Nonlinear numerical analysis of axisymmetrically loaded arbitrary shells of revolution

The nonlinear interaction between the meridional stress resultant and rotation is significant in discontinuity regions of highly strained, thin-shell structures. The nonlinear equilibrium equations may be linearized for any given axisymmetric-load condition by inserting the meridional stress resultant, obtained from membrane analysis, where it appears in product terms. Forward integration is used to solve the set of linear differential equations that is derived from the linear straindisplacement relations and the linearized equilibrium equations. By introducing artificial boundaries within the shell, the extent of integration is limited to conform with available numerical techniques. Influence coefficients for segments are computed, and standard methods of matrix structural analysis are used to obtain stress resultants and displacements at the segment interfaces. These are used as initial values for a final numerical integration to determine stresses and displacements throughout the shell. The differences between stresses calculated by means of linear and nonlinear equations are represented graphically from the results of the analysis of a typical pressure vessel support joint. The well-known reduction of peak stresses in the vessel wall is verified, but the bending stress in the support skirt is greater with the nonlinear analysis.