## Coupling Matrix Of The Damreservoir

The coupling matrix relates the pressure of the reservoir and the forces on the dam-reservoir interface as following:

where {f} is the force vector acting on the structure due to the hydrodynamic pressure.

Figure ?? shows a line element on the interaction boundary of the damreservoir. The work done by the hydrodynamic pressure on the interaction surface of the structure must be equal to the work of the equivalent nodal forces on the interface boundary of an element. Thus, for unit thickness elements as shown in figure ??, the following expression can be written:

where p and Un are the values of the hydrodynamic pressure and normal displacement along the element interface, respectively. {£} and {f }e are the displacement and force vector of an interface element. u and vj (fxj and fyj) are the displacements (forces) at node i of the interface element along the global X and Y coordinates, respectively. The integration is performed along each element on the dam-reservoir interface. The superscript and subscript 'e' refer to the element on the dam-reservoir interface. Writing u and v,

displacements along the global X and Y coordinates of the interface element, in terms of structure shape functions, then:

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