Open AccessThermal Stresses in an Elastic Clamped Square: 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 - 10.1088/1742-6596/1730/1/012143
Subject(s) - square (algebra) , eigenfunction , exact solutions in general relativity , boundary value problem , plane (geometry) , simple (philosophy) , mathematical analysis , thermal , mathematics , series (stratigraphy) , geometry , materials science , eigenvalues and eigenvectors , thermodynamics , physics , geology , paleontology , philosophy , epistemology , quantum mechanics
This paper presents a method for determining thermal stresses in an elastic clamped square with a given temperature distribution (the plane problem). First, the solution to the temperature problem for an infinite plane is constructed. Then, the solution for a square is added to this solution, with the help of which the boundary conditions on its sides are satisfied. The thermal stresses have been obtained in the form of series in Papkovich–Fadle eigenfunctions, the coefficients of which are determined explicitly. The final formulas are simple and can easily be used in engineering.