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3D Elasticity Buckling Solution for Transversely Isotropic Functionally Graded Rectangular Plates by Displacement Potential Function

Jafari, Ali | 2021

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 54594 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Khaloo, Alireza; Navayi Neya, Bahram
  7. Abstract:
  8. The importance of transversely isotropic and functionally graded materials and also plates in industry necessitates studies on these kinds of structures. This study works on the buckling of simply supported rectangular transversely isotropic FGM plates subjected to in-plane uniaxial or biaxial static loads. For this purpose, discretization method is applied and the aforesaid inhomogeneous plate is divided into arbitrary number of sublayers parametrically (N). With the help of displacement potential functions, coupled different equations for each sublayer are simplified to two uncoupled different equations in terms of the potential functions. These governing equations for transversely isotropic homogeneous sublayers are solved using the method of separation of variables and by applying the boundary conditions. To do so, boundary conditions for the edges are applied which leave each sublayer six unknowns, hence 6N unknowns are remained totally. Three stress boundary conditions for both upper and lower faces of the plate, and six boundary conditions for each N-1 interfaces of two adjacent sublayers are applied, thus providing 6N necessary equations and converting the problem into a system of 6N equations-6N unknowns. By making the determinant of the matrix of coefficients zero, characteristic equation appears. Through solving this equation, critical load is obtained. Verification is done by comparing the results with reliable past works. Finally tables and charts are presented using the results for different materials with different loadings and geometry and some conclusions are made based of them
  9. Keywords:
  10. Critical Buckling Load ; Rectangular Plate ; Transversely Isotropic ; Displacement Potentials Function ; Functionally Graded Materials (FGM) ; Simply Supported

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