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Multiple and maximal periodicity in linear elastostatics

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Abstract

Properties of elastic states in which the strain is periodic in an arbitrary number of directions are investigated. It is shown that, even though the corresponding displacements might not, in a non-trivial sense, be periodic, they do satisfy a “semi-periodicity” condition. Other general results, including a version of Betti's reciprocal theorem and a theorem of work and energy are derived and discussed. Problems involving periodicity in a maximal number of directions are examined in greater detail. Additional restrictions on the displacement corresponding to maximally periodic strains are derived and the uniqueness and periodicity of solutions to maximally periodic and “slightly” maximally periodic boundary value problems are discussed.

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Authors and Affiliations

  1. Department of Mathematics, University of Alabama in Huntsville, 35899, Huntsville, AL, USA

    Kenneth B. Howell

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  1. Kenneth B. Howell
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Howell, K.B. Multiple and maximal periodicity in linear elastostatics. J Elasticity 16, 333–347 (1986). https://doi.org/10.1007/BF00041759

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