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Some exact solutions of the equations of the mechanics of nonhomogeneous media

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Abstract

We consider problems of the torsion of nonhomogeneous prismatic rods and the oscillation of plats of variable thickness operating in shear. We obtain an inequality characterizing the dependence of the maximum tangential stress on the shear modulus. An estimate from below is obtained for the torsional moment. An optimization problem for plates of variable thickness for a specified class of thicknesses is reduced to a problem on characteristic values for the Helmholtz equation.

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References

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Authors
  1. A. I. Makeev
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  2. E. A. Moldavskii
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  3. R. B. Nudel'man
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Additional information

Translated from Matematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 25, pp. 87–90, 1987.

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Makeev, A.I., Moldavskii, E.A. & Nudel'man, R.B. Some exact solutions of the equations of the mechanics of nonhomogeneous media. J Math Sci 65, 2002–2006 (1993). https://doi.org/10.1007/BF01097489

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  • DOI: https://doi.org/10.1007/BF01097489

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