mehrdad jabbarzadeh

In this research, a new 3D elasticity numerical solution based on the Semi-Analytical Polynomial Method (SAPM) is presented for the nonlinear bending analysis of orthotropic annular/circular micro/nanoplates resting on a Winkler-Pasternak elastic foundation, utilizing re-modified couple stress theory. This is the first report of a 3D elasticity numerical solution specifically based on re-modified couple stress theory. Moreover, while previous 3D analytical solutions based on couple stress theory have primarily focused on the bending of rectangular plates with simply supported edges, this study investigates the nonlinear bending of circular plates under various boundary conditions. Additionally, the variation in thickness under different types of loading (mechanical, thermal, and thermo-mechanical) is reported for the first time. The effects of boundary conditions, couple stress scale parameters, aspect ratio, thickness, loading, and the elastic foundation are examined. Both the increasing and decreasing impacts of scale parameters on deflection are observed in this study.

This paper presents the first and third order shear deformation plate theory and von Karman theories to solve Thermo-elastic problems of functionally graded hollow rotating disk. The material properties of the disk are assumed to be graded in the direction of the thickness by a power law distribution of volume fractions of the constituents. New set of equilibrium equations with small and large deflections are developed. Using small deflection theory an exact solution for displacement field is given. Solutions are obtained in series form in case of large deflection. Numerical results are presented for various percentages of ceramic-metal volume fractions and have been compared with those obtained using first-and third-order shear deformation plate theories. Also the results are verified with ABAQUS soft, simulink method and the known data in the literature.

In this article، nonlinear bending analysis of single-layered circular graphene sheet is studied. The equilibrium equations are derived based on the nonlocal continuum mechanics and principle of virtual work and first order shear deformation plate theory (FSDT). Differential quadrature method is used to discretize the equilibrium equations. In this method a non-uniform mesh point distribution (Chebyshev- Gauss- Lobatto) is used for provide accuracy of solutions and convergence rate. The effect of nonlocal parameter، thickness، number of grid points and lateral loading are investigated on deflection of graphene sheet. The results are compared with valid results reported in the literature.

Abstract - In this article, thermal buckling analysis of functionally graded annular sector plate is studied. The mechanical and thermal properties of the functionally graded sector plate are assumed to be graded in the thickness direction. The equilibrium and stability equations are derived based on the first order shear deformation plate theory (FSDT) in conjunction with nonlinear von-karman assumptions. Differential quadrature method is used to discretize the equilibrium and stability equations. In this method a non-uniform mesh point distribution (Chebyshev-Gauss-Lobatto) is used for provide accuracy of solutions and convergence rate. By using this method, there is no restriction on implementation of boundary conditions and various boundary conditions can be implemented along any edges. Finally, The results compared with other researches and the effects of plate thickness, sector angle, annularity, power law index and various boundary conditions on the critical buckling temperature are discussed in details.

In this paper, the thermal buckling behavior of circular plates with variable thicknesses made of bimorph functionally graded materials, under uniform thermal loading circumstances, considering the first-order shear deformation plate theory and also assumptions of von Karman has been studied. The material characteristics are symmetric to the middle surface of the plate and, based on the power law, vary along with thickness; where the middle surface is intended pure metal, and the sides are pure ceramic. In order to determine the distribution of pre-buckling force in the radial direction, the membrane equation is solved using the shooting method. And the stability equations are solved numerically, with the help of pseudo-spectral method by choosing Chebyshev functions as basic functions. The numerical results in clamped and simply supported boundary conditions and the linear and parabolic thickness variations are presented. And the influence of various parameters like volume fraction index, the thickness profile and side ratio on the buckling behavior of these plates has been evaluated.

In this paper, the exact solution to the thermal buckling of circular plates made of two-way functional materials under uniform thermal loading has been studied. Also, the theory and assumptions of the classical nonlinear von karman for fixed and simple conditions have been considered. Material properties are symmetric with respect to the middle plane and vary according to the power law so that the middle plane and the sides are considered pure metal and ceramic, respectively. Nonlinear equations of equilibrium are determined using energy method, and stability equations are used to obtain the critical buckling temperature by equilibrium in the vicinity method and a closed solution is obtained. Effects of various parameters, including rate of change of plate thickness to its radius, change in volume percentage of the material. The Poisson ratio on the critical buckling temperature for the two fixed and simple conditions has been studied and the results are compared with each other and with those of previous researches.