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Reaction Forces/moments

Like most of Finite Elements tools, DeepLines deals with a duality between nodes and elements that compose a mesh.

As explained in the previous sections,when submitted to external loadings (gravity, hydrodynamic...), every element experiences strains depending on its elected type of element (cable/bar/beam/Spring...) which generate internal efforts and in dynamic inertia and damping efforts.

The global equations of motions are resolved at nodes but efforts are computed along the elements with an integration by Gauss points.

Each node gathers the contribution of all elements connected to it as well as all punctual loadings (lump masses, nodal force...) directly applied to it.

The resulting efforts at nodes are the so-called reactions efforts which obey the following "golden" rule:

  • For every nodal degree of freedom which is free , the associated reaction force or moment shall be theoretically null;

  • For every constaint or blocked degree of freedom , the associated reaction effort represents the effort that shall be applied by an external "operator" to keep the node in-place.

Reaction efforts are stored in specific database with extension DTBRS (for static) or DTBR (for Time domain) or DTBFR (frequency domain). These database are filled up during the simulations in a similar way as the nodes positions database with extension DTBS, DTB, DTBF...

For all nodes belonging to non-deformable objects (like floaters, rigid bodies...) or to specifc elements which may not be partitioned(like springs, pulleys, flexjoints...), the golden is applied.

For all nodes belonging to a group/line of elements (like riser, moorring, structural member...), a specifc rule is followed: to avoid storing useless zero values at all free nodes, it has been decided to store specific reaction efforts applying a strategy often used in continuum mechanics as such:

  • Every line has an arc length oriented from a first end node to the last one;
  • Every free node of this line receives only the contribution of the elements upstream.

That means that the by convention, the "reaction efforts" stored in the database at any intermediate node of a line represent the efforts to be applied to keep this free node in place, once all upstream elements are removed.