Determination of Fiber-Structure for the Effective Reinforcement of Planar Composite-Material Constructions

Abstract

To describe the behaviour of a composite material reinforced by fibers along curvilinear trajectories, a resolving system of differential equations has been obtained. I developed a structural model within the framework of the two-dimensional non-uniform linear elasticity problem. The reinforcement is performed on the basis of three approaches: according to the grid lines of the orthogonal coordinate system determined by the given conformal representation; according to trajectories isogonal to the given curves; according to the helical trajectories in the axisymmetric formulation of the problem. Particular solutions of the corresponding boundary problems have been obtained. Recommendations for the effective reinforcement of planar constructions have been presented.