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On the Generalized Plane Stress Problem, the Gregory Decomposition and the Filon Mean Method

Wang, Min-Zhong and Xu, Bai-Xiang and Zhao, Bao-Sheng (2012):
On the Generalized Plane Stress Problem, the Gregory Decomposition and the Filon Mean Method.
In: Journal of Elasticity, Springer, pp. 1-28, 108, (1), ISSN 0374-3535,
[Online-Edition: http://dx.doi.org/10.1007/s10659-011-9352-3],
[Article]

Abstract

In the present paper a stress general solution is obtained for the generalized plane stress problem with planar body forces, and it is demonstrated that only body force of biharmonic type ensures the compatibility with the generalized plane stress assumptions (σ33=0). Inspired by the Filon perspective of average values, two more generalized plane stress problems with weak assumptions on the out-of-plane stress averages (̄σ33=0or∇2̄σ33=0) are studied, and the averages of the corresponding stress fields are expressed by the Airy stress functions. The authors also provide an alternative proof of the Gregory decomposition theory.

Item Type: Article
Erschienen: 2012
Creators: Wang, Min-Zhong and Xu, Bai-Xiang and Zhao, Bao-Sheng
Title: On the Generalized Plane Stress Problem, the Gregory Decomposition and the Filon Mean Method
Language: English
Abstract:

In the present paper a stress general solution is obtained for the generalized plane stress problem with planar body forces, and it is demonstrated that only body force of biharmonic type ensures the compatibility with the generalized plane stress assumptions (σ33=0). Inspired by the Filon perspective of average values, two more generalized plane stress problems with weak assumptions on the out-of-plane stress averages (̄σ33=0or∇2̄σ33=0) are studied, and the averages of the corresponding stress fields are expressed by the Airy stress functions. The authors also provide an alternative proof of the Gregory decomposition theory.

Journal or Publication Title: Journal of Elasticity
Volume: 108
Number: 1
Publisher: Springer
Uncontrolled Keywords: Elasticity, Generalized plane stress problem, Filon average, Gregory, decomposition, General solution
Divisions: 11 Department of Materials and Earth Sciences
11 Department of Materials and Earth Sciences > Material Science
11 Department of Materials and Earth Sciences > Material Science > Mechanics of functional Materials
Zentrale Einrichtungen
Exzellenzinitiative
Exzellenzinitiative > Graduate Schools > Graduate School of Computational Engineering (CE)
Exzellenzinitiative > Graduate Schools
Date Deposited: 18 Apr 2013 08:04
Official URL: http://dx.doi.org/10.1007/s10659-011-9352-3
Identification Number: doi:10.1007/s10659-011-9352-3
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