Thermoelastoplastic deformation of a three-layer bar with a compressible filler | Mekhanika | kompozitsionnykh | materialov i konstruktsii

Thermoelastoplastic deformation of a three-layer bar with a compressible filler



Due to the intensive use of composite structures, including three-layer elements, in building and mechanical engineering there appeared a necessity to create adequate mathematical models in order to compute their stress-strain states. The present paper considers deformation of a three-layer elastoplastic bar with a compressible filler in the temperature field. To describe kinematic properties of an asymmetric through thickness pack we have accepted the hypotheses of a broken line as follows: Bernoulli’s hypothesis is true in the thin bearing layers; Timoshenko’s hypothesis is true in the compressible through thickness filler with a linear approximation of displacements through the layer thickness. The filler’s work is taken into account in the tangential direction. The physical stress-strain relations correspond to the theory of small elastoplastic deformations. Temperature variations were calculated by the formula obtained from averaging thermophysical properties of the materials of the layers through the barthickness. By the variational method a system of differential equilibrium equations has been derived. The kinematic conditions of simply supported faces of the bar on the immovable in space rigid bases are presumed on the boundary. The solution of the boundary problem is reduced to the search for four functions, namely: deflections and lengthwise displacements of the medial surfaces of the bearing layers. An analytical solution has been derived by the method of elastic solutions for the case of the uniform distribution of the continuous and local loads. Its numerical analysis has been performed. Variations of displacements in the external bearing layer have been studied under the isothermal and thermal force loads and deflections in the bearing layers depending on the spot value and the local load location Accuracy of obtained numerical results is substantiated.. The diagrams are shown for stress variations crosswise in the bar middle.