Contact Transform for the Biharmonic Equation Applicable to Plane Stress Elastoplastic Elliptical Hole Problems

An analytical technique is developed that reduces the unknown elastic-plastic boundary of a linear elastic-perfectly plastic material containing an elliptical hole under tensile plane stress loading conditions into an equivalent mathematical problem with known boundaries. This mathematical transform...

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Bibliographic Details
Published in:Journal of elasticity Vol. 117; no. 2; pp. 139 - 161
Main Author: Unger, David J.
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.12.2014
Springer Nature B.V
Subjects:
Automotive Engineering
Boundaries
Classical Mechanics
Contact
Equivalence
Mathematical analysis
Mathematical models
Perturbation methods
Physics
Physics and Astronomy
Plane stress
Transformations (mathematics)
Tresca yield condition
74C05
74A45
Perfectly plastic
Mode I crack
37J55
Linear elastic
ISSN:0374-3535, 1573-2681
Online Access:Get full text
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Summary:An analytical technique is developed that reduces the unknown elastic-plastic boundary of a linear elastic-perfectly plastic material containing an elliptical hole under tensile plane stress loading conditions into an equivalent mathematical problem with known boundaries. This mathematical transformation may facilitate this problem’s solution by either analytical or numerical means. Yield is assumed to occur in this analysis under the Tresca yield criterion. An example elastic-plastic problem illustrating this method is drawn from existing literature in the form of a perturbation solution for an elliptical hole derived by a series expansion about a circular boundary.
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ISSN:0374-3535
1573-2681
DOI:10.1007/s10659-014-9468-3