We investigate the effect of constitutive coupling of stretching, bending, and transverse shearing deformation on the deflection of an anisotropic cantilever beam with narrow rectangular cross-section. To this end, we have developed a hierarchy of beam models by applying a variational principle for displacements and transverse stresses to the associated plane stress problem.
Issue Section:
Research Papers
1.
Hashin
Z.
1967
, “Plane Anisotropic Beams
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 34
, pp. 257
–262
.2.
MARC Analysis Research Corporation, 1992, MARC Reference Library, Volume A: User Information, Rev. K. 5, Palo Alto, CA.
3.
Hildebrand
F. B.
1943
, “On the Stress Distribution in Cantilever Beams
,” Journal of Mathematics and Physics
, Vol. 22
, pp. 188
–203
.4.
Nair
S.
Reissner
E.
1975
, “Improved Upper and Lower Bounds for Deflections of Orthotropic Cantilever Beams
,” International Journal of Solids and Structures
, Vol. 11
, pp. 961
–971
.5.
Nair
S.
Reissner
E.
1976
, “On the Determination of Stresses and Deflections for Anisotropic Homogeneous Cantilever Beams
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 43
, pp. 75
–80
.6.
Reissner
E.
1940
, “A Contribution to the Theory of Elasticity of Non-Isotropic Materials (with Applications to Problems of Bending and Torsion)
,” Philosophical Magazine and Journal of Science
, Ser. 7, Vol. 30
, pp. 418
–427
.7.
Reissner
E.
1984
, “On a Certain Mixed Variational Theorem and a Proposed Application
,” International Journal for Numerical Methods in Engineering
, Vol. 20
, pp. 1366
–1368
.8.
Wolfram, S., 1991, Mathematica: A System for Doing Mathematics by Computer, 2nd ed., Addison-Wesley, Redwood City, CA.
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