Saint Venant’s principle in orthotropic planar elasticity: rates-of-diffusion for stress

Stronge, W. J.; Kashtalyan, M.

doi:10.1090/qam/1724303

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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