EFFECT OF SMALL INITIAL IRREGULARITIES ON THE STRESSES IN CYLINDRICAL SHELLS
Abstract
The Marbec method is used in the small-deflection case of predicting bending moments and stresses due to dents and initial out-of-roundness in rings under hydrostatic pressure. A numerical approach is developed for the large- deflection analysis of circular rings with initial imperfections, considering both the deflections and the extension of the ring axis. In a simplified method of analysis which includes the effect of axial forces, moments predicted by the small-deflection theory are multiplied by factors proportional to the relative amplitudes of the various buckling modes present in the original shape. The shape of a ring with initial out-of-roundness can be expressed as a Fourier series. The problem of a cylindrical shell with a dent varying in magnitude along the longitudinal axis of the cylinder is solved for a uniform-pressure load. The 3 governing displacement equations consist of the equations for a perfect circular cylinder shell plus the correction terms for the imperfections of the shell. Results indicate that when the wave length of the dent is large compared with the initial radius of the cylindrical shell, the solution coincides with the 2-dimensional case. As the wave length decreases, bending moments decrease and membrane stresses predominate. As the wave length decreases still further and the dent becomes more localized, bending moments again increase.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 07, 1953
- Accession Number
- AD0011754
Entities
People
- L. E. Goodman
- N. M. Newmark
- T. S. Wu
Organizations
- University of Illinois Urbana–Champaign