Bulging factors and geometrically nonlinear responses of cracked shell structures under internal pressure

An approach based on the transverse or out-of-plane nonlinear dynamic responses at the centers of edges of cracks is being proposed as a viable alternative to bulging factors for damage tolerance design and characterization of cracked cylindrical shell structures under applied internal pressure. This approach circumvents the problems of mesh selection at the crack tip in the finite element analysis for bulging factors and provides information about the influence of crack lengths as well as crack widths on responses. The influence of crack widths on responses has been found to be significant but it is not available in bulging factors. Furthermore, existing individual bulging factor only applies to a different range of ratios of crack length to radius of shell. It is concluded that (i) the proposed approach has no limit on the range of ratios of crack length to radius of shell; (ii) conceptually, the proposed approach is simple, and (iii) computationally, the nonlinear responses at the centers of edges of cracks are relatively easy to obtain accurately and efficiently by using the mixed formulation-based shell finite elements since the present dynamic approach converges quickly at very coarse meshes.