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Linear and Nonlinear Thermoelastic Analysis of Functionally Graded Circular Plates and Cylindrical Bending of FG Plates

Fallah Rajabzadeh, Famida | 2009

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 39806 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Nosier, Asghar
  7. Abstract:
  8. In the present study, analytical solutions within first-order shear deformation plate theory (FSDT), are presented for the linear and nonlinear asymmetric bending of functionally graded circular plates subjected to thermo-mechanical loading and boundary layer phenomenon is also investigated. To this end, cylindrical bending of long rectangular FG plates is also considered to study the perturbation technique which is used here to solve the nonlinear equations. Functionally graded materials are mostly used in high temperature environments and the study of their behavior under thermal and mechanical loadings and in small and large deflection ranges has become very important. Here, the linear and nonlinear equilibrium equations within FSDT describing the bending-extension problem of FG circular plates are reformulated into interior and edge-zone equations. This uncoupling makes it possible to present an analytical solution and also to study the boundary layer phenomenon. The nonlinear formulation accounts for moderately large deflection in von Karman sense. To reformulate the linear and nonlinear equations, two different methods are used. In linear analysis, by introducing three displacement functions, the linear governing equations which are five coupled differential equations in terms of five variables with a total order of ten are uncoupled into five equations, whose total order will be the same as that of the original equations. Then, using Fourier series method to model the problem asymmetries, analytical solutions for linear bending of complete FG circular plate and FG sectorial plate with various boundary supports are presented. To compare the results with FSDT, linear bending of an FG circular plate is also studied within classical plate theory with the same method. In nonlinear analysis, by introducing a displacement function and a stress function, the nonlinear equilibrium equations with the total order of ten are uncoupled into three equations with the same total order of ten. Then analytical solutions for nonlinear asymmetric bending of complete FG circular plate with various clamped and simply-supported boundary conditions under mechanical and thermo-mechanical loadings are presented. In order to solve the governing equations under mechanical loading, a single-parameter perturbation technique and for the plate under thermo-mechanical loading a two-parameter perturbation technique is used. The results of linear and nonlinear analysis are verified with known results in the literature. In this study, the usage of perturbation technique for the nonlinear analysis of FG plates with various boundary supports under mechanical, thermal and thermo-mechanical loadings are studied by using the exact solution presented for cylindrical bending of FG plates within FSDT. In this thesis, a ceramic-metal FGM is considered and it is modeled as a non-homogenous isotropic material whose properties vary continuously through the plate thickness according to a power-law distribution of the volume fraction of the constituents. In thermal loading problems it is assumed that the temperature variation is only in the thickness direction and the one-dimensional and steady heat conduction equation is solved.

  9. Keywords:
  10. Circular Plate ; Boundary Layer ; Perturbation Method ; Functionally Graded Materials (FGM) ; Sectorial Plate ; Asymmetric Bending ; Cylindrical Bending

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