The analysis method described in Part 1 of the present paper is designed to handle the general case of an axisymmetric shell under axisymmetric loadings. Incremental approach is used under the consideration of the first order approximation in determining the tangent stiffness characteristics of the finite element. Effects of strain hardening, both isotropic and kinematic, are included. In order to account for instability and large accumulated deformations during the loading of the structure, the effect of the initial stress on the element stiffness is included. Incremental principle of virtual work is used to derive the working equations. A computer program is then designed and utilized to generate the design charts for formed heads of pressure vessels of various configurations. Part 2 of the present paper will give a detailed description of the numerical techniques used to apply the theory developed in Part 1. Additional significant sample problem solutions will be given in Part 2.

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