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In this paper, arbitrary rotational symmetric loadings on circular and annular plates have been discussed. In this way, an approach is introduced in order to compute the critical load factor for the imposed loadings. The considered plates are assumed to be made of materials obeying arbitrary yield criteria. It is shown that the new approach not only generates the solutions that exist in the literature, but also it can create solutions for cases that have not yet been solved by other methods. Of special attention is the case of von Mises criterion. © 2002 Elsevier Science Ltd. All rights reserved  

The classical yield criteria do not describe the yield size-dependency that has been observed in micro-scale structures (Fleck, Muller, Ashby, & Hutchinson, 1994; Stolken and Evans 1998; Moreau et al. 2005), and may also significantly underestimate the yield loads of structures at micron and sub-micron scales (Son, Jeong, & Kwon, 2003; Liu et al., 2013). The present paper suggests a specific size-dependent yield criterion based on the strain gradient theory that is aimed at addressing this inadequacy. In order to develop the strain gradient based yield criterion, the deviatoric part of the strain energy is calculated based on this theory and equated to the deviatoric strain energy of a... 

In this paper, employing the limit analysis theorem, critical loading on functionally graded (FG) circular plate with simply supported boundary conditions and subjected to an arbitrary rotationally symmetric loading is determined. The material behavior follows a rigid-perfectly plastic model and yielding obeys the von-Mises criterion. In the homogeneous case, the highly nonlinear ordinary differential equation governing the problem is analytically solved using a variational iteration method. In other cases, numerical results are reported. Finally, the results are compared with those of the FG plate with Tresca yield criterion and also in the homogeneous case with those of employing the... 

The upper and lower bound principals of limit analysis are employed to determine the critical loading on solid circular plate with simply supported boundary conditions and subjected to any distributed loading with rotational symmetry. In this study, material behavior follows a rigid perfectly plastic model and yielding obeys the von-Mises criterion. Homotopy analysis method is employed to achieve the analytical solution to the high nonlinear ordinary differential equations governing the problem. This analytic solution has been obtained in terms of convergent series with easily computable terms. The results are verified with the Tresca yield criterion and presented as plots to show the... 

In this paper, distributions of stress and strain components of rotating disks with non-uniform thickness and material properties subjected to thermo-elasto-plastic loading are obtained by semi-exact method of Liao's homotopy analysis method (HAM) and finite element method (FEM). The materials are assumed to be elastic-linear strain hardening and isotropic. The analysis of rotating disk is based on Von Mises' yield criterion. A two dimensional plane stress analysis is used. The distribution of temperature is assumed to have power forms with the hotter point located at the outer surface of the disk. A mathematical technique of transformation has been proposed to solve the homotopy equations...