Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On torsion of prisms with longitudinal holes

Author: Chih-Bing Ling
Journal: Quart. Appl. Math. 9 (1951), 247-262
MSC: Primary 73.2X
DOI: https://doi.org/10.1090/qam/42923
MathSciNet review: 42923
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Abstract: This paper presents a method of solution, called the method of images, for the torsion of prisms having one or more longitudinal holes. The method is applicable to prisms of the following four, and only four, sections: a rectangle, an equilateral triangle, an isosceles triangle and a $ {30^ \circ } - {60^ \circ } - {90^ \circ }$ triangle. These four sections form a group by themselves.

The solution is obtained by adding to the known solution of a corresponding solid prism without holes a system of harmonic functions which vanish on the entire external boundary of the given section, and besides possess a singularity at the centre of each hole. Such a system of functions may be constructed from Weierstrass' Sigma function and its allied functions.

The solution is illustrated by applying it in detail to a rectangular prism having a central longitudinal hole. Numerical results are shown for the special case of a square prism.

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DOI: https://doi.org/10.1090/qam/42923
Article copyright: © Copyright 1951 American Mathematical Society

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