The asymptotic form of the stressed state near a three-dimensional boundary singularity of the "claw" type †

Research outputpeer-review

3 Citations (Scopus)

Abstract

Asymptotic formulae are derived for the fields of displacements, strains and stresses near a peak-shaped protrusion in the surface of an anisotropic elastic body (a "claw"-type singularity). The singular solutions constructed are interpreted as forces and torques concentrated at the tip of the peak, while the orders of growth of the displacement depend on the direction of the action of the force (longitudinal or transverse) and of the axis of the torque (twisting or bending) but not on the elastic properties of the material. The asymptotic analysis makes essential use of the observed analogy with one-dimensional models of thin rods of variable cross-section.

Original languageEnglish
Pages (from-to)943-951
Number of pages9
JournalJournal of Applied Mathematics and Mechanics
Volume63
Issue number6
DOIs
Publication statusPublished - 1 Jan 1999

Scopus subject areas

  • Modelling and Simulation
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Cite this

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N2 - Asymptotic formulae are derived for the fields of displacements, strains and stresses near a peak-shaped protrusion in the surface of an anisotropic elastic body (a "claw"-type singularity). The singular solutions constructed are interpreted as forces and torques concentrated at the tip of the peak, while the orders of growth of the displacement depend on the direction of the action of the force (longitudinal or transverse) and of the axis of the torque (twisting or bending) but not on the elastic properties of the material. The asymptotic analysis makes essential use of the observed analogy with one-dimensional models of thin rods of variable cross-section.

AB - Asymptotic formulae are derived for the fields of displacements, strains and stresses near a peak-shaped protrusion in the surface of an anisotropic elastic body (a "claw"-type singularity). The singular solutions constructed are interpreted as forces and torques concentrated at the tip of the peak, while the orders of growth of the displacement depend on the direction of the action of the force (longitudinal or transverse) and of the axis of the torque (twisting or bending) but not on the elastic properties of the material. The asymptotic analysis makes essential use of the observed analogy with one-dimensional models of thin rods of variable cross-section.

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