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Nonlinear Analysis of FG Rectangular Plates under Mechanical and Thermo-Mechanical Loads using the Extended Kantorovich Method

Moradkhani, Behrooz | 2018

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 50552 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Nasier, Asghar
  7. Abstract:
  8. The purpose of this research is to provide an analytical solution using first order shear deformation theory for nonlinear bending of rectangular FG plate under mechanical and thermal loads with different boundary conditions. To achieve this goal, extended Kantorovich method have been used. This method has a high convergence rate and is more accurate than other approximate methods, such as the Ritz and Galerkin methods, because the partially differential equations are converted to ordinary differential equations. In order to solving nonlinear odes the perturbation method is used. Material of the plate is a mixture of ceramic and metal and is modeled as an isotropic and non-homogeneous material whose properties change according to a power law distribution in the direction of thickness. To apply thermal load, it is assumed that the temperature variations are only in the thickness of the plate, so the one-dimensional heat transfer equation is solved in the FG plate and temperature distribution obtained in the thickness direction. In order to formulate the problem, nonlinear equations of a rectangular FG plate are obtained in the form of first-order shear deformation theory. Also the von-Karman nonlinearity sense is assumed, so there are five partial differential coupled equations. The first step is the extraction of decoupled equations, so that semi-analytic methods can be used to solve them. After defining the new parameters and obtaining decoupled equations, they are solved analytically and numerically. In order to verify the accuracy of this semi-analytical method, the results are compared with the available results and also numerical solution of the problem, which indicates the high accuracy of this method. The results are presented for different boundary conditions, and the effect of the boundary layer on the plat is also investigated, which shows that the effect of the boundary layer on the edges is as thick as the plate, and this effect in the free edge is larger than clamped and simply supported plate. By comparing nonlinear and linear results, it can be said that the difference between the two theories increases for large deflection problem. It is shown that Kantorovich method converges in second or third iteration irrespective of the type of initial guess function. Deflection in the FG plates lie between those of a fully metallic plate and a ceramic plate for different boundary conditions, but stress resultant in the immovable simply supported plate is not between those obtained for metal and ceramic plates
  9. Keywords:
  10. Extended Kantorovich Method ; Nonlinear Analysis ; Rectangular Plate ; Mechanical Loading ; Functionally Graded Materials (FGM) ; Perturbation Method

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