Nonlinear Static Bending and Free Vibration Analysis of Bidirectional Functionally Graded Material Plates

Hong, Nguyen Thi

doi:10.1155/2020/8831366

Cited by 18 publications

(9 citation statements)

References 21 publications

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“…To solve (27), the Newton-Raphson method is conducted [47,48]. For the convenience of explaining the solution, Equation ( 27) is abbreviated as follows:…”

Section: Equation (24) Now Becomesmentioning

confidence: 99%

Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory

Dung¹,

Thai²,

Tran³

et al. 2022

Comptes Rendus. Mécanique

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The nonlinear static bending analysis of microplates resting on imperfect Pasternak elastic foundations is carried out in this paper. The finite element method based on the modified couple stress theory is used to derive the nonlinear finite element formulations. The present theory and mathematical model are validated by comparisons of this work's results with those of other reputable publications, which show a very good agreement. The influences of length-scale parameter, nonlinearity, elastic foundation parameters, imperfect foundations, and boundary conditions on the nonlinear static bending response of microplates are then explored. The computed data of this study is very intriguing, particularly the interaction of the microplate with the imperfect elastic foundation, and this helps us better understand the mechanical behavior of this structure.

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“…To solve (27), the Newton-Raphson method is conducted [47,48]. For the convenience of explaining the solution, Equation ( 27) is abbreviated as follows:…”

Section: Equation (24) Now Becomesmentioning

confidence: 99%

Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory

Dung¹,

Thai²,

Tran³

et al. 2022

Comptes Rendus. Mécanique

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show abstract

“…Further, numerous investigations were performed to analyze the BDFGM plate structures in the framework of three-dimensional elasticity equations, analytical methods, finite element methods, iso-geometric approach, and several shear deformation theories. 7,[33][34][35][36][37][38][39] Many studies on BDFGM plates have been carried out to examine the flexural, 3,5,32,37,[40][41][42][43][44] vibrational, [45][46][47][48][49][50][51][52] and stability 7,40,53,54 behavior of the BDFGM and MDFGM plates. Besides, Lezgy-Nazargah 55 employed the NURBS-dependent isogeometric finite element (FE) approach to examine the thermo-mechanical behavior of BDFGM beams.…”

Section: Introductionmentioning

confidence: 99%

Geometrically nonlinear behavior of two-directional functionally graded porous plates with four different materials

Shivaramaiah

Kattimani

Shariati

et al. 2022

Proceedings of the Institution of Mechanical Engineers, Part C:

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This article investigates the influence of porosity distributions on the nonlinear behavior of two-directional functionally graded porous plates (TDFGPP) made from four distinct materials for the first time. A simple and effectual approach is established based on the improved generalized shear deformation plate theory (GSDPT) and von Karman’s assumptions. The GSDPT incorporates transverse shear strains with a higher order polynomial to avoid shear locking. The TDFGPP constitutes four different materials, and the modified power-law function is employed to vary the material properties continuously in both transverse and longitudinal directions. The governing equations are obtained using a nonlinear finite element approach in conjunction with Hamilton’s principle. Then, the direct iterative and Newmark’s methods are incorporated to accomplish the numerical results. Finally, the influence of volume fraction grading indices, porosity distributions, porosity volume, thickness ratio, and aspect ratio for different support conditions provides a thorough insight into the linear and nonlinear responses of the porous plate. In addition, this study emphasizes the influence of the volume fraction gradation profiles with four different materials on the linear frequency, nonlinear frequency, and deflections of the TDFGPP. The numerical analysis reveals that the frequencies and nonlinear deformations can be significantly regulated by changing the volume fraction gradation profiles in specified directions with appropriate materials. Hence, two-directional functionally graded materials panels can overcome the drawbacks of the functionally graded materials with a gradation of properties in a single direction.

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“…Finally, the principle parametric resonance behaviors of the beam were simulated, and the effects of various parameters, such as material properties/grading indices, magnitude and frequency of external excitation, and damping coefficients, on the dynamic response of the beam were investigated. (Hong, 2020) studied the nonlinear static bending and the nonlinear free vibration behaviors of 2D BDFG material plates using a combination of Finite Element Method (FEM) based on the third shear deformation theory and the Newton-Raphson method. The effects of some parameters, such as volume fraction index and thickness-to-length ratio on the nonlinear static, bending, and the nonlinear free vibration of the plates, were examined.…”

Section: Introductionmentioning

confidence: 99%

“…(Hong, 2020) studied the nonlinear static bending and the nonlinear free vibration behaviors of 2D BDFG material plates using a combination of Finite Element Method (FEM) based on the third shear deformation theory and the Newton–Raphson method. The effects of some parameters, such as volume fraction index and thickness-to-length ratio on the nonlinear static, bending, and the nonlinear free vibration of the plates, were examined.…”

Section: Introductionmentioning

confidence: 99%

Free and forced nonlinear vibrations of Bi-Directional functionally graded Euler–Bernoulli porous beams

Sari

Al‐Dahidi

Hammad

2022

Journal of Vibration and Control

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In this study, the free and forced vibrations of a bi-directional functionally graded porous beam are investigated. The governing equations of motion are derived by Hamilton’s principle, and the reduced temporal equation of motion with cubic and quintic nonlinear terms is obtained using the Galerkin approach. Analytical solutions for the nonlinear natural frequencies in addition to the primary resonance response curves are established by the method of multiple scales. The effects of the axial and transverse functionally graded indexes, initial amplitude, porosity parameter, and the elastic and mass density ratios on the nonlinear frequencies and the forced responses are examined.

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Nonlinear Static Bending and Free Vibration Analysis of Bidirectional Functionally Graded Material Plates

Cited by 18 publications

References 21 publications

Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory

Nonlinear static bending analysis of microplates resting on imperfect two-parameter elastic foundations using modified couple stress theory

Geometrically nonlinear behavior of two-directional functionally graded porous plates with four different materials

Free and forced nonlinear vibrations of Bi-Directional functionally graded Euler–Bernoulli porous beams

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