Static analysis under arbitrary loading of axially symmetric shells with variable material and geometric properties using equilibrated basis functions Sadegh Babaie Date of submission: September 15, 2020 Department of Civil Engineering Isfahan University of Technology, Isfahan, Iran Degree: M.Sc. Language: Farsi Supervisor: Assist. Prof. Nima Noormohammadi Shells are common structures in industry that are considered due to their high resistance for membrane loads with a widespread load-bearing surface and have many applications in civil, mechanics, aerospace and marine engineering. Due to the fact that the equations governing the shell are complex, their analysis by analytical methods is very time consuming and costly and is generally limited to specific simple cases. Therefore, numerical analysis of shells has been the subject of researchs by many researchers. The method considered in this research is such a way that makes possible to analyze the types of thin symmetrical axial shells with variable thickness and material properties subject to arbitrary loading. It should be noted that the shells considered in this research have a smooth curve equation. By using the domain decomposition methods and establishing the continuity conditions at interfaces, the method can be extended to solve axially symmetric multi-segment shells. The applied loads are first converted into a Fourier expansion and each component is applied to the structure separately. To estimate the response in the meridianal section of the shell, equilibrated basis functions as a new method in the field of the basis function methods to solve differential equations governing engineering problems, and for the circumferential direction the Fourier series expansion shall be used. Equilibrated basis functions method is a mesh free method with high accuracy and complete continuity of the solution function, which unlike other basis function methods, only applicable to equations with constant coefficients, can also be applied to equations with variable coefficients. By selecting bases for in a series for the homogeneous solution that do not satisfy the problem operator, the approximate satisfaction of its weighted residual integral is developed. The bases are selected from the Chebyshev polynomials of the first kind, and the corresponding weights are selected from exponential functions. With the shell cross-section in the form of a curved line andformulating in a corresponding coordinate system, the problem is formulated in a rectangular domain equivalent to the original domain, which along with the Fourier series expansion, converts the complex integrals in three-dimensional space into one-dimensional integral combinations and increases the speed of problem solving. Validation of the method is mainly done in comparison with the results obtained by commercial FEM softwares, which confirms the accuracy and efficiency of the method. Key words: Shells of revolution,Equilibrated basis functions, Chebyshev polynomials, Meshfree method