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In this paper, post-buckling behavior of laminated plates is investigated using mesh-free method. One of the most common powerful numerical methods in recent decades is mesh-free collocation method. Due to wildly oscillating solutions at the endpoints and occurrence of Runge phenomenon in the case of uniform distribution of points, the domain of the problem is discretized with Legendre-gauss-lobatto nodes. In this paper, the classical laminated plate theory is used and different out-of-plane boundary conditions with anti-symmetric cross-ply and angle-ply laminates are investigated. Equations system is introduced by discretizing von-Karman’s compatibility equations and boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Because of large deformations and nonlinear terms in the strain-displacement relations, the nonlinear system of equations is solved by using Newton-Raphson technique. Since number of equations is always more than the number of unknown parameters, the least square technique is used to solve the system of equations. Some results are obtained and compared with those available in the literature.

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In this paper, thermo‌-elastic analysis of functionally graded nanocomposite hollow cylinders reinforced by single walled carbon nanotube (SWCNT) subjected to a thermal load was carried out by a mesh-free method. It is assumed that the functionally graded nanocomposite hollow cylinder reinforced by carbon nanotube with finite length is simply supported. A uniform and three kinds of functionally graded (FG) distributions of carbon nanotubes in the radial direction of cylinder are considered. Nanocomposite mechanical properties are estimated by micro mechanical generalized rule mixture model. Applying the virtual work principle, the governing equations are obtained and are discretized by the mesh-free method. In the mesh-free analysis, moving least squares (MLSs) shape functions are used for approximation of displacement field. The transformation method was used for the imposition of essential boundary conditions. Using finite difference method, temperature distribution was obtained by solving the thermal equation. To validate, the results of this analysis were compared with previous published works and a good agreement was seen between them. Then the effects of various parameters, such as the kind of distribution and the volume fractions of carbon nanotubes and the different geometrical parameter, on the components of stress are studied.