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A New Specifying Method for Stress and Strain in an Elastic Solid

Published online by Cambridge University Press:  15 September 2014

Lord Kelvin
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The method for specifying stress and strain hitherto followed by all writers on elasticity has the great disadvantage that it essentially requires the strain to be infinitely small. As a notational method it has the inconvenience that the specifying elements are of two essentially different kinds (in the notation of Thomson and Tait e, f, g, simple elongations; a, b, c, shearings). Both these faults are avoided if we take the six lengths of the six edges of a tetrahedron of the solid, or, what amounts to the same, though less simple, the three pairs of face-diagonals of a hexahedron, as the specifying elements. This I have thought of for the last thirty years, but not till a few weeks ago have I seen how to make it conveniently practicable, especially for application to the generalised dynamics of a crystal.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 24 , 1904 , pp. 97 - 101
Copyright
Copyright © Royal Society of Edinburgh 1904

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References

page 97 note * This name, signifying a figure bounded by three pairs of parallel planes, is admitted in crystallography; but the longer and less expressive ‘parallelepiped’ is too frequently used instead of it by mathematical writers and teachers. A hexahedron, with its angles acute and obtuse, is what is commonly called, both in pure mathematics and crystallography, a rhombohedron. A right angled hexahedron is a brick, for which no Greek or other learned name is hitherto to the front in usage. A rectangular equilateral hexahedron is a cube.

page 97 note † For brevity I shall henceforth call the centre of gravity of a triangle, or of a tetrahedron, simply its centre.

page 99 note * Thomson and Tait's Natural Philosophy, § 155; Elements, § 136.

page 99 note † Thus we have an interesting theorem in the geometry of the tetrahedron:—If an ellipsoid touching the edges of a tetrahedron has its centre at the centre of the tetrahedron, the points of contact are at the middles of the edges.

page 99 note ‡ Thomson and Tait's Natural Philosophy, § 160; Elements, § 141.