A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates

Neves, A. M. A.; Ferreira, A.J.M.; Carrera, Erasmo; Cinefra, Maria; Roque, C.M.C.; Jorge, R.M. Natal; Soares, Carlos A. Mota

doi:10.1016/j.compstruct.2011.12.005

Cited by 242 publications

(90 citation statements)

References 28 publications

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“…In this example, the conditions are the same as the previous example except for the length-thickness ratio a/h. Table 4 shows the normalized central deflections obtained with the S-FSDT-based IGA, the FSDT-based IGA, and the analytical solutions [8,31,32]. The results from the present method are in good agreement with the analytical solutions [8,31,32] for both thin and thick plates, thus confirming the accuracy of the proposed approach.…”

Section: Numerical Applicationssupporting

confidence: 72%

Isogeometric locking-free plate element: A simple first order shear deformation theory for functionally graded plates

Yin

Hale

et al. 2014

Composite Structures

192

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An effective, simple, and locking-free plate formulation is proposed to analyze the static bending, buckling, and free vibration of homogeneous and functionally graded plates. The simple first-order shear deformation theory (S-FSDT), which was recently presented in Composite Structures (2013; 101:332-340), is naturally free from shear-locking and captures the physics of the shear-deformation effect present in the original FSDT, whilst also being less computationally expensive due to having fewer unknowns. The S-FSDT requires C 1 -continuity that is simple to satisfy with the inherent high-order continuity of the non-uniform rational B-spline (NURBS) basis functions, which we use in the framework of isogeometric analysis (IGA).Numerical examples are solved and the results are compared with reference solutions to confirm the accuracy of the proposed method. Furthermore, the effects of boundary conditions, gradient index, and geometric shape on the mechanical response of functionally graded plates are investigated.

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Section: Numerical Applicationssupporting

confidence: 72%

Isogeometric locking-free plate element: A simple first order shear deformation theory for functionally graded plates

Yin

Hale

et al. 2014

Composite Structures

192

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“…Typically, FG shell structures were presented using: (i) Kirchhoff-Love theory, Chi and Chung (2006), where the shear strains are assumed zero, which is not acceptable for FG shell; (ii) the First-order Shear Deformation Theory (FSDT) (Praveen and Reddy 1998;Thai and Kim 2015), which gives a correct overall assessment. Notice that the shear correction factors should be incorporated to adjust the transverse shear stiffness; (iii) the High-order Shear Deformation Theory (HSDT) (Neves et al 2012;Wali et al 2014Wali et al , 2015Frikha et al 2016) in which the equations of motion are more complicated to obtain than those of the FSDT; among other theories. …”

mentioning

confidence: 99%

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

Mars

Koubaa

Wali

et al. 2017

Lat. Am. j. solids struct.

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In this paper, a geometrically nonlinear analysis of functionally graded material (FGM) shells is investigated using Abaqus software. A user defined subroutine (UMAT) is developed and implemented in Abaqus/Standard to study the FG shells in large displacements and rotations. The material properties are introduced according to the integration points in Abaqus via the UMAT subroutine. The predictions of static response of several non-trivial structure problems are compared to some reference solutions in order to verify the accuracy and the effectiveness of the new developed nonlinear solution procedures. All the results indicate very good performance in comparison with references. Lee et al. 2009). Typically, FG shell structures were presented using: (i) Kirchhoff-Love theory, Chi and Chung (2006), where the shear strains are assumed zero, which is not acceptable for FG shell; (ii) the First-order Shear Deformation Theory (FSDT) (Praveen and Reddy 1998;Thai and Kim 2015), which gives a correct overall assessment. Notice that the shear correction factors should be incorporated to adjust the transverse shear stiffness; (iii) the High-order Shear Deformation Theory (HSDT) (Neves et al. 2012;Wali et al. 2014Wali et al. , 2015Frikha et al. 2016) in which the equations of motion are more complicated to obtain than those of the FSDT; among other theories. KeywordsIt is certainly plausible that linear finite element (FE) models cannot be able to accurately predict the structural response presenting large elastic deformations and finite rotations. Indeed, according to Yu et al. (2015), several practical problems of FG structures require a geometrically non-linear formulation, such as the post-buckling behavior of structures used in aeronautical, aerospace as well as in mechanical and civil engineering. In such cases, it becomes crucial to develop efficient and accurate nonlinear FE models.It is well known that analytical solutions of shell problems are very limited. Hence, most of reference solutions are previously reported numerical solutions. Particularly, for FE geometric nonlinear analysis of FG shells, several research papers are surveyed (Praveen and Reddy 1998;Reddy 2000;Kattimani and Ray 2015;Duc et al. 2017; Reddy 2007a, 2007b;Alinia and Ghannadpour 2009;Phung-Van et al. 2014;Kim et al. 2008;Hajlaoui et al. 2017;Frikha and Dammak 2017;Asemi et al. 2014 andAnsari et al. 2016). In these references, a number of theoretical formulation and finite element models based on von Karman, Kirchhoff-Love, FSDT and HSDT theories were proposed to study the geometrically non-linear behavior of FGMs Structures.Hosseini Kordkheili and Naghdabadi (2007) derived a FE formulation for the geometrically nonlinear thermoelastic analysis of FGM plates and shells using the updated Lagrangian approach. Later, Zhao and Liew (2009) conducted a geometrically non-linear analysis of FGM shells under mechanical and thermal loading using the element-free kp-Ritz method. The formulation was based on the modified version of Sander's non-li...

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“…In fact, the use of hyperbolic functions was first proposed by Soldatos [29], later used by Xiang et al [30], Akavci [31], and El Meiche et al [32], and recently by Neves et al [27]. According to Refs.…”

Section: Theoretical Formulationmentioning

confidence: 99%

“…Instead of using polynomial functions, Ferreira et al [25] employed the sinusoidal functions for all displacement components. Neves et al [26][27] employed the polynomial and the non-polynomial (sinusoidal [26] and hyperbolic [27]) functions for transverse and in-plane displacements, respectively. It should be noted that the abovementioned quasi-3D theories are too cumbersome and computationally expensive since they handle many unknowns (e.g., theories by Ref.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Thai

Bui

et al. 2013

Acta Mech

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A quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates

Cited by 242 publications

References 28 publications

Isogeometric locking-free plate element: A simple first order shear deformation theory for functionally graded plates

Isogeometric locking-free plate element: A simple first order shear deformation theory for functionally graded plates

Numerical Analysis of Geometrically Non-Linear Behavior of Functionally Graded Shells

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

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