In this paper a disc, discretized into Ncomposite elements is examined. Each composite element consists of the matrix reinforced by two families of fibres. The disc is therefore made of a non-homogeneous, anisotropic material and individual expressions of matrices connecting stresses with strains depend on the direction of fibre arrangement. The principal aim is to search fibre directions of two families that determine the minimum of strain energy of composite disc. The disc is calculated using a computer program based on Finite Element Method with built-in anisotropy model. The disc was discretized into 1200 elements and optimal orientation of fibres was determined by CAMOS computer program. The problem was solved using iterative method. In the first step it was assumed that the disc is made of homogeneous, isotropic material. Having determined the state of stress, optimum orientation of fibres was chosen and suitable expressions were determined in the stiffness matrix of the disc. With these values, the stress state of the disc was determined again and optimum fibre directions were adjusted. This way of proceeding was repeated many times. In each iteration step the total elastic energy in the disc was computed. The criterion for ending the iteration process was suitably small change in the elastic energy of the disc in successive steps.
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