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

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 ϖ in the presence of an initial heat flowing perpendicular to the plate. All previou...

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Bibliographic Details
Published inArchive of applied mechanics (1991) Vol. 92; no. 3; pp. 867 - 883
Main Authors Abdou, M. A., Basseem, M.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2022
Springer Nature B.V
Subjects
Caves
Classical Mechanics
Complex constants
Complex variables
Conformal mapping
Constants
Engineering
Original
Soil investigations
Soil stresses
Theoretical and Applied Mechanics
Complex variable
30C20
74B99
Curvilinear hole
Conformal mapping
Plane elasticity
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Summary: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 ϖ 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.
ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-021-02078-x