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A Remark on the Invariance of Solenoidal Vectors in Elastostatics

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Abstract

The linear elastostatic displacement boundary-value problem is considered for a bounded simply connected region Ω in Rn in the case of a homogeneous isotropic medium. For n = 2 it is shown that if all solenoidal forcing terms result in solenoidal displacements, then Ω is a disk. It is likely that the result is true for n ≥ 3 but that problem is not resolved.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Delaware, Newark, DE, 19716, U.S.A. E-mail

    R.J. Weinacht

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  1. R.J. Weinacht
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Weinacht, R. A Remark on the Invariance of Solenoidal Vectors in Elastostatics. Journal of Elasticity 57, 165–170 (1999). https://doi.org/10.1023/A:1007666602023

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  • DOI: https://doi.org/10.1023/A:1007666602023

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