Analysis and optimal design of pressurized, imperfect, anisotropic ring-stiffened cylinders

Development of an algorithm to perform the structural analysis and optimal sizing of buckling resistant, imperfect, anisotropic ring-stiffened cylinders subjected to axial compression, torsion, and internal pressure is presented. The structure is modeled as a branched shell. A nonlinear axisymmetric prebuckling equilibrium state is assumed which is amenable to exact solution within each branch. Buckling displacements are represented by a Fourier series in the circumferential coordinate and finite elements in the axial or radial coordinate. A separate, more detailed analytical model is employed to predict prebuckling stresses in the flange/skin interface region./p>

Results of case studies indicate that a nonlinear prebuckling analysis is needed to accurately predict buckling loads and mode shapes of these cylinders, that the rings have a greater influence on the buckling resistance as the relative magnitude of the torsional loading to axial compression loading is increased, but that this ring effectiveness decreases somewhat when internal pressure is added./p>

The enforcement of stability constraints is treated in a way that does not require any eigenvalue analysis. Case studies performed using a combination of penalty function and feasible direction optimization methods indicate that the presence of the axisymmetric initial imperfection in the cylinder wall can significantly affect the optimal designs. Weight savings associated with the addition of two rings to the unstiffened cylinder and/or the addition of internal pressure is substantial when torsion makes up a significant fraction of the combined load state./p>

Assumption of criticality of the stability constaints and neglect of the stress constraints during the optimal sizing of the cylinders produced designs that nevertheless satisfied all of the stress constraints, in general, as well as the stability constraints. Subsequent re-sizing of one cylinder to satisfy a violated in-plane matrix cracking constraint resulted in an optimal design that was 49% heavier than the optimal design produced when this constraint was ignored.

The additional internal pressure necessary to produce a violation of a stress constraint for each optimal design was calculated. Using an unsymmetrically laminated ring flange, a substantial increase in the strength of the flange/skin joint was observed.