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Three-dimensional exact elastic analysis of nanoplates

Wang Guoping, Zhang Yu, Arefi Mohammed

Archives of Civil and Mechanical Engineering

2021

Vol. 21, no. 3

63--76

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.

Inelastic behavior and numerical analysis in twin-roll casting process of AZ31 alloy

Ju D. Y., Hu X. D., Zhao H. Y.

Archives of Mechanics

2009

Vol. 61, nr 3-4

229-239

In this paper, Anand's model, a uni?ed visco-plasticity constitutive model, was employed to simulate the highly nonlinear behavior in the twin-roll casting process. Anand model's parameters were regressed based on compression tests at various temperatures and strain rates for magnesium alloy AZ31. To calculate the thermal mechanical stresses, the thermal ?ow of twin-roll casting process was simulated ?rstly; then the stresses were calculated by the imposed thermal ?ow as the body load, and a small displacement load along roller's tangential direction was imposed simultaneously in order to simulate the rolling action. The stresses and deformation results were compared with experimental data. Based on the stresses analysis and experimental tests, it reveals that separating force should be strictly controlled in the twin roll casting process in order to avoid cracks caused by thermal and deformation stresses.