Statics and Geometry of Underconstrained Axisymmetric 3-Nets

[+] Author and Article Information
E. N. Kuznetsov

Department of General Engineering, University of Illinois, Urbana, Ill. 61801

J. Appl. Mech 51(4), 827-830 (Dec 01, 1984) (4 pages) doi:10.1115/1.3167732 History: Received January 01, 1984; Online July 21, 2009


A 3-net is a system formed by three intersecting arrays of linear flexible members such that every intersection involves one member of each array. The subject of this study is an axisymmetric 3-net where the first array is meridional and the other two are inclined to a meridian at equal but opposite angles. If the net intersections are not fixed the system is underconstrained and, generally, does not possess a unique configuration. However, such systems allow exceptional configurations in which they lack kinematic mobility and admit prestress. Pertinent equations governing the intricately interrelated statics and geometry of axisymmetric 3-nets are developed and some closed-form solutions are obtained. On this basis, two particular classes of immobile (static) 3-nets are synthesized and two corresponding sets of feasible geometric shapes are investigated.

Copyright © 1984 by ASME
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