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

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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.

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Author notes

  1. two authors contributed equally to this work

Authors and Affiliations

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

    Jian Hua & Ming Dai

Authors
  1. Jian Hua
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  2. Ming Dai
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Corresponding author

Correspondence to Ming Dai.

Additional information

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

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Hua, J., Dai, M. Practical Green’s function for the thermal stress field induced by a heat source in plane thermoelasticity. Appl. Math. Mech.-Engl. Ed. 41, 543–550 (2020). https://doi.org/10.1007/s10483-020-2597-8

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  • DOI: https://doi.org/10.1007/s10483-020-2597-8

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2010 Mathematics Subject Classification

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