From elastic shallow shells to beams with elastic hinges by $$\Gamma $$-convergence

• DOI: 10.1007/s00033-024-02280-1
• Publication Date: 2024-07-05T15:02:50Z
• Authors: Roberto Paroni; Marco Picchi Scar...
• Keywords: Classification of discontinuities; Elastic energy

Abstract In this paper, we study the $$\Gamma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Γ</mml:mi> </mml:math> -limit of a properly rescaled family energies, defined on narrow strip, as width strip tends to zero. The limit energy is one-dimensional and able capture (and penalize) concentrations midline curvature. At best our knowledge, it first paper in -convergence field for dimension reduction that predicts elastic hinges. particular, starting from purely shell model with “smooth” solutions, obtain beam where derivatives displacement and/or rotation fields may have jump discontinuities. Mechanically speaking, hinges can occur beam.