# A closed-form solution for stress analysis of hollow circular cylinder structure under non-uniform external load and its engineering application

### Abstract

Hollow circular cylinder structures are widely used in industry for their high bearing capacity. In some engineering cases, these structures are always subjected to complicated non-uniform external loads. For example, casings used for oil production are subjected to non-uniform ground stresses. In this study, a generalized closed-form analytical solution for stress analysis of hollow circular cylinder under non-uniform external load was derived. The common non-uniform external load was decomposed by Fourier series under the principle of superposition by theory of elasticity. Analytical solutions for stress results of sine or cosine series external load problems were obtained by the semi-inverse method. A baseline analysis of a casing under non-uniform ground stress was presented using the proposed analytical method and the finite element method to validate the accuracy of the proposed analytical model. A parametric analysis was conducted finally to discuss the effects of non-uniform coefficients on the stress results. Results show that, the hollow circular cylinder structure’s anti-collapse capacity will be strongly weakened, when the non-uniform coefficient increases. This proposed analytical model can be referenced in strength verification of hollow circular cylinder structures in engineering practice.### References

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