From elastic shallow shells to beams with elastic hinges by Γ-convergence.

Autor: Paroni, Roberto, Picchi Scardaoni, Marco
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Zdroj: Zeitschrift für Angewandte Mathematik und Physik (ZAMP); Aug2024, Vol. 75 Issue 4, p1-23, 23p
Abstrakt: In this paper, we study the Γ -limit of a properly rescaled family of energies, defined on a narrow strip, as the width of the strip tends to zero. The limit energy is one-dimensional and is able to capture (and penalize) concentrations of the midline curvature. At the best of our knowledge, it is the first paper in the Γ -convergence field for dimension reduction that predicts elastic hinges. In particular, starting from a purely elastic shell model with "smooth" solutions, we obtain a beam model where the derivatives of the displacement and/or of the rotation fields may have jump discontinuities. Mechanically speaking, elastic hinges can occur in the beam. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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