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Remarks on a Question of Ericksen concerning Elastostatic Fields of Saint-Venant Type

Knowles, James K. (1985) Remarks on a Question of Ericksen concerning Elastostatic Fields of Saint-Venant Type. Archive for Rational Mechanics and Analysis, 90 (3). pp. 249-261. ISSN 0003-9527. doi:10.1007/BF00251733.

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In an effort to understand better the relationship between approximate theories - such as those for thin rods- and the three-dimensional theory of elasticity, ERICKSEN [1]- [3] has recently suggested a reconsideration of Saint-Yenant's problem for elastic cylinders with traction-free lateral surfaces. Among the various questions raised in [1]- [3], one concerns the structure and role of the set of all possible elastostatic fields in an infinitely long cylinder in the absence of lateral loading and body force, but in the presence of a restriction on the size of a suitable cross-sectional norm of the associated strain tensor field. Although the issues which emerge from ERICKSEN's discussion acquire their greatest significance in the setting of finite elasticity, some of them arise in simpler form in the classical infinitesimal theory, as he points out. In the present paper, we examine the question mentioned above in a context that permits elementary analysis, and yet is rich enough to illuminate some of the important features: that of linearized plane strain for homogeneous, isotropic materials. In particular, the analysis makes especially transparent the exceptional status of the analog in plane strain of the case of flexure by a transverse force in Saint-Venanfs cylinder problem. In the following section, we discuss plane strain for the infinite strip and the corresponding fields of Saint-Yenant type. One version of ERICKSEN's question is examined in Section 3 and, in modified form, in Section 4. Section 5 is devoted to related issues for a strip of finite length.

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Additional Information:© 1985 Springer. Received February 12, 1985.
Issue or Number:3
Record Number:CaltechAUTHORS:20151113-165202758
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:62107
Deposited By: Kristin Buxton
Deposited On:18 Nov 2015 19:52
Last Modified:10 Nov 2021 22:58

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