Design and fabrication of submerged cylindrical laminates—II. Effect of fiber pre-stress

This is the sequel to the first part of this paper (Dvorak et al., 1999, Int. J. Solids Structures 36, 3917–3943) , concerned with modeling and analysis of laminated composite cylinder fabrication procedures, such as filament winding or fiber placement, which involve fiber pre-stress for waviness reduction as well as overall or local heating to and cooling from matrix curing temperatures. The fiber pre-stress applied in individual plies is shown to cause a self-stress in the respective plies, and relaxation stresses in the already completed plies and in the supporting mandrel. The final residual stress state is reached after mandrel removal. Influence functions that relate the ply stresses to the applied pre-stress forces are derived. Direct problems are solved for ply stresses caused by prescribed constant or linearly or parabolically changing pre-stress magnitudes in the layers. A superposition of the constant and parabolic distributions is shown to lead to nearly uniform stresses through the cylinder wall. The magnitudes depend on the radial stiffness of the mandrel that supports the structure during fabrication. Inverse problems are formulated as nonlinear optimizations and solved by quadratic programming. The goal is to determine fiber pre-stress distributions through the wall thickness such that the total stresses due to external hydrostatic pressure and fiber pre-stress are as uniform as possible through the wall thickness and confined by the ply strength magnitudes.