Static and free vibration analyses of functionally graded plates based on an isogeometric scaled boundary finite element method

Zang, Quansheng; Liu, Jun; Fraser, Michael; Fan, Yue; Hao, Congkuan; Lin, Gao

doi:10.1016/j.compstruct.2022.115398

Cited by 10 publications

(4 citation statements)

References 79 publications

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“…The dimensionless natural frequency results for the square plates with a complicated cutout under simply supported or clamped boundary conditions are listed in Tables 4 and 5. These results are compared with the converged IGA results based on the 3D elasticity theory (3D-IGA) [66] and the semianalytical results obtained using the IGA and scaled boundary element method based on the 3D elasticity theory (3D-IGSBFEM) [67]. The results from the SDF-based IGA show good agreement with the reference solutions for different gradient indices.…”

Section: Spectral Displacement Formulamentioning

confidence: 76%

Isogeometric Analysis for Free Vibration of Functionally Graded Plates Using a New Quasi-3D Spectral Displacement Formulation

2023

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This paper presents a novel quasi-three-dimensional shear deformation theory called the spectral displacement formulation (SDF) for analyzing the free vibration of functionally graded plates. The SDF expresses the unknown displacement field as a unique form of the Chebyshev series in the thickness direction. By increasing the truncation number in the Chebyshev series, the bending analysis results can approach the three-dimensional elasticity solution and satisfy the traction-free boundary conditions without requiring a shear correction factor. The SDF is an extension of the classical plate theory, thereby naturally avoiding the shear-locking phenomenon. These characteristics enable the SDF to apply to plates of arbitrary thickness while maintaining accuracy. The nonuniform rational B-spline-based isogeometric approach is employed to enhance the applicability of this theory to free vibration analysis of functionally graded plates with complex geometries and different boundary conditions. Numerical examples are presented to demonstrate the accuracy and reliability of the proposed method in analyzing the free vibration of functionally graded plates.

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Section: Spectral Displacement Formulamentioning

confidence: 76%

Isogeometric Analysis for Free Vibration of Functionally Graded Plates Using a New Quasi-3D Spectral Displacement Formulation

2023

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“…The effects of the key parameters of an in-plane bidirectional FGP rectangular plate on its nonlinear frequency were investigated based on the Hamilton principle and von Karman nonlinearity strain-displacement relations by Hashemi et al [17]. A novel semianalytical plate formulation was proposed by Zang et al [18] to investigate the effects of the gradient index and aspect ratios on the static and free vibration responses of FGP plates. The effects of the key parameters on the bending and free vibration of the functionally graded plates were investigated by Hadji and Alazwari et al [19,20], which revealed the potential effects of geometric parameters and material properties on the vibration characteristics and mechanical properties of the plates.…”

Section: Introductionmentioning

confidence: 99%

Parametric Analysis of Free Vibration of Functionally Graded Porous Sandwich Rectangular Plates Resting on Elastic Foundation

Qin,

Mei,

Wang

2024

Materials

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Based on the three-dimensional elasticity theory, the free vibration of functionally graded porous (FGP) sandwich rectangular plates is studied, and a unified solution for free vibration of the plates is proposed in this study. The arbitrary boundary conditions of FGP sandwich rectangular plates are simulated by using the Rayleigh–Ritz method combined with artificial spring theory. The calculation performances of the unified solution for FGP sandwich rectangular plates such as convergence speed and computational efficiency are compared extensively under different displacement functions. In addition, three kinds of elastic foundation (Winkler/Pasternak/Kerr foundations) and three porosity distributions are considered. Some benchmark results and accurate values for the free vibration of FGP sandwich rectangular plates resting on elastic foundations are given. Finally, the effects of diverse structural parameters, elastic foundations with different parameters, and boundary conditions on the free vibration of the FGP sandwich rectangular plates are analyzed.

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“…They claimed that the proposed technique was superior to other traditional methods in terms of both simplicity and accuracy. Zang et al (2022) employed Isogeometric Scaled Boundary Finite Element Method (IGSBFEM) for free vibration and static analyses of FGM plates. They also measured the impact of the aspect ratio and gradient index on the free vibration and static responses of FGM plates.…”

Section: Introductionmentioning

confidence: 99%

İzotropik Plakaların Regressif Topluluk Öğrenmesi Kullanarak Serbest Titreşim Analizi

Daş

2022

EJOSAT

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The Finite Element Method (FEM) is a popular technique that is employed to analyze and understand the behavior of a structure. Although it has various advantages, there are some drawbacks such as developing accurate mathematical models, the computational cost for complex systems, and expertise. Thanks to recent advancements in computational science, those drawbacks can be eliminated by integrating artificial intelligence. This study presents an ensemble learning regressor-based technique to evaluate the fundamental natural frequencies of isotropic plate structures. For this purpose, Random Forest Regressor (RFR) has been considered. The isotropic plates have been taken into account as square and rectangular thin and thick plates whose materials have been selected as Structural Steel, Aernet 100, Al 7108, and Al 2024 since they are frequently used in various engineering fields. It has been evaluated that the proposed technique has a 0.9936 correlation score (R2) and 0.0019 mean square error (MSE). The average prediction accuracy has been obtained by 99.12% for the test set. Those indicated that the proposed approach is not only an appropriate model for such a problem but also predicts the fundamental natural frequency accurately. Considering its success (99.12%) and the execution speed (0.127 seconds), it is concluded that the proposed approach is an advantageous alternative technique to the other mathematical models.

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Static and free vibration analyses of functionally graded plates based on an isogeometric scaled boundary finite element method

Cited by 10 publications

References 79 publications

Isogeometric Analysis for Free Vibration of Functionally Graded Plates Using a New Quasi-3D Spectral Displacement Formulation

Isogeometric Analysis for Free Vibration of Functionally Graded Plates Using a New Quasi-3D Spectral Displacement Formulation

Parametric Analysis of Free Vibration of Functionally Graded Porous Sandwich Rectangular Plates Resting on Elastic Foundation

İzotropik Plakaların Regressif Topluluk Öğrenmesi Kullanarak Serbest Titreşim Analizi

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