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Thermopotential function in position and time for a plate weakened by curvilinear hole

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Abstract

In this paper, we consider a conformal mapping function with complex constants coefficients to solve the problem of infinite plate weakened by a curvilinear hole. The conformal mapped is used outside the unit circle \(\varpi \) in the presence of an initial heat flowing perpendicular to the plate. All previous works, in this field, considered this problem without time and most of them regarded the conformal mapping with real constants. Here, we use complex variable method by new rational mapping to give convenient expression of Gaursat functions in applications with time effect. The hole takes different shapes that make this study applicable to many cases, such as caves, tunnels, excavations in soils or rocks. Stress components are obtained and plotted to investigate their physical meaning. Using maple 18, the different forms a hole are received and distribution of stresses in 3-D are obtained.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Education, Alexandria University, Alexandria, Egypt

    M. A. Abdou & M. Basseem

  2. Department of Mathematics, Faculty of Engineering, Sinai University, Al-Arish, Egypt

    M. A. Abdou & M. Basseem

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  1. M. A. Abdou
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  2. M. Basseem
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Abdou, M.A., Basseem, M. Thermopotential function in position and time for a plate weakened by curvilinear hole. Arch Appl Mech 92, 867–883 (2022). https://doi.org/10.1007/s00419-021-02078-x

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  • DOI: https://doi.org/10.1007/s00419-021-02078-x

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