Z. Barouei, M. Jabbarzadeh,
Volume 39, Issue 2 (2-2021)
Abstract
In this paper, the nonlinear bending analysis for annular circular nano plates is conducted based on the modified coupled stress and three-dimensional elasticity theories. For this purpose, the equilibrium equations, considering nonlinear strain terms, are calculated using the least energy potential method and solved by the numerical semi-analytical polynomial method. According to the previous works, there have been no studies calculating all boundary conditions numerically based on three-dimensional elasticity. Typically, the research done on three-dimensional elasticity is either finite element or only for a simply-supported boundary condition. In this research, for the first time, the nonlinear analysis of bending is calculated with the help of three-dimensional elasticity for a variety of boundary conditions. Also, with the help of the modified couple stress theory, the results on the nano-scale scale have been studied. In the following, while validating the results, we investigate the changes in the scale parameter for the types of boundary conditions, the effect of changing the parameter of scale in different thicknesses, and the impact of the parameter of scale on the linear and nonlinear results.
M. Hashemian, M. Jabbarzadeh,
Volume 40, Issue 1 (9-2021)
Abstract
In this paper, nonlinear bending analysis of functionally graded rectangular and sectorial micro/nano plates is investigated using the modified couple stress theory. For this purpose, a higher-order shear deformation theory and von Kármán geometrically nonlinear theory are employed. The equilibrium equations and the boundary conditions for rectangular and annular sector plates are derived from the principle of minimum total potential energy and solved using the Semi-Analytical Polynomial Method (SAPM). One of the advantages of the implemented shear deformation theory is removing the defects of higher order shear deformation theory, and obtaining the response of the first and the third-order shear deformation theories at the same time. Afterwards, beside investigating the benefits of this theory compared with other ones, the results are verified with those by other researches. At the end, the effects of length scale parameter, boundary conditions, power law index, and geometrical dimensions are investigated
