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Equilibrium of immersed hyperelastic solids

  • * Corresponding author: Ulisse Stefanelli

    * Corresponding author: Ulisse Stefanelli
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  • We discuss different equilibrium problems for hyperelastic solids immersed in a fluid at rest. In particular, solids are subjected to gravity and hydrostatic pressure on their immersed boundaries. By means of a variational approach, we discuss free-floating bodies, anchored solids, and floating vessels. Conditions for the existence of local and global energy minimizers are presented.

    Mathematics Subject Classification: Primary:49S05, 74F10; Secondary:49J45, 74B20.


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  • Figure 1.  The basic setting

    Figure 2.  The submarine setting

    Figure 3.  Two anchored situations: prescribed deformation on $ \omega \subset \Omega $ (left) and elastic boundary conditions on $ \Gamma\subset \partial \Omega $ (right)

    Figure 4.  The bounded-reservoir setting

    Figure 5.  The ship setting

    Figure 6.  A barely floating solid (left) and an admissible $ y\in A $ with $ A $ from (33) (right)

    Figure 7.  A deformation with $ \omega^{y^*}\subset\Omega^{y^*} $ with $ \sup_{\omega^{y^*}} y^*_3 = 0 $ and $ \sup_{\Omega^{y*}}y^*_3>0 $

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