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

doi:10.1007/s10483-020-2597-8

Applied Mathematics and Mechanics (English Edition) ›› 2020, Vol. 41 ›› Issue (4): 543-550.doi: https://doi.org/10.1007/s10483-020-2597-8

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

Jian HUA, Ming DAI

State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

收稿日期:2019-12-20 修回日期:2020-01-20 发布日期:2020-03-26
通讯作者: Ming DAI E-mail:m.dai@foxmail.com
基金资助:
Project supported by the National Natural Science Foundation of China (No. 11902147), the Natural Science Foundation of Jiangsu Province of China (No. BK20190393), and the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions

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

Jian HUA, Ming DAI

State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Received:2019-12-20 Revised:2020-01-20 Published:2020-03-26
Contact: Ming DAI E-mail:m.dai@foxmail.com
Supported by:
Project supported by the National Natural Science Foundation of China (No. 11902147), the Natural Science Foundation of Jiangsu Province of China (No. BK20190393), and the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions

摘要/Abstract

摘要： 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.

关键词: heat source, Green’s function, thermal stress, finite matrix

Abstract: 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.

Key words: heat source, Green’s function, thermal stress, finite matrix

中图分类号:

74B05
74G05

Jian HUA, Ming DAI. Practical Green’s function for the thermal stress field induced by a heat source in plane thermoelasticity[J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(4): 543-550.

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

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

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