Author(s)

P. Procházka

Abstract

This paper is concerned with the analysis of a laminated composite cylinder, considering both the pre-stress and lay-ups of unilateral filaments, i.e. filament winding or fiber placement, which involve fiber pre-stress and the best lay-up in laminas for waviness reduction. The fiber pre-stress applied in individual plies is shown to cause an eigenstress in the respective plies, and relaxation stresses in the already completed plies. Influence functions (influence tensors) that relate the ply stresses to the applied pre-stress forces are derived. The goal is to determine fiber pre-stress distributions through the wall thickness such that the total stresses due to external hydrostatic pressure and the fiber pre-stress in individual plies are as uniform as possible through the wall thickness and confined by the ply strength magnitudes. Generalized plain strain is the starting model for the formulation of the problem, which is to be solved. Optimal pre-stress of the pseudo 3D problem based on the generalized plain strain is solved in some previous papers by the author, which leads to uniformly distributed stresses in a selected direction through the thickness of the cylinder. It is of great interest to engineers to consider the optimization of stresses that are dependent also on the lay-ups of reinforcing filaments, for example in classical composites. In order to attain the optimal result, which depends also on the arrangement of filaments, an extended cost functional has to be suggested. For the practical production and creation of such composites, see the description of the build-up process in the previous publication by Dvorak and Procházka (Thick-walled composite cylinders with optimal fiber prestress. Composites Part B 27B: 643-649 1996). The great advantage of the theoretical pseudo 3D model is in the fact that the solution of the basic problem of laminated cylinders, which describe the behavior of layered composite cylinders, is quite simple and leads to

Keywords

optimal fiber pre-stress, optimal lay-ups, laminated cylinder, hydrostatic pressure