State space elastostatics of prismatic structures

Stephen, N.G. (2004) State space elastostatics of prismatic structures. International Journal of Mechanical Sciences, 46, (9), 1327-1347. (doi:10.1016/j.ijmecsci.2004.07.008).


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This paper provides an exposition of the problem of a prismatic elastic rod or beam subject to static end loading only, using a state space formulation of the linear theory of elasticity. The approach, which employs the machinery of eigenanalysis, provides a logical and complete resolution of the transmission (Saint-Venant's) problem for arbitrary cross-section, subject to determination of the Saint-Venant torsion and flexure functions which are cross-section specific. For the decay problem (Saint-Venant's principle), the approach is applied to the plane stress elastic strip, but in the transverse rather than the axial direction, leading to the well-known Papkovitch–Fadle eigenequations, which determine the decay rates of self-equilibrated loading; however, extension to other cross-sections appears unlikely. It is shown that only a repeating zero eigenvalue can lead to a non-trivial Jordan block; thus degenerate decay modes cannot exist for a prismatic structure.

Item Type: Article
ISSNs: 0020-7403 (print)
Related URLs:
Keywords: linear elasticity, hamiltonian, saint-venant, state space, degenerate modes
Subjects: T Technology > TJ Mechanical engineering and machinery
Q Science > QC Physics
Divisions: University Structure - Pre August 2011 > School of Engineering Sciences
ePrint ID: 22912
Date Deposited: 23 Mar 2006
Last Modified: 27 Mar 2014 18:12
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