Torsion of tubes with quasi-polygonal holes using complex variable method

Abstract

In this paper, torsional analysis of hollow bars with specially shaped non-circular cross-sections is presented. The well-known formulation of the torsion problem in complex variable theory is used to obtain an expression for shear stresses, angle of twist and cross-sectional warping. The most important part of the solution of the torsion problem here is to obtain an appropriate closed-form conformal mapping for specially shaped cross-sections. The obtained mapping is used to achieve a solution for torsion problem of bars with specially shaped hollow cross-section. Finally, the calculated results are compared with the finite-element method solution. The presented solution is capable of accurately predicting the angle of twist, warping, and shear stress in the studied hollow bars.

Torsion of elastic solids with sparse voids parallel to the twist axis

“…It is worth remarking that, due to linearity of the governing equation (5), the mechanical fields (1) and (3) can be considered as the result of the superposition of two 'simple' remote loadings referred to the system x 1 − x 2 (Fig. 2):…”

“…cylinders with elliptical cross-section containing a single crack [18,37]; (iii.) circular shafts with quasi-regular polygonal voids [5]; (iv.) cross sections weakened by edge cracks [18,22,37,41]; (v.) neutrality of coated cavities of various shapes in cylinders with elliptical crosssection [42]; (vi.)…”

“…Beside the strong research effort in planar and three-dimensional problems of elasticity, relatively little attention has been devoted to the stress intensification in inhomogeneous solids subject to torsional loading. Within this framework, the research has mainly been focused on (i) cylindrical shafts containing notches of different geometries [20][21][22][23], (ii) cylinders with elliptical cross-sections, each containing a single crack [24,25], (iii) circular shafts with quasi-regular polygonal voids [26], (iv) cross-sections weakened by edge cracks [24,25,27,28], (v) the neutrality of coated cavities of various shapes in cylinders with elliptical cross-sections [29], (vi) multiply connected domains [24,[30][31][32][33][34][35][36] and (vii) star-shaped cracks in square and circular cross-sections [37,38]. However, except for some special geometries, the results are usually obtained through the implementation of numerical techniques; very few analytical expressions are currently available as a 'guide tool' for engineers.…”

Analyzing the structural behavior of conducting polymer actuators and its interdependence with the electrochemical phenomenon

“…The general focus of the working groups on such actuators has been towards either gaining higher bending displacement or better frequency response for the same [32,33]. Torsional displacements have been achieved only by using some kind of reinforcement [34,35]. Even though being a soft, continuous structure, such an actuator is more likely to exhibit a combination of torsion and bending.…”