Saint Venant’s principle in orthotropic planar elasticity: rates-of-diffusion for stress
Authors:
W. J. Stronge and M. Kashtalyan
Journal:
Quart. Appl. Math. 57 (1999), 741-755
MSC:
Primary 74G50; Secondary 74B05
DOI:
https://doi.org/10.1090/qam/1724303
MathSciNet review:
MR1724303
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Abstract: For plane deformations generated by an arbitrary distribution of tractions applied in a small region on the boundary of an elastic half-plane, the rates-of-decay for displacements, stresses and strain energy density are obtained as functions of complexity of the load distribution. The rates-of-decay increase in proportion to the complexity of the load distribution; i.e., they increase with the order of the smallest nonvanishing moment of the traction distribution. In orthotropic materials the elastic moduli differ in two perpendicular directions of principal stiffness; in this case as the modulus ratio ${E_2}/{E_1}$ increases, the angular distributions of the displacement and energy density fields become channeled towards the direction of the larger elastic modulus.
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R. von Mises, On Saint-Venant’s principle, Bull. American Mathematical Society 51, 555–562 (1945)
E. Sternberg, On Saint-Venant’s principle, Quart. Appl. Math. 11, 393–402 (1954)
W. J. Stronge and M. Kashtalyan, St. Venant’s principle for two-dimensional anisotropic elasticity, Acta Mechanica 124, 213–218 (1997)
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Y. Arimitsu, K. Nishioka, and T. Senda, A study of Saint-Venant’s principle for composite materials by means of internal stress fields, ASME J. Appl. Mechanics 62, 53–58 (1995)
D. Durban and W. J. Stronge, Plane strain incremental response and sensitivity of stretched plates, European J. Mechanics - Solids 14, 553–575 (1995)
G. C. Everstine and A. C. Pipkin, Stress channeling in transversely isotropic composites, J. Elasticity 2, 335–339 (1971)
M. E. Gurtin, The linear theory of elasticity, Handbuch der Physik (ed. S. Flugge), 1973, pp. 190–207
C. O. Horgan, Some remarks on Saint-Venant’s principle for transversely isotropic composites, J. of Elasticity 2, 335–339 (1972)
C. O. Horgan, Recent developments concerning Saint-Venant’s principle: A second update, Appl. Mech. Reviews 49(10) , S101–111 (1996)
C. O. Horgan and J. K. Knowles, Recent developments concerning Saint-Venant’s principle, Advances in Applied Mechanics, Vol. 23, Academic Press, 1983, pp. 179–267
C. O. Horgan and J. G. Simmonds, Saint Venant end effects in composite structures, Composites Engineering 3, 279–286 (1994)
S. G. Lekhnitskii, Theory of Elasticity of an Anisotropic Elastic Body, translated from the Russian edition, Holden-Day, Inc., San Francisco, 1981
X. Markenscoff, Some remarks on the wedge paradox and Saint Venant’s principle, ASME J. Appl. Mechanics 61, 519–523 (1994)
S. A. Matemilola, W. J. Stronge, and D. Durban, Diffusion rate for stress in orthotropic materials, ASME J. Appl. Mechanics 62, 654–661 (1995)
R. von Mises, On Saint-Venant’s principle, Bull. American Mathematical Society 51, 555–562 (1945)
E. Sternberg, On Saint-Venant’s principle, Quart. Appl. Math. 11, 393–402 (1954)
W. J. Stronge and M. Kashtalyan, St. Venant’s principle for two-dimensional anisotropic elasticity, Acta Mechanica 124, 213–218 (1997)
R. A. Toupin, Saint-Venant’s Principle, Arch. Rat. Mech. Analysis 18, 83–96 (1965)
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© Copyright 1999
American Mathematical Society