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Will someone please crack a textbook and find a good definition for virtual force and place it at the top of the article, as I have done for virtual displacement? Thanks. ChrisChiasson 05:42, 24 September 2007 (UTC)
The article mentions that virtual force can refer to a force or a moment. Can someone explain how moments are used in the basic equations? (I don't see moments mentioned anywhere else...) 141.83.42.10 ( talk) 05:45, 8 July 2011 (UTC) Ok, understood my problem: If there are external moments, they can simply replace the product of force and its infinitesimal displacement. Is this correct? Can this be mentioned somewhere? Thanks. — Preceding unsigned comment added by 141.83.42.10 ( talk) 06:08, 8 July 2011 (UTC)
Virtual work doesn't just provide a method of obtaining deflections in continuum mechanics. It also forms the basis of Lagrangian mechanics - a point which seems to have escaped (most of) that article. I intend to write some stuff about that aspect of virtual work here so that I may refer to it from there. Hopefully, this will be an opportunity to make the virtual work article more well rounded. ChrisChiasson 05:42, 24 September 2007 (UTC)
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)
This needs something about rotational vs. translational systems, and how you can treat the virtual work along rotations and translations as seperate.
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)
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
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)
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
- 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:
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)
If you want an idea of how the article should be written with clarity, take a look at:-
212.139.80.204 18:47, 22 April 2007 (UTC)
What is the use of the principle of virtual work? Does it allow you to solve problems you couldn't solve with a force diagram? Does it make solutions simpler? I think the article would benefit from an example of how and why this principle is used. 128.135.230.129 ( talk) 20:32, 1 October 2009 (UTC)
"I have a opinion that the results from a displacment method and a force method would be different depending shape functions used in the displacement method and it would be helpful to adress this issue to the reader's of this topic." Changhee1220 ( talk) 12:39, 30 April 2011 (UTC)
I would like to propose some revisions to this article. In its most basic form the principle of virtual work is critical to the analysis of machines modeled as assemblies of rigid bodies. Separately, this principle finds use in the study of deformable bodies. These are two very important but different areas in mechanics. Can we provide a general introduction and then separate the presentation of these topics to help the reader? Prof McCarthy ( talk) 06:13, 7 July 2011 (UTC)
The current version of this article addresses much space to deformable bodies. I will focus my efforts on the classical formulation of virtual work for rigid body systems. You can see what I am developing at the Virtual work draft. I would appreciate any advice. Prof McCarthy ( talk) 20:11, 8 July 2011 (UTC)
I added the new introduction, and commented out the old one. I thought it became too technical too fast, but anything that is considered important can be added by just selecting it from the commented section. Prof McCarthy ( talk) 21:21, 8 July 2011 (UTC)
I added a small section on the history of virtual work. Prof McCarthy ( talk) 17:27, 9 July 2011 (UTC)
I added the introduction section that I hope provides useful definitions of the basic concepts of the principle of virtual work. Prof McCarthy ( talk) 01:40, 10 July 2011 (UTC)
I expanded the section on static equilibrium. I commented out some of what was there before. I hope that is ok. I am close to being done. I would like to add a couple examples. Prof McCarthy ( talk) 03:19, 11 July 2011 (UTC)
I am thinking about adding the figure shown at right to the article. Hopefully this will be of some help in explaining the concept. Please comment. Thanks!-- LaoChen ( talk) 05:46, 13 July 2011 (UTC)
I added a section on the use of virtual work in the static analysis of one degree-of-freedom mechanisms. I hope to add examples in the near future. Prof McCarthy ( talk) 06:17, 20 July 2011 (UTC)
I have added a detailed derivation of the law of the lever using the principle of virtual work. It is probably over-done, but I believe it illustrates the calculations and the insight that they can provide. Prof McCarthy ( talk) 15:24, 21 July 2011 (UTC)
I have added the virtual work analysis of a gear train, which is rather straight forward. Prof McCarthy ( talk) 03:12, 22 July 2011 (UTC)
This seems incorrect to me: "The principle of virtual work requires that a system of rigid bodies acted on by the forces and moments Fj and Mj is in equilibrium if the generalized forces Fi are zero."
