Wire Tension Formula: Shape Expression w/ 3 Pivots

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Discussion Overview

The discussion revolves around finding an expression for the shape of a wire bent by three pivots, considering the tension in the wire and other physical factors. The scope includes theoretical aspects of elasticity and the mathematical representation of curves related to bending problems.

Discussion Character

  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant seeks to express the shape of a wire bent by three pivots, indicating that tension and other physical factors are involved.
  • Another participant introduces the term "elastica" as a relevant concept, linking it to the mathematical study of curves.
  • Some participants argue that the elastica is not applicable to the OP's bending problem, suggesting that it pertains to post-buckled columns rather than the specific scenario described.
  • There are mentions of other mathematical constructs like meanders, splines, and Bezier curves as potentially relevant to the discussion.
  • One participant emphasizes the need for a more complete description of the problem, questioning the definitions of "pivot" and "wire" used by the OP.
  • Another participant asserts that the elastica is a multidisciplinary field and not limited to structural engineering applications, challenging the restrictive view of its definition.
  • There is a call for further study of the elastica concept in broader contexts, such as biological structures.

Areas of Agreement / Disagreement

Participants express competing views on the applicability of the elastica concept to the OP's question. There is no consensus on the definitions and relevance of the terms used, leading to an unresolved debate.

Contextual Notes

The discussion highlights the complexity of the elastica problem and the need for clarity regarding the definitions of key terms, such as "pivot" and "wire." There are unresolved assumptions about the physical context and mathematical representation of the bending problem.

Goinger
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TL;DR
If the wire is bent by three pivots, I want to find an expression that represents its shape.
If the wire is bent by three pivots, I want to find an expression that represents its shape.
There will be tension of wire and other physical factors.
How can it be expressed?
 
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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.
 
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.
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.

The "pivots" are control points or boundary conditions, while the elastic deformation is distributed through the elastic bending of the rod between the pivots.

Because the elastica problem can become complex, the OP needs to present a more complete description of the question. Maybe define "pivot" and "wire".
 
Baluncore said:
The elastica is a more general field. You are considering only your experience
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.
 
Dr.D said:
No, you are mistaken.
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.

As a narrow minded structural engineer you have no right to censor the OP, nor to deny the use of Elastica, for example, to biological structural membranes and their equilibrium positions.

I suggest you find and study a copy of “The Many Faces of Elastica” by Ivaïlo M. Mladenov and Mariana Hadzhilazova. 2017.
 
Thread closed for Moderation...

After a Mentor discussion, the thread will stay closed.
 
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