Instability Analysis of Pressure-Loaded Thin Arches of Arbitrary Shape

The governing differential equations and the virtual work expressions for the large displacement analysis of thin arches of arbitrary shape, subjected to pressure loads, are derived. The virtual work expressions are employed as the basis for formulation of finite element stiffness equations. Classical solutions are obtained, from the differential equations, for the buckling of circular rings under uniform “follower” (hydrostatic) and “dead” (constant direction) pressure loadings. Finite element solutions are calculated for elliptical rings for a wide range of axis ratios.