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.
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The basic setting
The submarine setting
Two anchored situations: prescribed deformation on
The bounded-reservoir setting
The ship setting
A barely floating solid (left) and an admissible
A deformation with