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The Construction Of The Full Asymptotics In The Method Of The Stiffness Functions For Spatial Problem Of Deformation Of Thermo-Elastic Composite Rod

Yankovskii A.P.

#### Abstract:

In dimensionless form, the linear thermo-elastic problem is formulated for the static deformation of laminated composite rods of constant cross-section in three-dimensional formulation under the influence of surface and mass loads. The rods and their layers, are considered as straight. The materials of the layers are isotropic and homogeneous in the longitudinal direction. The conditions of ideal thermo-mechanical contact are met between layers. According to the principle of independence of forces applied, the solution is sought as a sum of particular solutions, obtained independently of the temperature, surface and mass loads. In the framework of the stiffness functions method, a complete asymptotic representation is constructed for each particular solution depending on the boundary value problem given, this allows defining complex stress-strain state of composite rods outside the extreme zones of the edge effects. Relative thickness of the rods is taken as a small parameter. Every particular solution of the problem under consideration is represented as same in the form of expansions in ordinary derivatives of different orders from generalized displacements, depending on the longitudinal coordinate only. As generalized displacements, the ones averaged of cross-section of the rod are taken in three independent directions and the averaged angle of rotation relative to the longitudinal axis. Two-dimensional and one-dimensional boundary value problems that arise as a result of the splitting of the original equations of elastic deformation of composite rods are analyzed under the action both of mass and surface forces and thermal effects. The necessary conditions of solvability of these boundary value problems were obtained. It is shown that, under thermal loading of composite rod spatial thermo-elastic problem cannot be solved by the method of stiffness functions.

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