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I finished this whole article before finding the Linear elasticity article, which covers this idea in a different way. I think the 15 equations are still useful to be able to reference, if only because they help to explain the nature of stress. The two pages should probably be combined, but I'm not sure how exactly. Someone could even go as far as to delete this page, as long as the equations were added to the Linear elasticity page somehow. - EndingPop 17:19, 23 December 2005 (UTC)Reply[reply]

Hello everyone. I am actually pretty new to Wikipedia so I thought I’d post something here before making any significant changes to this article. I think that the equations presented here are clearer for most people to understand than in the Linear elasticity page, since a lot of people are not familiar (or comfortable) with the more compact and abstract way of expressing the equations through index or symbolic notation. For this reason I think this page is extremely helpful, although it presents much of the same material included in the Linear Elasticity page.

I do, however, have some questions and suggestions about the current article. The first line reads, “3D elasticity is one of three methods of structural analysis”. What are these three methods?

The next sentence reads, “This method is used for analyzing structures that behave in a linearly elastic fashion.” From my experience, 3D Elasticity does not denote Linear Elasticity. In general, Elasticity means that the deformation of a structure due to loading is such that it can be expressed through constitutive equations relating the internal forces (components of stress) to the displacements (components of strain). These relationships need not be linear which is why Hyperelasticity is a subset of Elasticity.

In addition, the strain-displacement and compatibility equations presented here are only valid for small deformations (an inherent assumption of the Linear Theory of Elasticity). For these reason I think that the title of this article does not totally correspond with the subject matter. This article presents a description of the three dimensional Theory of Linear Isotropic Elasticity which is a special case of the more general Nonlinear Theory of Elasticity or what I think of when I hear 3D Elasticity.Gpayette 21:37, 10 February 2007 (UTC)Reply[reply]

The line about the "3 methods of structural analysis" refers to the Structural analysis page, I'll update this page with the appropriate link.

As for the sentence "This method is used for analyzing structures that behave in a linearly elastic fashion." How would just "...in an elastic fashion." sit with you? A link to Elasticity should be included.

As for the rest of your comments, as the original author, I agree entirely. I would entirely support a more general form, though I'd like to preserve the LEHI version of the equations as a special (but important) case. - EndingPop 15:52, 12 February 2007 (UTC)Reply[reply]

My first point is already taken care of. If you check out the Structural analysis page, you'll see what is mentioned. - EndingPop 15:54, 12 February 2007 (UTC)Reply[reply]

I updated the Equilibrium Equations section to provide a more thorough background into the origin of these equations and the meanings of the terms (i.e., Cauchy Stress tensor, body forces, etc.). Let me know what you think of the additions. As I mentioned before, I'm really new to editing Wikipedia articles, so I hope that I didn't get too carried away.

I would also like to add to the Strain-Displacements Equations section. I think that it would be good to begin this section with a very brief discussion of the Green-Lagrange strain tensor, which is often used in modeling structures undergoing large deformations. We can then show that when deformations are small, the nonlinear Green-Lagrange strain tensor reduces to the linear strain equations that you already have in this section. Gpayette 05:04, 15 February 2007 (UTC)Reply[reply]

I, for one, like what you did with the page. As they say Be bold!. I started this page after taking an undergraduate level linear elasticity course, so that is where I was coming from then. Now that I'm in grad school, I'm learning that quite a bit is missing from that basis. To summarize, keep doing what you are doing. - EndingPop 19:53, 15 February 2007 (UTC)Reply[reply]

I think we should stick to 3D in the article title, as 3D redirects to 3D. But I am more in favour of merging this article into linear elasticity. Berland 07:15, 20 February 2007 (UTC)Reply[reply]