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Analytical Static and Dynamic Solution of a Mindlin Rectangular Plate under In-Plane Loads Using Fourier Series and Auxiliary Polynomial Functions

Mohammad Esmaeili, Reyhaneh | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53026 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mofid, Masoud
  7. Abstract:
  8. This research presents an innovative analytical solution to static, free vibration and buckling of an isotropic, homogeneous Mindlin plate with uniform thickness. This method satisfies all classical boundary conditions including free, simply supported and clamped as well as non-classical ones. Moreover, Mindlin plates on Winkler foundation of arbitrary stiffness function are investigated. In this study, the deflection and rotation of straight normal line of the plate about x and y axes are represented as the functions of sine and cosine Fourier series, accompanied by auxiliary functions. These auxiliary functions are of great importance because these functions satisfy arbitrary boundary conditions, whether classical ones or elastic restraints such as translational and rotational spring with arbitrary stiffness functions. In other words, considering unknown coefficients, we can implement general boundary condition. Additionally, applying auxiliary functions guarantees the continuity of stress functions over the plate area. In the absence of supplementary functions, the moments and shear forces of the plate, which are obtained through differentiating the deflection and rotation functions, would have some discontinuities. Finally, the results acquired by the proposed method would be compared by ones from other studies and Finite Element Method
  9. Keywords:
  10. General Boundary Conditions ; Free Vibration ; Static Analysis ; Buckling ; Fourier Series ; Auxiliary Functions ; Mindlin Rectangular Plate

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