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The solution of a complex integro differential equation in the right half-plane via an infinite plate weakened by a curvilinear hole |
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PP: 493-503 |
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doi:10.18576/amis/180301
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Author(s) |
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Azhar R. Jan,
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Abstract |
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| This paper reports on a new study of a flexible plate reduced by a curvilinear slot with the cavity transported conformally to the right half-plane with complex constant parameters of the rational mapping function. Some figures of the conformal mapping for different values of complex constants were also obtained. Some special and important cases have been derived. Also, a closed form of the two Gaursat functions was derived using the complex variable method for the first and second fundamental problems. This is done by converting the first and second basic equations, in the presence of heat, into an integral differential equation in the right half plane with a Cauchy kernel. In addition, the researcher was able to discuss some important applications while studying the effect of temperature in each case. All calculations and computations of various stress components for each application are performed using the Maple 18 program. This study differs from previously published literature, which had areas mapped identically outside or inside the unit circle.
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