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Submitted to the Department of Mechanical Engineering in Partial Fulfilment of the Requirements for the Degree of Doctor of Philosophy in Mechanical Engineering

Taati, Ehsan | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 51989 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Asghari, Mohsen; Fallah Rajabzadeh, Famida
  7. Abstract:
  8. Circular cylindrical shells have been widely used in many engineering structures such as spacecraft, submarines, offshores, and storage tanks. Their high stiffness-to-weight ratio and load-carrying capability make them well suited for use in civil and aerospace structures. The consecutive development of material engineering along with the increasing demands for lightweight, heat-resistant, and high strength structures have led to the usage of advanced materials namely functionally graded (FG) materials in designing such structures. In this thesis, the nonlinear static analysis of thin FG cylindrical shells is carried out using the Donnell’s shell theory with first-order approximation and the von Karman nonlinearity. From the literature review, it appears that only a boundary layer perturbation technique has been developed to solve nonlinear governing equations of cylindrical shells which has deficiencies and ambiguities in its procedures. In the first part of this thesis, the axisymmetric behavior of sandwich cylindrical shells is selected as a benchmark problem to evaluate boundary layer and standard perturbation techniques. In the second part, the asymmetric behavior of sandwich cylindrical shells subjected to various types of thermo-mechanical loadings is studied based on the findings of the first part. For axisymmetric analysis of laminated sandwich cylindrical shells with isotropic, FG or isogrid lattice layers, three nonlinear equations of Donnell’s shell theories with first order approximation governing stretching and bending behavior are decoupled. This uncoupling makes it possible to present an analytical solution for the nonlinear bending and post-buckling behavior of short and long cylindrical shells with different boundary conditions. A new boundary layer perturbation solution is presented by reducing the governing equations to a normalized form of boundary-layer type. Also, the uncoupled governing equations are solved using standard one-, two-, and three-parameter expansions. By comparing results of analytical and perturbation solutions, the feasibility and performance of standard and boundary layer perturbation techniques in nonlinear analyses of cylindrical shells are investigated. A very important point of the first part is that the boundary layer technique cannot predict the post-buckling behavior of cylindrical shells with any geometric ratios, since after occurrence of instability, the behavior of shell is not boundary-layer type and it is impossible to satisfy the matching conditions. This conclusion challenges the validity of many studies carried out so far. For asymmetric analysis of doubly curved sandwich panels under thermomechanical loadings, five partial differential equations, which are based on the Donnell’s shell and first-order shear deformation theory, are reduced to three ones by introducing a new potential function. Consequently, the governing equations are reformulated to three differential equations in terms of force function, transverse defection and new potential function. This reformulation is then used to conveniently present an analytical and perturbation solutions for the buckling and nonlinear asymmetric bending of cylindrical shells. Using the adjacent equilibrium method, one decoupled stability equation which is an eighth-order differential equation in terms of transverse deflection is obtained and conveniently solved to present analytical expressions for buckling loads of cylindrical shells under any type of loading. Next, a two parameter perturbation technique in conjunction with Fourier series method is used to obtain the nonlinear transverse deflection of cylindrical shells various clamped and simply supported boundary conditions
  9. Keywords:
  10. Perturbation Method ; Cylindrical Shells ; Functionally Graded Materials (FGM) ; Boundary Layer ; Thermomechanical Loading ; Nonlinear Static Analysis ; Analytical Solution ; Static Behavior

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