Large deformations of gradient elastic beams

Marcelo Epstein; Mohammadjavad Javad

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arXiv · 2209.12319

Large deformations of gradient elastic beams

Marcelo Epstein·Mohammadjavad Javad

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Abstract

Budiansky's nonlinear shell theory is particularized to a 2D setting, and thereupon generalized to a fully nonlinear, statically and kinematically exact, theory of strain-gradient elasticity of beams. The governing equations are displayed in their weak and strong forms. A suitable finite element is used to accommodate the new degrees of freedom emanating from the theory and several numerical examples with large geometrical nonlinearities are displayed showing the relative influence of the strain gradient. The numerical apparatus is then applied to permanently magnetized bodies under the action of external magnetic fields.

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Marcelo Epstein, Mohammadjavad Javad. 2022-09-25. Large deformations of gradient elastic beams. https://arxiv.org/abs/2209.12319

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