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In this thesis the theorems of Poncelet and Cayley will be discussed. We will use algebraic geometry and in particular the theory of elliptic curves to present a proof following the works of Griffiths and Harris (refrence 1).
The P2-version of poncelet’s theorem that we prove in our thesis says:let C , D be smooth conic in general position. Suppose there is an n-sided olygon inscribed in C and circumscribed about D.Then for any point of C, there exists an n-sided polygen, also inscribed in C and circumscribe about D, which has this point for one of its vertics.the Cayley’s theorem provides a criterion on the existence of such an n-gon given the conics C and D as above  

In this study, the thermal buckling behavior of thin metal liner reinforced by composite shell in present of the initial imperfection is investigated. For this purpose, the Ryzener – Myndlyn shear-deformation theory & the virtual work method are used to extract equilibrium equations. In this work, the conical shell with c-c, s-s, c-f boundary conditions has been studied. The outer layer of reinforced composite is exposed to constant ambient temperature and iner layer is exposed to heat. Metal liner and reinforced composite shell are merged with together. In other words, the degrees of freedom at each node for both shells are assumed to be equal. Solution method is finite element method using... 

In this dissertation, the buckling and postbuckling analysis of lattice conical shells are presented. The outer skins of the shell may be reinforced by cross-ply laminated composites. The shell is subjected to uniform axial compression and the boundary conditions are simply supported. This problem is solved using two different approaches. At first approach, the main priority is high speed calculations, which is investigated in static and dynamic types of loadings. In the case of static loads, the equilibrium equations are formulated based on the classical theory and von Karman type of nonlinearity. The equations are solved by Galerkin method and a closed-form relation is derived. In the case...