Utilizing general stress functions expressed in polar coordinates, plane strain solutions are developed for large diameter thick cylindrical shells. The solutions provide field stresses and strains which consider the effect of gravity body forces, and arbitrary boundary loadings expressed in terms of a Fourier series. To illustrate the theory and its application, a Fourier series expansion is given for a set of boundary stresses partially distributed and in equilibrium. An example is also presented which considers a long cylindrical shell subjected to a gravity body force, a nonuniform hydrostatic pressure, and an arbitrary counterbuoyancy force at the inner boundary. Field stresses and numerical results are provided for the given loading condition.

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