NURBS-based finite element analysis of functionally graded plates: Static bending, vibration, buckling and flutter

By Navid Valizadeh, Sundararajan Natarajan, Octavio Andrés González-Estrada, Timon Rabczuk, Tinh Quoc Bui, Stéphane P.A. Bordas. 2012

345 citations recorded by the source corpus.

In this paper, a non-uniform rational B-spline based iso-geometric finite element method is used to study the static and dynamic characteristics of functionally graded material (FGM) plates. The material properties are assumed to be graded only in the thickness direction and the effective properties are computed either using the rule of mixtures or by Mori–Tanaka homogenization scheme. The plate kinematics is based on the first order shear deformation plate theory (FSDT). The shear correction factors are evaluated employing the energy equivalence principle and a simple modification to the shear correction factor is presented to alleviate shear locking. Static bending, mechanical and thermal buckling, linear free flexural vibration and supersonic flutter analysis of FGM plates are numerically studied. The accuracy of the present formulation is validated against available three-dimensional solutions. A detailed numerical study is carried out to examine the influence of the gradient index, the plate aspect ratio and the plate thickness on the global response of functionally graded material plates.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/708a5ce69d6d9c805912430a846e51a372bb5ac1

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Static and frequency optimization of folded laminated composite plates using an adjusted Differential Evolution algorithm and a smoothed triangular plate element (2015, methodology): “It is worth noting that apart from conventional Finite Element Method, there are also various methods for calculating behavior of laminated composite plates such as Non-Uniform Rational Bsplines (NURBS) [44,45], alternative alpha finite element method [46], NURBS-based finite element method [47], et”
A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation (2016, methodology): “According to Mori–Tanaka homogenization scheme, the effective Bulk Modulus (K) and the effective shear modulus (G) are given by (Belabed et al. 2014, Valizadeh et al. 2013, Cheng and Batra 2000, Qian et al. 2004) mm mc c c mc m GK KKV V KK KK 43 311 (1a) 1 11 fG GGV V GG GG m mc…”
Thermal analysis of FGM plates – A critical review of various modeling techniques and solution methods (2017, methodology): “FEM formulations were developed using NURBS based Isogeometric Analysis (IGA) and were discretized using C1 continuity of displacement field.”
Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory (2014, methodology): “It is clear that the difference between results of using FSDT model and HSDT model is very 23 M AN US CR IP T AC CE PT ED Table 8: A non-dimensional frequency parameter ϖ = ( ωa2/h ) (ρ/E2)1/2 of a [00/900/900/00] simply supported laminated square plate (a/h=5) Method E1/E2 10 20 30 40 RBFs-FSDT[59]”
On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model (2015, methodology): “According to Mori–Tanaka homogenization scheme, the effective Bulk Modulus (K) and the effective shear modulus (G) are given by (Belabed et al. 2014, Valizadeh et al. 2013, Cheng and Batra 2000, Qian et al. 2004) mm mC C C mC m GK KKV V KK KK 43 311 (1a) 1 )(11 fG GGV V GG GG m mC…”