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Stability of rigid solids embedded in an elastic medium

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Abstract

The stability of a two-dimensional continuum consisting of rigid solids embedded in an elastic homogeneous medium with a fixed boundary is investigated. With each solid is associated the scalar \(\sigma = \frac{1}{S}\sum\limits_\alpha {\vec F_\alpha } \user1{ }.\user1{ }\overrightarrow {0M} _\alpha\) where \(\vec F_\alpha\) are balanced dead loads acting at points M α of the solid, and where S is the area of the surface of the solid. If μ is the shear modulus of the elastic medium, it is shown that (i) the inequality σ+4μ>0, when it applies to each solid, is a sufficient condition for stability of the continuum; (ii) the inequality σ+4μ≧0 is a necessary condition for stability of a single circular solid embedded in an infinite elastic medium.

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Communicated by C. C. Wang

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Weber, J.D., Molinari, A. Stability of rigid solids embedded in an elastic medium. Arch. Rational Mech. Anal. 48, 205–212 (1972). https://doi.org/10.1007/BF00256054

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Keywords

  • Neural Network
  • Complex System
  • Shear Modulus
  • Nonlinear Dynamics
  • Electromagnetism