Torsion of uniform bars with polygon cross-section
The author uses Trefftz's integral for the complex torsion function to solve the corresponding problem in the case of a polygonal cross-section. By means of Schwartz-Christoffel mapping one derives the governing equations of the problem. The solution is carried out in series form according to von Koppenfels and Stallmann method, by the separation into regular and singular corner functions; Frobenius and Taylor series are thus used. Torsion stiffness is computed, and the effect of rounding of corners, even of concave ones, by circular arcs is estimated. We notice that the convergence disks of Schwarz-Christoffel and Trefftz integrals are the same, which is very convenient. A triangle cross-section, in particular equilateral, isoscele, and rectangulare ones, is considered, as well as regular and general \(n\)-sided polygonal cross-sections. Two appendices contain numerical results.
scientific article; zbMATH DE number 2082586
scientific article