Fibre composite optimization

Fibre composites are steadily becoming more and more popular both in industry and science. This progress is unvarying for decades. The call for optimization and tailoring of the properties of the fibre composites is still clamorous and the author of the lecture is going to present his humble contribution to this field of knowledge. The paper is devoted to an optimization, namely to the stiffness maximization, of fibre composites. The fibre composite is a composite composed of a fibre (or fibres) and matrix (or matrices). The point is that the fibre can be oriented or even bent and twisted in a suitable way. The paper starts with a definition of the measure of stiffness as a quantity to be maximized. Then there is excursion into the stiffness maximization of thin plates. In the following, the emphasis is on curved fibres and structures; as the curved shapes are more natural for fibre composites. There arise the necessity to use the curvilinear tensor calculus. For the consistence of the used symbology the section shortly describing tensor calculus is placed at the begining of the paper. The implementation of the tensor calculus into the problems of fibre composite stiffness maximization is demonstrated on stiffness maximization of a thick walled elliptic tube. The paper is concluded with views on the future research that is based on the free fibre composite optimization.