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Abstract
A general three-dimensional (3D) shape assumed by a perfectly elastic rod buckled by appropriate forces and twisted couples at its ends was presented. It is shown that the elastica rod dimensions are dependent on the ratio of its bending rigidity to the torsional rigidity. The torsional angle at the ends of elastica also influences the values of twisted elastica dimensions. Also, by comparing the 3D and 2D shapes of the loop, it was confirmed that the ratio of maximum height to maximum width (aspect ratio) of buckled–twisted elastic rod is less than that of buckled rod (2.08). The theoretical analysis was evaluated experimentally by measuring the geometrical properties of the rods made from the common textile material (polyester, nylon 6, polyethylene, and polypropylene) with different elastic properties. A good agreement is observed between the theoretical assessment and experimental measuring data.
Acknowledgement
The authors thank Dr. Amirbayat, Professor of Textiles Department of UMIST, Manchester, United Kingdom, for his advice and help in regards to some theoretical part of this research.