Talk:Virtual work

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Contents 1 Use of the term "Imaginary" 2 Rotations and Translations 3 Virtual? 4 Rewrite

[edit] Use of the term "Imaginary"

In certain cases, it is not clear if the original author(s) intended to use the term "imaginary" for terms being expressed as complex numbers, or if those terms are to be thought of as non-physical, i.e. virtual or "make-believe" as we would suspect. There are conjugates for virtul work in the complex plane (sorry, no reference). I suspect that because the formulation of virtual displacements and work is related to a differential formulation of equilibrium, and because the differential operator of the differential form is usually positive-definite, that complex numbers may not be not expressible by the principle of virtual work/displacements. In other words, the principle of virtual work/displacement is applicable for real (i.e. not complex numbers) numbers. Please consider revising. - URjyoung 15:54, 28 September 2006 (UTC)

Thanks for pointing out the need for clarification. Revised version now defines "real" as being "actual" while "imaginary" as "fictitious". TVBZ28 14:59, 30 September 2006 (UTC)

[edit] Rotations and Translations

This needs something about rotational vs. translational systems, and how you can treat the virtual work along rotations and translations as seperate.

Translations and rotations need not be treated separately, if both are required. We use what we need for the particular system and objective. For example, for particles and truss systems, there is no need for virtual rotations. On the other hand, for rigid bodies and frames, both translations and rotations are often needed, but again, that depends on what we want. Admittedly, virtual work principle is an abstract concept that even text-book authors confuse it with the principle of conservation of energy. After all, virtual displacements (rotations) are arbitrary: you choose to impose what you want, as long as it's consistent with the nature of the system. One part of the difficulty is that those who really understand it often expound it in complex mathematical terms. The second part is that the applications are so wide that a beginner might have experienced only a few situations, similar to a blind man who thinks of an elephant as a big worm while touching the elephant's trunk. The worst part is that many things are arbitrary, and most people don't know what they want, or how to get what they want. The fact that virtual displacements\forces are arbitrary is precisely the reason why virtual work principle is so powerful, unlike the principle of conservation of energy, which is nearly useless in structural mechanics. I'd hope though that most readers will be able to grasp all the nuances of the article after some pretty serious thinking and practice with the examples and exercises in the references.TVBZ28 19:43, 3 January 2006 (UTC)

[edit] Virtual?

Nowhere in the article is the term "virtual" defined. It just describes multiplying random Ds by the forces and then says those Ds are "virtual displacements". Overall, the article seems like a circular definition. —BenFrantzDale 19:51, 28 September 2005 (UTC)

That seems to be a valid criticism. The article relies on prior knowledge of calculus, particularly the differential. Since the work done is infinitesimal, it can only be defined in terms of other infinitessimals, but the concept of a differential should be introduced or at least linked to in a more accessible way if you were confused.--Joel 02:36, 29 September 2005 (UTC)

A defintion of "virtual" has been introduced. Virtual work is also valid for finite displacements and rotations (even though in applications, small displacements & rotations are often used). In any case, little is gained by introducing the more rigorous concept of "variations" at this stage. —TVBZ28 23:45, 14 December 2005

[edit] Rewrite

I'm considering doing a rewrite, but first I want to make sure I understand things. It seems that finding equilibrium using virtual work is just a special name for finding equilibrium by setting the variation of the energy of the system. Another way of saying this, I think, is that in as much as forces "want" to cause displacements, if you can find a configuration for which any small variation from that configuration results in no net work being done by the forces, you have found a configuration that is stable. Does this sound right? Does this sound like a starting point for a clearer article? —BenFrantzDale 04:47, 1 December 2005 (UTC)

OK, I rewrote it. Please fix it furhter if it needs fixing. —BenFrantzDale 05:28, 5 December 2005 (UTC)

One of the applications of the virtual work principle is to find the equilibrium configuration, and in such case, it is more apt to call it the principle of virtual displacements. On the other hand, the principle of virtual forces will lead to compatbility equations.

Since the objective of the article is to introduce the concept of virtual work, it should be kept simple as is. More in-depth treatment of the two principles and their applications as well as of variational principles and calculus can be dealt with, if desired, in additional articles. —TVBZ28 24:00, 14 December 2005

Keeping it simple is all well and good but, while I think I understand virtual work (at least as I described it in a previous version of the article), I do not understand the current version; I get lost at the first sentence: "Virtual work is the mathematical product of unrelated forces and displacements or of moments and rotations." When I read that I think "Ok, so if I multiply the weight of Chewbacca on Endor by the distance from the earth to the sun, that must be virtual work", which makes no sense. While I can basically see that the current article says what virtual work is, it doesn't answer for why it is useful or how it came about. That is what I was trying to accomplish in my rewrite. —BenFrantzDale 16:37, 15 December 2005 (UTC)

That is correct as long as the "weight of Chewbacca on Endor" and "the distance from the earth to the sun" are in the same direction; however, (i) what is the use of such virtual work is another matter; (ii) the use of large displacements will cause complications in the case of deformable bodies. We should not mix up the general definition and the usual applications. The main point is that the forces and/or the displacements could be arbitrary but in the same direction--otherwise the product is not work. —TVBZ28 18:46, 15 December 2005

Actually, I suppose as long as we use a dot product, direction shouldn't matter. But still, in the current version I don't see an explanation of what virtual work means, why this approach is useful, or how it comes about. As I understand it, virtual displacements only make sense when they are infinitessmal—that is, when you take the variation of the position of the system. In that context, its utility is that the configuration with zero virtual work is the stable configuration, and physically that configuration means "if the configuration were to change a little bit, no forces would 'get to' do any work; since no forces would get to do any work, they won't do work so the configuration won't change." In short, I would like to see the article address the questions of what it means, why it is useful, and how it is used; at the moment I only see an answer to "what it is" and one which at least I didn't find very approachable. —BenFrantzDale 00:24, 16 December 2005 (UTC)

- Agreed that if we use dot product, then direction shouldn't matter, but that needs more pre-requisite knowledge.
- Virtual displacements could be finite, and in the case of a single particle where compatibility of displacements is a non-issue, they are completely arbitrary as shown in Eq.(b). Obviously finite displacements (& rotations) cause lot of complications including the need to use different kind of stress tensors.
- The example on the particle shows:

• What is virtual work: Eq.(b) & (c) define virtual work.
• Application: Eq.(c) leading back to (a) shows how virtual work can be used for imposing equilibrium. This application should show the motivation.

Obviously, such demonstration is a bit more complex for the case of deformable bodies, and serious readers should refer to more specialized books or reference material. — TVBZ28 00:59, 16 December 2005 (UTC)