Theory of Anisotropic Layered Beams in Spatial Statement. Updating the Theoretical Heritage of Prof. P.A. Zhilin

A theory of deformation of layered composite beams is developed based on the application of the asymptotic splitting method to a spatial problem of elasticity theory. A system of four ordinary differential equations with constant coefficients for three unknown macrodisplacements functions and an unknown function of the twist angle of the beam cross section is obtained. The type and order of these equations depend on the number of the asymptotic approximation. The coefficients of the specified system are integral characteristics of auxiliary boundary value problems in the cross section of the beam. The theory presented contains a system of four coupled equations, i.e. in the general case, the processes of bending in two planes, tension-compression and torsion are coupled. The theory obtained includes as a special case the following theories: the classical Bernoulli-Euler beam theory; the Timoshenko beam theory; the Saint-Venant free torsion theory; the Vlasov theory of thin-walled beams of open cross section.