Open AccessAn analytical solution to the problem of thermoelastic bending of a multilayer beam with different temperature of longitudinal faces
Author(s) -
С. Б. Ковальчук,
O. V. Goryk
Publication year - 2021
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/1164/1/012037
Subject(s) - thermoelastic damping , quasistatic process , beam (structure) , mechanics , materials science , elasticity (physics) , transverse plane , thermal , shear (geology) , exact solutions in general relativity , plane (geometry) , classical mechanics , mathematical analysis , structural engineering , physics , mathematics , geometry , thermodynamics , composite material , optics , engineering
An exact analytical solution of the quasistatic problem of thermoelasticity is presented for a section of a narrow multilayer beam with different temperatures of the longitudinal lower and upper faces and a heat flow of arbitrary height across the sections through the lateral faces. The solution was obtained for the entire package of layers by sequentially solving the heat equation for an inhomogeneous beam, taking into account the ideal thermal contact of the layers and the system of equations of the plane problem of the theory of elasticity under the assumption of a rigid connection of the layers. To take into account the inhomogeneity of the beam, a continuum approach is used, in which the multilayer material is considered continuous with variable physical and mechanical characteristics. The resulting relations take into account the orthotropy of the physico-mechanical properties of the materials of the layers and their compliance with the transverse shear and compression strains. An example of implementation of a solution for a five-layer beam with combined rigid and articulated fastening of the ends is given.