Modified single variable shear deformation plate theory for free vibration analysis of rectangular FGM plates

Vinh, Pham Van; Dung, Nguyen Thai; Tho, Nguyen Chi; Thom, Do Van; Hoa, Le Kha

doi:10.1016/j.istruc.2020.12.027

Cited by 27 publications

(3 citation statements)

References 49 publications

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“…As for LST element has six nodes in each element, which are the midpoint of three sides and three vertices. The edges of a triangle can be straight lines or curves, for the dispersion of irregular regions, curved triangular elements have more advantages [39][40][41][42], the basis function of the six vertices corresponding to each triangular element is:…”

Section: Considering the Computational Domainmentioning

confidence: 99%

ARIMA-FEM Method with Prediction Function to Solve the Stress–Strain of Perforated Elastic Metal Plates

Chen

Dai

Zheng

2022

Metals

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Stress analysis and deformation prediction have always been the focuses of the field of mechanics. The accurate force prediction in plate deformation plays important role in the production, processing and performance analysis of materials. In this paper, we propose an ARIMA-FEM method, which can be used to solve some mechanical problems of 2D porous elastic plate. We have given a detailed theory and solving steps of ARIMA-FEM. In addition, three numerical examples are given to predict the stress–strain of thin porous elastic metal plates. This article uses CST, LST and Q4 elements to discrete the rectangular plates, square plates and circle plates with holes. As for variable force prediction, this paper compared with linear regression, nonlinear regression and neural network prediction, and the results show that the ARIMA method has a higher prediction accuracy. Furthermore, we calculate the numerical solution at four mesh scales, and the numerical convergence is consistent with the theoretical convergence, which also shows the effectiveness of our method. The image smoothing algorithm is applied to keep edge information with high resolution, which can more concisely describe the plate internal changes. Finally, the application scope of ARIMA-FEM, model expansion, superconvergence analysis and other issues have been given enlightening views in the discussion section. In fact, this algorithm combined statistics and mechanics. It also reflects the knowledge integration of interdisciplinary and uses it better to serve practical applications.

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Section: Considering the Computational Domainmentioning

confidence: 99%

ARIMA-FEM Method with Prediction Function to Solve the Stress–Strain of Perforated Elastic Metal Plates

Chen

Dai

Zheng

2022

Metals

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“…where E(z), ρ(z), ](z), and μ(z) are the effective Young's modulus, mass density, Poisson's ratio, and nonlocal parameter of the perfect FGM nanoplates; they are calculated via the power-law function as follows [58,71,73]:…”

Section: Materials Properties Of Fgm Nanoplates With Porositymentioning

confidence: 99%

Influence of Variable Nonlocal Parameter and Porosity on the Free Vibration Behavior of Functionally Graded Nanoplates

Vinh

Huy

2021

Shock and Vibration

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This paper studies the influence of the variable nonlocal parameter and porosity on the free vibration behavior of the functionally graded nanoplates with porosity. Four patterns of distribution of the porosity through the thickness direction are considered. The classical nonlocal elasticity theory is modified to take into account the variation of the nonlocal parameter through the thickness of the nanoplates. The governing equations of motion are established using simple first-order shear deformation theory and Hamilton’s principle. The closed-form solution based on Navier’s technique is employed to solve the governing equations of motion of fully simply supported nanoplates. The accuracy of the present algorithm is proved via some comparison studies in some special cases. Then, the effects of the porosity, the variation of the nonlocal parameter, the power-law index, aspect ratio, and the side-to-thickness ratio on the free vibration of nanoscale porous plates are investigated carefully. The numerical results show that the porosity and nonlocal parameter have strong effects on the free vibration behavior of the nanoplates.

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“…The most common type of FGM is made of ceramic and metal, while beam, plate, and shell structures made of FG material store many features that increase the efficiency of these structures such as high strength, resistance to friction and abrasion, good heat resistance, and being difficult to crack. The study of the mechanical responses of these components is interested in researching the scientific community [1][2][3][4][5]. Besides, to increase the efficiency of use for structures made of FG materials, scientists also consider the addition of piezoelectric layers, where the piezoelectric effect produces special effects that are much more prominent without the piezoelectric layer.…”

Section: Introductionmentioning

confidence: 99%

On the Vibration Analysis of Rotating Piezoelectric Functionally Graded Beams Resting on Elastic Foundation with a Higher-Order Theory

Phuc

Thanh

2022

International Journal of Aerospace Engineering

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This work numerically simulates the natural vibration response of rotating piezoelectric functionally graded (FG) beams resting on two-parameter elastic mediums. This is a common kind of design seen in reality, such as marine engine gas turbine blades, rotating railway bridges, and helicopter rotors, where these components may be thought of as beam models rotating around a fixed axis. For the first time, this study uses the finite element method (FEM) in conjunction with Reddy’s theory of high-order shear deformation to model the vibration response of a beam rotating around one fixed axis. The present theory eliminates the necessity for shear correction factors while precisely describing the structure’s mechanical response. The piezoelectric layers are firmly connected to the top and bottom surfaces of the beam, while the core layer is composed of the FG material, whose material and physical characteristics are expected to gradually change along the thickness direction of the beam in accordance with a power law function as the thickness of the beam is increased. This study is conducted to determine the influences of the structure’s geometric and material characteristics on the beam’s free vibration behavior, including the rotational speed, distance between the fixed axis and beam endpoint, thickness of piezoelectric layers, and elastic foundation parameters, among other things. Due to the obvious calculation results, the free vibration response of this structure can be easily seen by readers, which serves as a foundation for its design and use in engineering practice.

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Modified single variable shear deformation plate theory for free vibration analysis of rectangular FGM plates

Cited by 27 publications

References 49 publications

ARIMA-FEM Method with Prediction Function to Solve the Stress–Strain of Perforated Elastic Metal Plates

ARIMA-FEM Method with Prediction Function to Solve the Stress–Strain of Perforated Elastic Metal Plates

Influence of Variable Nonlocal Parameter and Porosity on the Free Vibration Behavior of Functionally Graded Nanoplates

On the Vibration Analysis of Rotating Piezoelectric Functionally Graded Beams Resting on Elastic Foundation with a Higher-Order Theory

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