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Energy-minimizing deformations of elastic sheets with bending stiffness

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Abstract

Necessary conditions for energy-minimizing deformations are derived for a theory of sheets in which the strain energy function depends on the second derivatives of the deformation as well as its first derivatives. All of these conditions are extensions of well-known necessary conditions in classical calculus of variations. The interpretation of some of these conditions as material stability conditions is explained.

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Authors and Affiliations

  1. Division of Applied Mathematics, Brown University, 02912, Providence, RI, USA

    M. G. Hilgers & A. C. Pipkin

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  1. M. G. Hilgers
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  2. A. C. Pipkin
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Hilgers, M.G., Pipkin, A.C. Energy-minimizing deformations of elastic sheets with bending stiffness. J Elasticity 31, 125–139 (1993). https://doi.org/10.1007/BF00041227

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  • DOI: https://doi.org/10.1007/BF00041227

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