Practical Green’s function for the thermal stress field induced by a heat source in plane thermoelasticity

• Published in: Applied mathematics and mechanics Vol. 41; no. 4; pp. 543 - 550
• Main Authors: Hua, Jian, Dai, Ming
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.04.2020; Springer Nature B.V; State Key Laboratory of Mechanics and Control of Mechanical Structures,Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Cylinders; Elastic deformation; Elastic media; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; Stress distribution; Thermal stress; Thermoelasticity; 74G05; finite matrix; Green’s function; O343.1; 74B05; heat source; thermal stress; O343.6; Green's function
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-020-2597-8

The classical Green’s functions used in the literature for a heat source in a homogeneous elastic medium cannot lead to finite remote thermal stresses in the medium, so that they may not work well in practical thermal stress analyses. In this paper, we develop a practical Green’s function for a heat source disposed eccentrically into an elastic disk/cylinder subject to plane deformation. The edge of the disk/cylinder is assumed to be thermally permeable and traction-free. The full thermal stress field induced by the heat source in the disk/cylinder is determined exactly and explicitly via the Cauchy integral techniques. In particular, a very simple formula is obtained to describe the hoop thermal stress on the edge of the disk/cylinder, which may be conveniently useful for analyzing the thermal stresses in microelectronic components.