State space elastostatics of prismatic structures
State space elastostatics of prismatic structures
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.
linear elasticity, hamiltonian, saint-venant, state space, degenerate modes
1327-1347
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
2004
Stephen, N.G.
af39d0e9-b190-421d-86fe-28b793d5bca3
Abstract
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.
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Published date: 2004
Keywords:
linear elasticity, hamiltonian, saint-venant, state space, degenerate modes
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Local EPrints ID: 22912
URI: http://eprints.soton.ac.uk/id/eprint/22912
ISSN: 0020-7403
PURE UUID: 1a89f3e8-0376-443d-93d9-7051eb4061c8
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Date deposited: 23 Mar 2006
Last modified: 15 Mar 2024 06:42
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