Open AccessThermoelastic Problem for a Free Square Plate: Exact Solution
Author(s) -
Alexander P. Kerzhaev
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1936/1/012008
Subject(s) - thermoelastic damping , eigenfunction , square (algebra) , exact solutions in general relativity , mathematical analysis , plane (geometry) , boundary value problem , mathematics , boundary (topology) , series (stratigraphy) , thermal , geometry , eigenvalues and eigenvectors , physics , thermodynamics , geology , paleontology , quantum mechanics
The paper presents a method for determining thermal stresses in an elastic free square plate (the plane problem). First, we construct the solution to the nonhomogeneous temperature problem for an infinite plane. Then, we add to this solution the solution for a square, with the help of which the required boundary conditions on its sides are satisfied. The temperature factors are obtained in the form of explicit series in Papkovich–Fadle eigenfunctions.