Optimization of fibrous laminates undergoing progressive damage

Laminates made of brous composites are optimized with the objective of maximizing the remaining sti ness at the end of some given load history, during which damage and deterioration of the material have occurred. The material behaviour is thus both highly non-linear and history dependent. The design variables are the bre orientations of each of the plies. The progressive and anisotropic damage is modelled by a continuum damage model in which a set of internal damage variables describes the decrease of the elastic moduli and Poisson ratios and yet another set describes the reduction of the strength properties in each of the plies. The evolution of the deterioration is based on a principle of maximum energy dissipation. The numerical model and the formulation of a consistent tangent operator is thoroughly described. The involved design sensitivity analysis is performed by direct di erentiation in a manner fully compatible with the numerical model. The importance of taking the damage into consideration in the design process is clearly demonstrated by some computational examples where also the advantages of the optimization process become evident