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Three-dimensional exact elastic analysis of nanoplates

Abstract

This work investigates the application of three-dimensional nonlocal elasticity theory to elastic static analysis of nanoplates. Unlike all previous papers that considered two-dimensional Laplacian operator to stress components, this work uses the general three-dimensional nonlocal operator with thickness direction operator. The displacement field of nanoplate is assumed a function of three-dimensional coordinate x, y, z. The principle of virtual work is used to derive the governing equations. A solution procedure is developed for simply supported nanoplate. The solution along the thickness direction is derived using the characteristic equation and application of boundary conditions including free transverse shear stress and applied normal stress. The eigenvalue–eigenvector methodology is used to extract general solution along the transverse direction. The stress and deformation distribution along the transverse direction is presented with changes of significant parameters such as nonlocal parameter and aspect ratio.

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Acknowledgements

This work was supported by Science and Technology Program of Guangdong Province (2020B121201013); Science and Technology Special Fund Program of Guangdong Province (2020A0102009); Rural Science and Technology Commissioner Program of Guangdong Province (KTP20200278); National Natural Science Foundation of Guangdong Province (2021A1515012597).

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Correspondence to Yu Zhang.

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Wang, G., Zhang, Y. & Arefi, M. Three-dimensional exact elastic analysis of nanoplates. Archiv.Civ.Mech.Eng 21, 91 (2021). https://doi.org/10.1007/s43452-021-00247-x

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Keywords

  • Nonlocal elasticity theory
  • Three-dimensional elasticity
  • Laplacian operator
  • Stress and deformation analysis