From elastic shallow shells to beams with elastic hinges by \(\Gamma\)-convergence. (English) Zbl 07900951
Summary: In this paper, we study the \(\Gamma\)-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 \(\Gamma\)-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.
MSC:
| 74K20 | Plates |
| 74B10 | Linear elasticity with initial stresses |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
Keywords:
shallow shells; \(\Gamma\)-convergence; ribbons; elastic hinges; tape spring; dimension reductionReferences:
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