APPROXIMATE SOLUTION TO THE PROBLEM OF TORSION OF AN IN NITE ELASTIC ROD OF NORMAL CROSS-SECTION IN THE FORM OF A NEPHROID BY A BOUNDARY INTEGRAL METHOD

Document Type : Original Article

Authors

1 Departments of Mathematics, Faculty of Science, Al-Azhar University

2 Departments of Mathematics, Faculty of Science, Cairo University

Abstract

The torsion of a long elastic bar possessing a normal cross-section bounded by a nephroid is considered by means of an
expansion in polar harmonics, in conjunction with boundary collocation method and the boundary representation of harmonic
functions.
Three types of nephroids are investigated and comparison is carried out between all three cases in what concerns the e¢
ciency of the used method.
The results are illustrated in three-dimensional plots of the unknown functions of practical interest.

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