The problem of plane bending a direct composite beam of arbitrary cross-section and the prerequisites for its approximate analytical solution

The approach to the reduction of the spatial problem of plane bending a composite discrete-inhomogeneous beam of arbitrary cross-section to the approximate two-dimensional bending problem of the equivalent multilayer beam has been discussed here. The result is represented in the form of relations for determination the characteristics of the equivalent multilayer structure by physical and mechanical materials characteristics of the original beam's phases and the system of static, geometric and physical relations of the corresponding two-dimensional problem. The obtained equations are similar to the plane problem equations of the elasticity theory, but instead of stresses, they contain internal efforts consolidated to the main plane of the beam. The equations of the approximate two-dimensional problem were used to solve the problem of static bending a composite console of arbitrary structure with a load on the free end, taking into account the uniform change of the temperature field. The given system of equations and relations is the starting point for the construction of non-classical deformation models and solving a wide range of problems concerning the deformation of a direct composite beams.
multilayer beam, plane bending, analytical solution, stress, strains, displacement, багатошаровий брус, плоский згин, аналітичний розв'язок, напруження, деформації, переміщення, многослойный брус, плоский изгиб, аналитическое решение, напряжения, деформации, перемещения