Treatise on natural philosophy : Vol 1. Part 2 / by Sir William Thomson and Peter Guthrie Tait.
- Date:
- 1883
Licence: Public Domain Mark
Credit: Treatise on natural philosophy : Vol 1. Part 2 / by Sir William Thomson and Peter Guthrie Tait. Source: Wellcome Collection.
Provider: This material has been provided by the Royal College of Physicians of Edinburgh. The original may be consulted at the Royal College of Physicians of Edinburgh.
491/594 page 461
![The following Appendices are reprints of papers published at various times. Excepting where it is expressly so stated, or where it is obvious from the context, they speak as from the date of publication. The marginal notes are however now added for the first time. (C.)—Equations of Equilibrium of an Elastic Solid DEDUCED FROM THE PRINCIPLE OF ENERGY*. (a) Let a solid composed of matter fulfilling no condition of isotropy in any part, and not homogeneous from part to part, be given of any shape, unstrained, and let every point of its surface be altered in position to a given distance in a given direction. It is required to find the displacement of every point of its substance, in equilibrium. Let x, y, 2 be the co-ordinates of any particle, P, of the substance in its undisturbed position, and x + a, y + (3, z + y its co-ordinates when displaced in the manner strain of specified: that is to say, let a, (3, y be the components of the tude sped-' required displacement. Then, if for brevity we put elements* £ = G = a = b = c — e *■)'*©'* (s dx da\ dy) © + (iHs-y \dy J dz dy\dz J \ , , (dy , Ady J dz dx \dz )dx fa + + dfi(dj3 \ dydy \dx J dy dx \dy J dx dy da da dy dz da /da dz \dx + (i); these six quantities A, B, C, a, b, c are proved [§ 190 (e) and §181 (5)] to thoroughly determine the strain experienced by the * Appendix to a paper by Sir W. Thomson on “ Dynamical problems re- garding Elastic Spheroidal Shells and Spheroids of incompressible liquid.” Pliil. Trans. 18G3, Vol. 153, p. 010.](https://iiif.wellcomecollection.org/image/b21987312_0491.jp2/full/800%2C/0/default.jpg)
