CUED Publications database

Graphic kinematics, visual virtual work and elastographics.

McRobie, A and Konstantatou, M and Athanasopoulos, G and Hannigan, L (2017) Graphic kinematics, visual virtual work and elastographics. R Soc Open Sci, 4. 170202-. ISSN 2054-5703

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Abstract

In this paper, recent progress in graphic statics is combined with Williot displacement diagrams to create a graphical description of both statics and kinematics for two- and three-dimensional pin-jointed trusses. We begin with reciprocal form and force diagrams. The force diagram is dissected into its component cells which are then translated relative to each other. This defines a displacement diagram which is topologically equivalent to the form diagram (the structure). The various contributions to the overall Virtual Work appear as parallelograms (for two-dimensional trusses) or parallelopipeds (for three-dimensional trusses) that separate the force and the displacement pieces. Structural mechanisms can be identified by translating the force cells such that their shared faces slide across each other without separating. Elastic solutions can be obtained by choosing parallelograms or parallelopipeds of the appropriate aspect ratio. Finally, a new type of 'elastographic' diagram-termed a deformed Maxwell-Williot diagram (two-dimensional) or a deformed Rankine-Williot diagram (three-dimensional)-is presented which combines the deflected structure with the forces carried by its members.

Item Type: Article
Uncontrolled Keywords: Maxwell reciprocal diagrams Rankine reciprocal diagrams Williot diagrams graphic statics kinematics virtual work
Subjects: UNSPECIFIED
Divisions: Div D > Structures
Depositing User: Cron Job
Date Deposited: 17 Jul 2017 19:26
Last Modified: 08 Aug 2017 01:53
DOI: