  A discrete-module-finite element (DMFE) based hydroelasticity method has been
proposed and well developed. Firstly, a freely floating flexible structure is
discretized into several macro-submodules in two horizontal directions to
perform a multi-rigid-body hydrodynamic analysis. Each macro-submodule is then
abstracted to a lumped mass at the center of gravity that bears the external
forces including inertia force, hydrodynamic force and hydrostatic force. Apart
from external forces, all lumped masses are also subjected to structural forces
that reflect the structural deformation features of the original flexible
structure. The key to calculating the structural forces is derivation of the
equivalent overall structural stiffness matrix with respect to the
displacements of all lumped masses, which is tackled following the finite
element procedure. More specifically, each macro-submodule is discretized into
a number of microelements to derive the corresponding structural stiffness
matrix, which is manipulated to a new one including only the nodes at the
position of the lumped masses and surrounding boundaries by using the
substructure approach, and subsequently the target overall stiffness matrix is
obtained by combining together all macro-submodules. Finally, based on
equivalence between external and structural forces, the DMFE method establishes
the hydroelastic equation on all lumped masses with their displacements as
unknown variables. Solving the equation gives the displacement response of all
lumped masses. Displacement and structural force responses are first calculated
on the interfaces of every two adjacent macro-submodules, after which at any
given position of the flexible structure, the recovery of displacement is based
on the structural stiffness matrix of the corresponding macro-submodule and the
recovery of structural force uses the spline interpolation scheme.