Since you can define your generalize coordinates such that the generalized forces are exactly equal to the real forces, how could this possibly be true? You can easily construct a trivial system in equilibrium such that the generalized forces are not zero. Or am I misunderstanding something?
On the other hand, the sum of all the virtual work done by each generalized force is zero in a system at equilibrium. Perhaps this is a misstatement of this? PenguiN42 ( talk) 00:57, 5 November 2011 (UTC)
I find the equation about the virtual work done by an applied moment misleading, since it suggests that you have to differentiate the rotation vector towards the generalized coordinates (calculate a jacobian), but that is not true. Every time I need to apply a moment I come across this topic and I'm struggling with it but it does not need to be so difficult. Therefore i would like to add something in plain English on how to calculate the virtual work done by a moment. If w is a (3x1)unit vector pointing in the direction of the moment M, seen in an absolute coordinate system and r is the (3x1)unit vector pointing in the direction of generalized coordinate i, also seen in an absolute coordinate system, then the virtual work Q done by M in the direction of qi is
Q(i) = w.'*r*T,
Where T is the norm of M. That said I hope i will never be confused again. — Preceding unsigned comment added by Street missile ( talk • contribs) 11:18, 23 November 2011 (UTC)
An editor has revised the sentence "that nature selects from from a set of "tentative" realities.." to "the outcome is selected from a set of "tentative" realities." I guess the passive voice eliminates the need to think about who or what is doing the selecting, but the fact remains that the theory is clear that of the many trajectories the one that we experience is the one that optimizes a quantity. While the personalization of this as "selection" may bother some today, it was the culture of the time to consider this indeed to be a selection. We can acknowledge this though it may not match our current understanding. Then again it is worth noting that modern physics and cosmology are ambiguous on this issue of our selection among possible universes. Prof McCarthy ( talk) 02:33, 12 May 2012 (UTC)
Where are the figures cited for the deformable bodies section? — Preceding unsigned comment added by 2620:83:8001:24:0:0:1:174D ( talk) 18:29, 10 January 2017 (UTC)
![]() | This ![]() It is of interest to the following WikiProjects: | ||||||||||||||||||||||||||||||||||||
|
Will someone please crack a textbook and find a good definition for virtual force and place it at the top of the article, as I have done for virtual displacement? Thanks. ChrisChiasson 05:42, 24 September 2007 (UTC)
The article mentions that virtual force can refer to a force or a moment. Can someone explain how moments are used in the basic equations? (I don't see moments mentioned anywhere else...) 141.83.42.10 ( talk) 05:45, 8 July 2011 (UTC) Ok, understood my problem: If there are external moments, they can simply replace the product of force and its infinitesimal displacement. Is this correct? Can this be mentioned somewhere? Thanks. — Preceding unsigned comment added by 141.83.42.10 ( talk) 06:08, 8 July 2011 (UTC)
Virtual work doesn't just provide a method of obtaining deflections in continuum mechanics. It also forms the basis of Lagrangian mechanics - a point which seems to have escaped (most of) that article. I intend to write some stuff about that aspect of virtual work here so that I may refer to it from there. Hopefully, this will be an opportunity to make the virtual work article more well rounded. ChrisChiasson 05:42, 24 September 2007 (UTC)
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)
This needs something about rotational vs. translational systems, and how you can treat the virtual work along rotations and translations as seperate.
