Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory

2018 ◽  
Vol 233 (1) ◽  
pp. 287-301 ◽  
Author(s):  
Behrouz Karami ◽  
Davood Shahsavari ◽  
Li Li ◽  
Moein Karami ◽  
Maziar Janghorban
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Thermal Buckling ◽  
Second Order ◽  
Functionally Graded ◽  
Electric Voltage ◽  
Size Dependent

The effective elastic-piezoelectric properties of nanostructures have been shown to be strongly size-dependent. In this paper, a nonlocal second-order shear deformation formulation is presented to study the size-dependent thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core. Temperature is considered as uniform and nonlinear distributions across plate’s thickness direction. Based on the developed nonlocal second-order shear deformation theory, the size-dependent equations of motion are derived. The nonlocal thermal buckling responses of simply supported nanoplates are solved via Navier method. The reliability of present approach is verified by comparing the existing results provided in the open literature. The influences of nonlocal parameter, gradient index, electric voltage, and Winkler–Pasternak parameters on the thermal buckling characteristics of functionally graded nanoplates are examined.

Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory

2017 ◽  
Vol 21 (8) ◽  
pp. 2751-2778 ◽  
Author(s):  
Mohammad Arefi ◽  
Ashraf M Zenkour
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Virtual Work ◽  
Nonlocal Parameter ◽  
Shear Deformation Theory ◽  
Radius Of Curvature ◽  
Governing Equations ◽  
Size Dependent ◽  
Magnetic Potentials ◽  
Sinusoidal Shear Deformation Theory

In this work, an analytical solution for bending analysis of the three-layer curved nanobeams is presented. The nanobeams are including a nanocore and two piezomagnetic face-sheets. The structure is subjected to applied electric and magnetic potentials while is resting on Pasternak's foundation. To reach more accurate results, sinusoidal shear deformation theory is employed to derive displacement field of the curved nanobeams. In addition, nonlocal electro-magneto-elasticity relations are employed to derive governing equations of bending based on the principle of virtual work. The analytical results are presented for simply supported curved nanobeam to discuss the influence of important parameters on the vibration and bending results. The important parameters are included spring and shear parameters of the foundation, applied electric and magnetic potentials, nonlocal parameter, and radius of curvature of curved nanobeam.

scholarly journals A New Sinusoidal Shear Deformation Theory for Static Bending Analysis of Functionally Graded Plates Resting on Winkler–Pasternak Foundations

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Pham Minh Phuc ◽  
Vu Nguyen Thanh
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Solution Technique ◽  
Functionally Graded Plates ◽  
Bending Analysis ◽  
Foundation Parameters ◽  
Sinusoidal Shear Deformation Theory

In this article, a new sinusoidal shear deformation theory was developed for static bending analysis of functionally graded plates resting on elastic foundations. The proposed theory used an undefined integral term to reduce the number of the unknown to four without any shear correction factors. The high accuracy and efficiency of the proposed theory were proved thanks to the comparisons of the present results with other available solutions. And then, the proposed theory was successfully applied to investigate the bending behavior of the functionally graded plates resting on Winkler–Pasternak foundations. The governing equations of motion were established by using Hamilton’s principle, and the Navier’s solution technique was employed to solve these equations. The effects of some factors of the geometrics, the materials properties, and the elastic foundation parameters on the bending behaviors of the FGM plates were investigated intensely. Also, some novel results and special phenomenon were carried out.

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