The discussion centers around the mathematical representation of wire shape under tension when bent by three pivots, referred to as an "elastica." Participants debate the applicability of the elastica concept, clarifying that it encompasses more than just post-buckled columns, extending to various forms of elastic deformation. The conversation highlights the importance of defining terms like "pivot" and "wire" for clarity. A recommended resource for further understanding is “The Many Faces of Elastica” by Ivaïlo M. Mladenov and Mariana Hadzhilazova (2017).
PREREQUISITESMathematicians, structural engineers, and anyone interested in the applications of elastica theory in various fields, including biology and engineering design.
The elastica is a more general field. You are considering only your experience and should also consider other things like meanders, splines and Bezier curves.Dr.D said:That does not sound like the elastica problem at all to me. The elastica is the shape of a post-buckled column, but OP is talking about a bending problem.
No, you are mistaken. The term elastica is well defined as the shape of the post-buckled column. For all the other items you mention, we have their own names to identify them.Baluncore said:The elastica is a more general field. You are considering only your experience
The Elastica is now a multidisciplinary field of applied mathematics. While it can obviously be applied to the shape of a slender column, it is not restricted to buckling failures in structural engineering.Dr.D said:No, you are mistaken.