The RLINK element, which is automatically inserted into the place of a defined rigid link during calculations, provides the ability to use a concentrated mass matrix for dynamic problems.
S - Secondary Node
P - Primary Node
The stiffness matrix for the element presented in the drawing above is as follows:
Cms= matrix of transformation of displacements from the primary node to the secondary node
Cms trans= matrix of transformation of reactions from the secondary node to the primary node
Us= displacement vector for the secondary node
Um= displacement vector for the primary node
Rs= reaction vector for the secondary node
Rm= reaction vector for the primary node
diag(k)= diagonal matrix created from vector k, which is a vector of stiffness ascribed to individual degrees of freedom.
Advantages:
The RLINK element is treated as a regular finite element allowing for:
- Concentrated mass matrix for dynamic problems
- Releases in a secondary node
- Compatible nodes in a secondary node
- Rotated support in the primary node.
Disadvantages:
There is an increased number of degrees of freedom in a system. Those in standard rigid links of a secondary node are inherited from the primary node. Degrees of freedom in an RLINK element of the primary node and the secondary node are treated separately.
The poorer conditioning of the stiffness matrix may have an adverse effect on the convergence of the iterative solvers.