Stress Singularities in a Model of a Wood Disk under Sinusoidal Pressure

A thin, solid, circular wood disk, cut from the transverse plane of a tree stem, can be modeled as a cylindrically orthotropic elastic material. It is known that a stress singularity can occur at the center of a cylindrically orthotropic disk subjected to uniform pressure. If a solid cylindrically o...

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Bibliographic Details
Published in:Journal of engineering mechanics 2005-02, Vol.131 (2), p.153-160
Main Authors: Johnson, Jay A, Hermanson, John C, Cramer, Steven M, Amundson, Charles
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Structural and continuum mechanics
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Summary:A thin, solid, circular wood disk, cut from the transverse plane of a tree stem, can be modeled as a cylindrically orthotropic elastic material. It is known that a stress singularity can occur at the center of a cylindrically orthotropic disk subjected to uniform pressure. If a solid cylindrically orthotropic disk is subjected to sinusoidal pressure distributions, then other stress singularities can also occur in the disk. The criterion for the existence of these singularities is based on a simple relationship between two dimensionless elastic constant parameters and the sinusoidal pressure loading mode number. For a given set of elastic constants, only a finite number of lower sinusoidal modes will produce stress singularities. In this paper, the mathematical relationships between these parameters are derived.
ISSN:0733-9399
1943-7889
DOI:10.1061/(ASCE)0733-9399(2005)131:2(153)