Isoperimetric solution to problem of prismatic bar torsion

Abstract

In the article the simple torsion problem of an elastic prismatic bar is presented in the isoperimetric form. It proves that equal sections with a convex contour have a geometrical rigidity of torsion, depending only on one parameter – the form factor. The main isoperimetric properties of the form factor are stated, and on their basis, isoperimetric properties of the given geometrical rigidity of torsion are formulated. Elliptic sections, rectangular, and triangular sections in the form of the regular figures are considered. For these subsets of bars, the approximating functions satisfying known decisions for the corresponding forms of sections with an accuracy of 2%, are constructed.