Monday, 11 October 2004 - 5:35 PM

This presentation is part of : Surface Stress in Nature and Technology

Finite-strain thin-shell theory for elastic solids

David J. Steigmann, University of California, University of California, Department of Mechanical Engineering, 6133 Etcheverry Hall, Berkeley, CA 94720

A model for elastic shells accurate to second order in a scaled thickness parameter is derived. Unlike most theories that are derived from three-dimensional considerations, all kinematical and dynamical fields are expanded to a consistent order of approximation. For equilibria, the higher-order kinematical fields are eliminated by using minimum-energy arguments at the pointwise level, for suitable boundary data. For materials having appropriate symmetry, what emerges is a variant of the semi-classical Kirchhoff-Love model with thickness stretch. To the extent that our analysis pertains to equilibria, it suggests that Kirchhoff-Love kinematics are not appropriate in a dynamical setting. The framework also furnishes a concept of material symmetry for elastic surfaces that is consistent with established ideas in three-dimensional elasticity.

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