Strength And Stability Analyses For Sphere–Toroid–Cone Rotational Shells

Pursuing deep dive is one of the main development directions of modern submarine. With thedepth increasing, the pressured structure should not only to endure the higher pressure, butalso to possess lesser weight. The spherical bulkhead can endure the heavier pressure whilethe weight of structure is light, because that its stress distribution is uniform and its materialstrength is taken full advantage under external pressure. So the spherical bulkhead is thecommon structure form of the submarine. The strength of the conjunction and the stability ofthe spherical shell, however, are urgent to be resolved in design. This paper is focus on thesetwo aspects of the spherical bulkhead joined with pressured cone (sphere-toroid-conerotational shells).Firstly, an application of the transfer matrix method and the homogenization of high precisiondirect integration method for strength calculation of the sphere-toroid-cone rotational shellunder external pressure is presented. In comparison with the finite element method, thetransfer matrix method, which is a semi-analytical method developed in recent years, hasmore accuracy and efficiency. The influence of the parameters, including slopes of thetoroid-cone, radii of the sphere shell,radii of the toroid shell, and the distance between thetoroid-cone conjunction and the close rib, is investigated. The conclusion can be referencedata for design. The linear stability of the sphere-toroid-cone combined shell is carried out bythe same method. The parametric study is also conducted, considering the effect of the conesemi-vertex angle, the radius of the spherical shell, the thickness of the spherical shell, theradius of the toroid shell, and the thickness of the toroidal shell on the stability analysis. Theresult, which can be reference data for design, shows that the radius of the spherical shell andthe thickness of the spherical shell play the vital roles on the critical pressure.A new method called the differential quadrate method is developed for the nonlinear stabilityanalysis of spherical shells with local axisymmetric imperfections under uniform external pressure. The local axisymmetric imperfection area is separated from the structure and treatedas the shallow spherical shell which is elastically supported on the rest part.The formulationof the shallow spherical shell is firstly derived through the differential quadrate method. Bymeans of the Newton-Raphson method, the nonlinear solution is obtained. The influence ofdifferent amplitudes of imperfections and the thickness of the shallow spherical shell arestudied.Combined with the interrelated issue research, two scale models of sphere-toroid-conecombined shells are established. The reliability of the transfer matrix method calculating thestrength of the sphere-toroid-cone rotational shell is validated by the experimental result ofthe first model. And the result of predicting the critical pressure by the differential quadratemethod is in good agreement with the experimental result of the second model.The strength and stability of the sphere-toroid-cone rotational shell are carried out thoroughlyby the theoretical and experimental method, which can serve as a valuable reference formodern submarine designer of of the spherical bulkhead.