NDLI: On Saint-Venant’s Problem for an Inhomogeneous, Anisotropic Cylinder—Part I: Methodology for Saint-Venant Solutions

Content Provider	The American Society of Mechanical Engineers (ASME) Digital Collection
Author	Dong, S. B. Kosmatka, J. B. Lin, H. C.
Copyright Year	2001
Abstract	In this paper, the first in a series of three, a procedure based on semi-analytical finite elements is presented for constructing Saint-Venant solutions for extension, bending, torsion, and flexure of a prismatic cylinder with inhomogeneous, anisotropic cross-sectional properties. Extension-bending-torsion involve stress fields independent of the axial coordinate and their displacements may be decomposed into two distinct parts which are called the primal field and the cross-sectional warpages herein. The primal field embodies the essence of the kinematic hypotheses of elementary bar and beam theories and that for unrestrained torsion. The cross-sectional warpages are independent of the axial coordinate and they are determined by testing the variationally derived finite element displacement equations of equilibrium with the primal field. For flexure, a restricted three-dimensional stress field is in effect where the stress can vary at most linearly along the axis. Integrating the displacement field based for extension-bending-torsion gives that for the flexure problem. The cross-sectional warpages for flexure are determined by testing the displacement equations of equilibrium with this displacement field. In the next paper, the cross-sectional properties such as the weighted-average centroid, center of twist and shear center are defined based on the Saint-Venant solutions established in the present paper and numerical examples are given. In the third paper, end effects or the quantification of Saint-Venant’s principle for the inhomogeneous, anisotropic cylinder is considered.
Starting Page	376
Ending Page	381
Page Count	6
File Format	PDF
ISSN	00218936
e-ISSN	15289036
Journal	Journal of Applied Mechanics
Volume Number	68
Issue Number	3
DOI	10.1115/1.1363598
Language	English
Publisher	The American Society of Mechanical Engineers
Publisher Date	2000-07-21
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Bending (Stress) Cylinders Displacement Equations Equilibrium (Physics) Finite element analysis Force Saint-Venant's principle Shear (Mechanics) Stress Torsion Warping
Content Type	Text
Resource Type	Article
Subject	Mechanics of Materials Mechanical Engineering Condensed Matter Physics

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