General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels

Viola, Erasmo; Tornabene, Francesco; Fantuzzi, Nicholas

doi:10.1016/j.compstruct.2012.08.005

Cited by 211 publications

(81 citation statements)

References 74 publications

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“…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%

“…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%

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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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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“…These analysis shows that higher order displacement fields gives more accurate results respect to the lower ones but higher ones are computationally expensive. Additionally, Tornabene et al (Tornabene, 2009(Tornabene, , 2011aTornabene et al, 2014;Tornabene et al, 2012;Tornabene et al, 2013;Viola et al, 2013) have developed generalized differential quadrature (GDQ) to analyzed various FG structures. Furthermore, Zhang and Liew with their coworkers have applied mesh-less methods to analyze different FG shells Liew et al, 2014;Liew et al, 2011;Zhang et al, 2014a, b;Zhang et al, 2014c;Zhu et al, 2014).…”

Section: Introductionmentioning

confidence: 99%

Closed-form Solution for Freely Vibrating Functionally Graded Thick Doubly Curved Panel-A New Generic Approach

Fadaee

Ilkhani

2015

Lat. Am. j. solids struct.

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Today, double curvature shell panels are the main parts of each design because their geometrical characteristics provide high strength to weight ratio, aerodynamic form and beauty for the structures such as boats, submarines, automobiles and buildings. Also, functionally graded materials which present multiple properties such as high mechanical and heat resistant, simultaneously, have attracted designers. So, as the first step of any dynamic analysis, this paper concentrates on presenting a high precision and reliable method for free vibration analysis of functionally graded doubly curved shell panels. To this end, panel is modeled based on third order shear deformation theory and both of the Donnell and Sanders strain-displacement relations. A new set of potential functions and auxiliary variables are proposed to present an exact Levy-type close-form solution for vibrating FG panel. The validity and accuracy of present method are confirmed by comparing results with literature and finite element method. Also, effect of various parameters on natural frequencies are studied which are helpful for designers.

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“…Tornabene and his team [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] extended the generalized differential quadrature (GDQ) method for the free vibration analysis of functionally graded circular and parabolic panels and shells of revolution with classical boundary conditions. Other related research results with the layered composite parabolic and circular panels can be seen in Refs [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46]. From the above literature review, it's easy to see that the computational accuracy and the range of application of boundary conditions strongly lie on the shell theories and solution methods for the most of studies on the titled problem.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of functionally graded parabolic and circular panels with general boundary conditions

Zhang

Shi

Wang

et al. 2017

Curved and Layered Structures

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Abstract:The purpose of this content is to investigate the free vibration of functionally graded parabolic and circular panels with general boundary conditions by using the Fourier-Ritz method. The first-order shear deformation theory is adopted to consider the effects of the transverse shear and rotary inertia of the panel structures. The functionally graded panel structures consist of ceramic and metal which are assumed to vary continuously through the thickness according to the power-law distribution, and two types of power-law distributions are considered for the ceramic volume fraction. The improved Fourier series method is applied to construct the new admissible function of the panels to surmount the weakness of the relevant discontinuities with the original displacement and its derivatives at the boundaries while using the traditional Fourier series method. The boundary spring technique is adopted to simulate the general boundary condition. The unknown coefficients appearing in the admissible function are determined by using the Ritz procedure based on the energy functional of the panels. The numerical results show the present method has good convergence, reliability and accuracy. Some new results for functionally graded parabolic and circular panels with different material distributions and boundary conditions are provided, which may serve as benchmark solutions.

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General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels

Cited by 211 publications

References 74 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

Closed-form Solution for Freely Vibrating Functionally Graded Thick Doubly Curved Panel-A New Generic Approach

Free vibration of functionally graded parabolic and circular panels with general boundary conditions

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