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 Network
theory, developed for electrical circuits has been applied to the solution
of Saint-Venant torsion and bending of multi-cell thin walled sections.
The theory has been previously employed on a variety of problems including
mechanical space-frame structures. However, in that case a direct
mechanical analogue of the electrical problem was impractical. Thin
walled sections are particularly suited to the network approach, much more
so even than electrical circuits, as they do not suffer from elements
with zero 'resistance' or zero 'conductance' that give rise to singularities
in the solution.
The principal advantage of the Network approach
is that it enables the topological aspects of a problem to be separated
from its physical characteristics. Graph theory can be usefully employed
as a mathematical abstraction of the physical network.
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Published Work
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Grant C., Shear centre of thin-walled sections, J.Strain Anal., 1992, 27(3),
p151-155.
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Grant C., Shear flow in multi-cell sections, Proc.I.Mech.E., Part C: J.Mech.Eng.Sci.,
1993, 207, p247-253.
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Grant C., Structural Networks, Third World Congress on Computational Mechanics,
IACM, 1994, Tokyo.
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Grant C., Network analysis of thin walled sections in uniform torsion,
Proc.I.Mech.E., Part C: J.Mech.Eng.Sci., 1995, 209, p133-140.
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Grant C., Uncoupled torsion of thin walled sections , Proc.I.Mech.E., Part
C: J.Mech.Eng.Sci., 1995, 209, p141-146.
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Grant C., Network modelling of torsion in thin walled beams: Restrained
warping, Proceedings 15th Canadian Congress of Applied Mechanics, Victoria
B.C., Vol 1, p80-81, 1995.
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Grant C., Network theory of torsion and bending in thin-walled sections,
Proceedings International Conference on Mechanics of Solids and Materials
Engineering, Singapore, Vol C, p980-985, 1995.
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