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The article presents a solution to a problem on the establishment of mathematical relations between elastic constants of anisotropic fiber composites in principal anisotropy directions. A stress function in the form of a polynomial sum was used to solve the fourth-order differential equation in partial derivatives for an orthotropic body, thus allowing determining elastic constants of fiber composites with different directions of reinforcing fibers by means of mathematical calculations. It wasdoi:10.23968/2500-0055-2018-3-4-13-23 fatcat:r3gdk5ceejbq3ezu7c4we76puy