The exact theory of linearly elastic beams developed by Ladeve`ze and Ladeve`ze and Simmonds is illustrated using the equations of plane stress for a fully anisotropic elastic body of rectangular shape. Explicit formulas are given for the cross-sectional material operators that appear in the special Saint-Venant solutions of Ladeve`ze and Simmonds and in the overall beamlike stress-strain relations between forces and a moment (the generalized stress) and derivatives of certain one-dimensional displacements and a rotation (the generalized displacement). A new definition is proposed for built-in boundary conditions in which the generalized displacement vanishes rather than pointwise displacements or geometric averages.
Issue Section:
Technical Papers
1.
Ladeve`ze
, P.
, 1983
, “Sur le principe de Saint-Venant en e´lasticite´
,” J. Mec. Theor. Appl.
, 1
, pp. 161
–184
.2.
Ladeve`ze, P., 1985, “On Saint-Venant’s Principle in Elasticity,” Local Effects in Structures, P. Ladeve`ze, ed., Elsevier, New York, pp. 3–34.
3.
Ladeve`ze
, P.
, and Simmonds
, J. G.
, 1996
, “New Concepts for Linear Beam Theory With Arbitrary Geometry and Loading
,” Comptes Rendus Acad. Sci. Paris
, 332
, Ser IIb, pp. 455
–462
(partially in French).4.
Ladeve`ze
, P.
, and Simmonds
, J. G.
, 1998
, “New Concepts for Linear Beam Theory With Arbitrary Geometry and Loading
,” Eur. J. Mech. A/Solids
, 17
, pp. 377
–402
.5.
Ladeve`ze
, P.
, 1982
, “Principes de Saint-Venant en de´placement et en contrainte pour les poutres droites e´lastique semi-infinies
,” Z. Angew. Math. Phys.
, 33
, pp. 132
–139
.6.
Libai, A., and Simmonds, J. G., 1998, The Nonlinear Theory of Elastic Shells, 2nd Ed., Cambridge University Press, Cambridge, UK.
7.
Gregory
, R. D.
, and Wan
, F. Y. M.
, 1984
, “Decaying States of Plane Strain in a Semi-Infinite Strip and Boundary Conditions for Plate Theory
,” J. Elast.
, 14
, pp. 27
–64
.8.
Gregory
, R. D.
, and Gladwell
, I.
, 1982
, “The Cantilever Beam Under Tension, Bending, or Flexure at Infinity
,” J. Elast.
, 12
, pp. 317
–343
.9.
Crafter
, E. C.
, Heise
, R. M.
, Horgan
, C. O.
, and Simmonds
, J. G.
, 1993
, “The Eigenvalues for a Self-Equilibrated, Semi-Infinite, Elastically Anisotropic Strip
,” ASME J. Appl. Mech.
, 60
, pp. 276
–281
.10.
Wang
, M. Z.
, Ting
, T. C. T.
, and Yan
, G.
, 1993
, “The Anisotropic Elastic Semi-Infinite Strip
,” Q. J. Mech. Appl. Math.
, 51
, pp. 283
–297
.Copyright © 2001
by ASME
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