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Saint-Venant's principle and the plane elastic wedge

Record type: Article

The stress field due to self-equilibrating loading on the inner or outer arc of a plane strain elastic wedge sector is affected by two agencies: a geometric effect of increasing or decreasing area, and decay as anticipated by Saint-Venants principle (SVP) . When the load is applied to the inner arc the two effects act in concert ; however, when the load is applied to the outer arc the two effects act in opposition and for a wedge angle in excess of the half-space, 2? > ?, for the symmetric case, and for 2? > 1.43? for the asymmetric case, the geometric effect is dominant over Saint-Venant decay and stress level increases as one moves away from the outer arc, confirming the inapplicability of SVP. This is additional to previously reported difficulties at these angle when a self-equilibrated load on the inner arc decays at the same rate as does a concentrated moment, and is explained in terms of the interaction of a near-field geometric effect and a far-field stress interference effect at a traction-free edge. For wedge angle 2? = 2? the unique Modes I and II inverse square root stress singularities at the crack tip, which are at the heart of Linear Elastic Fracture Mechanics (LEFM) , can be attributed to this inapplicability for just one symmetric and one asymmetric eigenmode.

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Citation

Stephen, N.G. and Wang, P.J. (1999) Saint-Venant's principle and the plane elastic wedge International Journal of Solids and Structures, 36, (3), pp. 345-361. (doi:10.1016/S0020-7683(98)00027-4).

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Published date: 1999

Identifiers

Local EPrints ID: 21203
URI: http://eprints.soton.ac.uk/id/eprint/21203
ISSN: 0020-7683
PURE UUID: 506bbcbd-da93-446f-ae8f-c6da9fed3b5f

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Date deposited: 09 Nov 2006
Last modified: 17 Jul 2017 16:27

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Contributors

Author: N.G. Stephen
Author: P.J. Wang

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