. Through a kind of comparative analysis, the emphasis was put on the use of HSDTs based on shape functions. Comparative values of results obtained using different shape functions are presented in tabular form. The paper considers simply supported thin, moderately thick and thick laminate plates. Moreover, it shows the influence of the laminate class of symmetry on the method of obtaining results. Simply supported laminate plates were primarily considered, specifically symmetric and anti-symmetric cross-ply laminate plates.KEY WORDS: free vibrations, high-order deformation theories, shape functions, composite materials, analytical solutions ANALIZA SLOBODNIH VIBRACIJA KOMPOZITNIH LAMINANTNIH PLOČA KORIŠĆENIH U AUTOMOBILSKOJ INDUSTRIJI REZIME: Rad opisuje proces primene matematičkih metoda za dobijanje analitičkih rešenja u dinamičkim problemima slobodnih vibracija kompozitnih laminantnih materijala koji se koriste u automobilskoj industriji. Za izabrane teorije deformacije visokog reda u radu je predstavljen matematički metod za analitičko rešavanje parcijalnih diferencijalnih jednačina kretanja. Sproveden je postupak dobijanja rezultata kombinovanjem simboličkih i numeričkih vrednosti relevantnih promenljivih. Kroz vrstu komparativnih analiza, naglasak je stavljen na upotrebu HSDT-a baziranih na funkcijama oblika. Komparativne vrednosti rezultata dobijene korišćenjem različitih funkcija oblika prikazane su u tabelarnom obliku. Rad razmatra jednostavno podržane tanke, umereno debele i debele laminantne ploče. Štaviše, pokazuje uticaj laminantne klase simetrije na način dobijanja rezultata. Pre svega se uzimaju u obzir jednostavno podržane laminantne ploče, posebno simetrične i nesimetrične unakrsne laminatne ploče.

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Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

et al. 2023

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In this article, various non‐polynomial higher‐order shear deformation theories are applied for the first time to analyze the free vibration and transient responses of plates with functionally graded material (FGM) supported on an elastic foundation. The shear deformation theories account for the non‐linear variation of the transverse shear strains with various warping functions, namely trigonometric, inverse hyperbolic, and inverse trigonometric ones. These models also inherently satisfy the traction‐free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plates and do not require any shear correction factor. A two‐parameter model, namely Winkler‐Pasternak's elastic foundation model, is utilized to develop the interaction between the FGM plates and the elastic medium. The governing equations of motion are obtained using Hamilton's principle and solved analytically using Navier's solution scheme. Furthermore, the transient responses of the plates are obtained using Newmark's average acceleration method. The applicability of the present theories is established by solving several numerical problems and validating the results with the solutions available in the literature. The effects of various parameters like span‐thickness ratios, aspect ratios, gradation coefficients, mechanical loads, and foundation stiffness on the fundamental frequencies and the transient responses of the plates are thoroughly investigated. The comparison of the results reveals the efficiency of the non‐polynomial functions, and the capability of efficient prediction of the structural responses of the FGM plates at a similar computational cost compared to established models in the literature. Furthermore, the results show that the stiffness of the elastic foundation can tweak the stiffness characteristics of the FGM plate resulting in significant changes in the natural frequencies and more controlled displacement‐time responses.

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Bending analysis of thick exponentially graded plates using a new trigonometric higher order shear deformation theory

Cited by 110 publications

References 38 publications

A quasi-3D hyperbolic shear deformation theory for functionally graded plates

A quasi-3D hyperbolic shear deformation theory for functionally graded plates

Free Vibrations Analysis of Composite Laminate Plates Used in Automotive Industry

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

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