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)
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
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)
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
- 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:
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)
If you want an idea of how the article should be written with clarity, take a look at:-
212.139.80.204 18:47, 22 April 2007 (UTC)
What is the use of the principle of virtual work? Does it allow you to solve problems you couldn't solve with a force diagram? Does it make solutions simpler? I think the article would benefit from an example of how and why this principle is used. 128.135.230.129 ( talk) 20:32, 1 October 2009 (UTC)
"I have a opinion that the results from a displacment method and a force method would be different depending shape functions used in the displacement method and it would be helpful to adress this issue to the reader's of this topic." Changhee1220 ( talk) 12:39, 30 April 2011 (UTC)
I would like to propose some revisions to this article. In its most basic form the principle of virtual work is critical to the analysis of machines modeled as assemblies of rigid bodies. Separately, this principle finds use in the study of deformable bodies. These are two very important but different areas in mechanics. Can we provide a general introduction and then separate the presentation of these topics to help the reader? Prof McCarthy ( talk) 06:13, 7 July 2011 (UTC)
The current version of this article addresses much space to deformable bodies. I will focus my efforts on the classical formulation of virtual work for rigid body systems. You can see what I am developing at the Virtual work draft. I would appreciate any advice. Prof McCarthy ( talk) 20:11, 8 July 2011 (UTC)
I added the new introduction, and commented out the old one. I thought it became too technical too fast, but anything that is considered important can be added by just selecting it from the commented section. Prof McCarthy ( talk) 21:21, 8 July 2011 (UTC)
I added a small section on the history of virtual work. Prof McCarthy ( talk) 17:27, 9 July 2011 (UTC)
I added the introduction section that I hope provides useful definitions of the basic concepts of the principle of virtual work. Prof McCarthy ( talk) 01:40, 10 July 2011 (UTC)
I expanded the section on static equilibrium. I commented out some of what was there before. I hope that is ok. I am close to being done. I would like to add a couple examples. Prof McCarthy ( talk) 03:19, 11 July 2011 (UTC)
I am thinking about adding the figure shown at right to the article. Hopefully this will be of some help in explaining the concept. Please comment. Thanks!-- LaoChen ( talk) 05:46, 13 July 2011 (UTC)
I added a section on the use of virtual work in the static analysis of one degree-of-freedom mechanisms. I hope to add examples in the near future. Prof McCarthy ( talk) 06:17, 20 July 2011 (UTC)
I have added a detailed derivation of the law of the lever using the principle of virtual work. It is probably over-done, but I believe it illustrates the calculations and the insight that they can provide. Prof McCarthy ( talk) 15:24, 21 July 2011 (UTC)
I have added the virtual work analysis of a gear train, which is rather straight forward. Prof McCarthy ( talk) 03:12, 22 July 2011 (UTC)
This seems incorrect to me: "The principle of virtual work requires that a system of rigid bodies acted on by the forces and moments Fj and Mj is in equilibrium if the generalized forces Fi are zero."
Since you can define your generalize coordinates such that the generalized forces are exactly equal to the real forces, how could this possibly be true? You can easily construct a trivial system in equilibrium such that the generalized forces are not zero. Or am I misunderstanding something?
On the other hand, the sum of all the virtual work done by each generalized force is zero in a system at equilibrium. Perhaps this is a misstatement of this? PenguiN42 ( talk) 00:57, 5 November 2011 (UTC)
I find the equation about the virtual work done by an applied moment misleading, since it suggests that you have to differentiate the rotation vector towards the generalized coordinates (calculate a jacobian), but that is not true. Every time I need to apply a moment I come across this topic and I'm struggling with it but it does not need to be so difficult. Therefore i would like to add something in plain English on how to calculate the virtual work done by a moment. If w is a (3x1)unit vector pointing in the direction of the moment M, seen in an absolute coordinate system and r is the (3x1)unit vector pointing in the direction of generalized coordinate i, also seen in an absolute coordinate system, then the virtual work Q done by M in the direction of qi is
Q(i) = w.'*r*T,
Where T is the norm of M. That said I hope i will never be confused again. — Preceding unsigned comment added by Street missile ( talk • contribs) 11:18, 23 November 2011 (UTC)
An editor has revised the sentence "that nature selects from from a set of "tentative" realities.." to "the outcome is selected from a set of "tentative" realities." I guess the passive voice eliminates the need to think about who or what is doing the selecting, but the fact remains that the theory is clear that of the many trajectories the one that we experience is the one that optimizes a quantity. While the personalization of this as "selection" may bother some today, it was the culture of the time to consider this indeed to be a selection. We can acknowledge this though it may not match our current understanding. Then again it is worth noting that modern physics and cosmology are ambiguous on this issue of our selection among possible universes. Prof McCarthy ( talk) 02:33, 12 May 2012 (UTC)
Where are the figures cited for the deformable bodies section? — Preceding unsigned comment added by 2620:83:8001:24:0:0:1:174D ( talk) 18:29, 10 January 2017 (UTC)