Stability of conical shells
Object and purpose of research. This paper discusses stability verification of conical shells belonging to the class of pressure hull structures for underwater technology. Materials and methods. Solution to the problem is based on an approximate formula derived through generalization of Mushtari solution for constant thickness-radius ratio t/r of conical shell and, accordingly for r-dependent parameters of shellstiffeners. This paper only investigates the shells with straight generatrix. A number of terms in the basic formula was found numerically. Main results. This paper gives an assessment of boundary conditions for conical shells, determined by a special parame- ter, G. Four variants of boundary conditions are discussed: both ends simply supported; both ends fixed; greater diameterfixed, smaller simply supported; greater diameter simply supported, smaller fixed. Comparison of numerical and theoretical solution demonstrates quite a good correlation of G parameter for above-mentioned variants of boundary conditions in a wide range of r 1/ r 2 ratios, where r 1 and r 2 are greatest and smallest radii of conical shells respectively.For shells without stiffeners, the paper suggests a calculation formula yielding the value of constant thickness for an equally stable shell, corresponding to given theoretical critical pressure for a conical shell with constant t/r ratio.To calculate the least theoretical pressure at constant t/r, this paper suggests a simplified formula that works well for “medium- length” shells.Stability analysis of stiffened conical shells has demonstrated that the basic formula yields satisfactory results for critical theo- retical pressures of medium-length shells with internal stiffeners, whereas for those with external ones these results are some-what too high.Conclusion. Calculation & analysis method suggested in this paper for stability assessment of conical bearing structures of underwater technology could be useful for the experts of dedicated research institutes and design offices.