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Linear and Nonlinear Analysis of Functionally Graded Annular Sector Plate with Various Boundary Condition under Tranverse Mechanical Loading by Using Extended Kantorovich Method

Khakbaz, Ali | 2015

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 47686 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Fallah Rajabzadeh, Famida
  7. Abstract:
  8. In this study, linear and nonlinear mechanical behavior of moderately thick annular sector plates made of functionally graded materials is investigated. In linear analysis, based on first order shear deformation theory, governing equation with two different approaches are derived. In first approach, by application of extended Kantorovich method (EKM), displacements field variables are expressed as separable function of and together, and two sets of ordinary differential equations (ODEs) by using the principle of minimum total potential energy are derived. In the second approach, within FSDT and using the principle of minimum total potential energy, the governing partial differential equations are derived and then converted into two sets of ordinary differential equations in and directions by applying extended Kantorovich method. In nonlinear analysis, utilizing the principle of minimum total potential energy and von-karman strain-displacement relations, five nonlinear partial differential equations are obtained and with perturbation technique converted to linear form. These linear Equations are convert to linear ordinary differanial equations in radial and circumferential directions. According to a power-law distribution, the material properties are assumed and then these ODEs are solved iteratively in each approach. Comparison of the results for different cases including rectangular and solid sector plates shows close agreement with very fast convergence in plate with simply or clamped supports in both approaches but for plates with free edges, it would be concluded that in linear analysis just 1st approach is acceptable. The effect of different boundary conditions and material properties on the behavior of the FG annular sector plate is also investigated
  9. Keywords:
  10. Functionally Graded Materials (FGM) ; Nonlinear Analysis ; Extended Kantorovich Method ; Perturbation Method ; Differential Quadrature (DQ) ; Annular Sector

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