Nonlinear Bending Analysis of Micro/Nano Rectangular and Annular Sector Plates Using a Modified Higher-Order Shear Deformation Theory and the Modified Couple Stress Theory

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

Keywords

• nonlinear bending
• modified higher-order shear deformation theory (mhsdt)
• modified couple stress theory
• functionally graded material (fgm)
• semi-analytical polynomial method (sapm)