A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates

Mantari, J.L.; Öktem, Ahmet Sinan; Soares, C. Guedes

doi:10.1016/j.ijsolstr.2011.09.008

Cited by 310 publications

(133 citation statements)

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“…(23) In addition, in terms of ( ) w x  and ψ(x) (Aydogdu , 2009;Akavci and Tanrikulu, 2008;El Meiche et al, 2011;Karama et al, 1998Karama et al, , 2003Levinson, 1981;Mantari et al, 2012;Soldatos, 1992;Touratier, 1991), moment M can be expressed in a unified form as Interestingly, we can obtain the following relationship…”

Section: Latinmentioning

confidence: 99%

“…Rohwer (1992) indicated that the kinematics and the rotation play important roles in the HSD model. For the kinematics, besides the third-order shear deformation model (Levinson, 1981;Murthy, 1981), the trigonometric model Civalek, 2014a, 2014b;Karama et al, 1998;Mantari et al, 2012;Touratier, 1991), the hyperbolic sine model (Akgöz and Civalek, 2015;Akavci and Tanrikulu, 2008;El Meiche et al, 2011;Soldatos, 1992) and the exponential model (Aydogdu, 2009;Karama et al, 2003) have been developed. For the rotation, two definitions are usually adopted in the existing work.…”

Section: Introductionmentioning

confidence: 99%

“…As the first one, the rotation variable ψ is defined as the rotation at the neutral surface (e.g. Akgöz and Civalek, 2015;Civalek, 2014a, 2014b;Aydogdu, 2009;Bickford, 1982;El Meiche et al, 2011;Groh, 2015;Karama et al, 2003;Karama et al, 1998;Levison, 1981;Mantari et al, 2012;Qu, et al, 2013;Reddy, 1984aReddy, , 1984bSimsek, 2010;Soldatos, 1992;Touratier, 1991;Viola, et al, 2013) while, as the second one, the rotation variable ϕ is defined as the average rotation over the cross section in some sense (e.g. Cowper, 1966;Murthy, 1981;Reissner, 1975;Shi, 2011Shi, , 2007.…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, HSD models have been widely used in composite structures (Aydogdu, 2009;Karama et al, 2003;Mantari et al, 2012;Viola, et al, 2013) and functionally graded (FG) structures (El Meiche et al, 2011;Simsek, 2010). Much attention was also paid to real world applications by using beam theories.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models

Duan

2016

Lat. Am. j. solids struct.

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The unified solution is studied for a beam of rectangular cross section. With the rotation defined in the average sense over the cross section, the kinematics with higher-order shear deformation models in axial displacement is first expressed in a unified form by using the fundamental higher-order term with some properties. The shear correction factor is then derived and discussed for the four commonly used higher-order shear deformation models including the third-order model, the sine model, the hyperbolic sine model and the exponential model. The unified solution is finally obtained for a beam subjected to an arbitrarily distributed load. The relation with that from the conventional beam theory is established, and therefore the difference is reasonably explained. A very good agreement with the elasticity theory validates the present solution.

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Section: Latinmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models

Duan

2016

Lat. Am. j. solids struct.

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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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An efficient eight‐node quadrilateral element for free vibration analysis of multilayer sandwich plates

Belarbi

Zenkour

Tati

et al. 2021

Numerical Meth Engineering

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This article presents a free vibration analysis of laminated sandwich plates under various boundary conditions by using an efficient C0 eight‐node quadrilateral element. This new element is formulated based on the recently proposed layerwise model. The present model assumes an improved first‐order shear deformation theory for the face sheets while a higher‐order theory is assumed for the core maintaining an interlaminar displacement continuity. The advantage of this model relies on its number of variables is fixed, does not increase when increasing the number of lamina layers. This is a very important feature compared to the conventional layerwise models and facilitates significantly the engineering analysis. Indeed, the developed finite element is free of the shear locking phenomenon without requiring any shear correction factors. The governing equations of motion of the sandwich plate are derived via the classical Hamilton's principle. Several examples covering the various features such as the effect of modular ratio, aspect ratios, core‐to‐face thickness ratio, boundary conditions, skew angle, number of layers, geometry and ply orientations are solved for laminated composites and sandwich plates. The obtained results are compared with 3D, quasi‐3D, 2D analytical solutions, and those predicted by other advanced finite element models. The comparison studies indicate that the developed finite element model is of fast convergence to the reference and valid for both thick and thin laminated sandwich plates. Finally, it can be concluded that the present model is not only simple and accurate than the conventional ones, but also comparable with refined analytical solutions found in the literature.

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A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates

Cited by 310 publications

References 73 publications

The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models

The Unified Solution for a Beam of Rectangular Cross-Section with Different Higher-Order Shear Deformation Models

Free Vibrations Analysis of Composite Laminate Plates Used in Automotive Industry

An efficient eight‐node quadrilateral element for free vibration analysis of multilayer sandwich plates

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