An error is introduced by the conventional approach of applying beam theory in the presence of interiorly applied loads. This error arises from neglecting the influence of the precise distribution of surface tractions and body forces on the warping displacements. This paper intends to show that beam theory is capable of accounting for this influence on warping and accomplishes this by the variational asymptotic method. Correlations between elasticity solutions and beam solutions provide not only validations of beam solutions, but also illustrate the resulting errors from the conventional approach. Correlations are provided here for an isotropic parallelepiped undergoing pure extensional deformations and for an isotropic elliptic cylinder undergoing pure torsional deformations.

References

References
1.
Giavotto
,
V.
,
Borri
,
M.
,
Mantegazza
,
P.
,
Ghiringhelli
,
G.
,
Carmaschi
,
V.
,
Maffioli
,
G. C.
, and
Mussi
,
F.
,
1983
, “
Anisotropic Beam Theory and Applications
,”
Comput. Struct.
,
16
(
1-4
),
pp.
403
413
.10.1016/0045-7949(83)90179-7
2.
Cesnik
,
C. E. S.
, and
Hodges
,
D. H.
,
1997
, “
VABS: A New Concept for Composite Rotor Blade Cross-Sectional Modeling
,”
J. Am. Helicopter Soc.
,
42
(
1
),
pp.
27
38
.10.4050/JAHS.42.27
3.
Yu
,
W.
, and
Hodges
,
D. H.
,
2005
, “
Generalized Timoshenko Theory of the Variational Asymptotic Beam Sectional Analysis
,”
J. Am. Helicopter Soc.
,
50
(
1
),
pp.
46
55
.10.4050/1.3092842
4.
Vlasov
,
V. Z.
,
1961
,
Thin-Walled Elastic Beams
,
National Science Foundation and Department of Commerce
,
Washington, DC
.
5.
Hodges
,
D. H.
,
2003
, “
Contact Stress From Asymptotic Reissner-Mindlin Plate Theory
,”
AIAA Journal
,
41
(2)
, pp.
329
331
10.2514/2.1953.
6.
Yu
,
W.
, and
Hodges
,
D. H.
,
2004
, “
Elasticity Solutions Versus Asymptotic Sectional Analysis of Homogeneous, Isotropic, Prismatic Beams
,”
ASME J. Appl. Mech.
,
71
(
1
),
pp.
15
23
.10.1115/1.1640367
7.
Berdichevsky
,
V. L.
,
1979
, “
Variational-Asymptotic Method of Constructing a Theory of Shells
,”
Prikl. Mat. Mekh.
,
43
(
4
),
pp.
664
687
.
8.
Hodges
,
D. H.
,
2006
,
Nonlinear Composite Beam Theory
,
Vol.
213
(Progress in Astronautics and Aeronautics)
,
AIAA
,
Reston, VA
.
9.
Yu
,
W.
,
Hodges
,
D. H.
, and
Ho
,
J. C.
, “
Variational Asymptotic Beam Sectional Analysis—An Updated Version
,”
Int. J. Eng. Sci.
(in press)
. 10.1016/j.ijengsci.2012.03.006
10.
Love
,
A. E. H.
,
1934
,
A Treatise on the Mathematical Theory of Elasticity
,
4th ed.
,
Cambridge University Press
,
London, UK
.
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