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Keywords = symmetrical sandwich plate

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11 pages, 425 KiB  
Article
Degenerated Boundary Layers and Long-Wave Low-Frequency Motion in High-Contrast Elastic Laminates
by Lenser A. Aghalovyan, Lusine G. Ghulghazaryan, Julius Kaplunov and Danila Prikazchikov
Mathematics 2023, 11(18), 3905; https://doi.org/10.3390/math11183905 - 14 Sep 2023
Cited by 1 | Viewed by 1112
Abstract
The effect of high contrast on the multiscale behaviour of elastic laminates is studied. Mathematical modelling in this area is of significant interest for a variety of modern applications, including but not limited to advanced sandwich structures and photovoltaic panels. As an example, [...] Read more.
The effect of high contrast on the multiscale behaviour of elastic laminates is studied. Mathematical modelling in this area is of significant interest for a variety of modern applications, including but not limited to advanced sandwich structures and photovoltaic panels. As an example, the antiplane shear of a symmetric, three-layered plate is considered. The problem parameters expressing relative thickness, stiffness and density are assumed to be independent. The high contrast may generally support extra length and time scales corresponding to degenerated boundary layers and propagating long-wave low-frequency vibration modes. The main focus is on the relation between these two phenomena. The developed multiparametric approach demonstrates that those do not always appear simultaneously. The associated explicit estimates on contrast parameters are established. In addition, the recent asymptotic extension of the classical Saint-Venant’s principle is adapted for calculating the contribution of the degenerate boundary layer or long-wave low-frequency propagation mode. The peculiarity of the limiting absorption principle in application to layered media is also addressed. Full article
(This article belongs to the Special Issue Multiscale Mathematical Modeling)
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16 pages, 1681 KiB  
Article
Thermal Mechanical Bending Response of Symmetrical Functionally Graded Material Plates
by Mengna Han, Zichan Li, Zhicheng Huang, Xingguo Wang and Wenjie Gao
Materials 2023, 16(13), 4683; https://doi.org/10.3390/ma16134683 - 28 Jun 2023
Cited by 4 | Viewed by 1533
Abstract
This paper investigates the thermal mechanical bending response of symmetric functionally graded material (FGM) plates. This article proposes a thermodynamic analysis model of both the FGM plate and FGM sandwich plate, and the model only involves four control equations and four unknown variables. [...] Read more.
This paper investigates the thermal mechanical bending response of symmetric functionally graded material (FGM) plates. This article proposes a thermodynamic analysis model of both the FGM plate and FGM sandwich plate, and the model only involves four control equations and four unknown variables. The control equation is based on the refined shear deformation theory and the principle of minimum potential energy. The Navier method is used to solve the control equation. According to the method, numerical examples are provided for the thermo-mechanical bending of the symmetric FGM plate and FGM sandwich plate under a simply supported boundary condition, and the accuracy of the model is verified. Finally, parameter analysis is conducted to investigate the effects of the volume fraction index, side-to-thickness ratio, thermal load, and changes in core thickness on the thermal mechanical bending behavior of the symmetric FGM plate and FGM sandwich plate in detail. It was found that the deflection of the FGM plate is greater than that of the FGM sandwich plate, while the normal stress of the FGM plate is smaller than that of the FGM sandwich plate. Moreover, the FGM plate and FGM sandwich plate are sensitive to nonlinear temperature changes. Full article
(This article belongs to the Special Issue The Composite Materials of Today and Tomorrow)
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