Transformations

1. Node Local DOF Transformations

The node local transformation tests with NBC's compute deformations and forces in a clamped beam with a node-local coordinate system (fundamental test of transformation mechanism). The applied force is specified in the node local system of node 5 rotated 45° with respect to the branch global system (see figure below). The beam is modeled by linear beam elements.

Geometry of clamped beam

Figure 122. Geometry of clamped beam


The analytical y-displacement of node 5 is obtained with the simple formula v = F l3 / (3 E J). The test checks that the node-local transformation is performed properly:

  • The global dof 1 of node 5 must be equal to 0.707*v.

  • The branch global dof 2 of node 5 must be equal to v.

The node local transformation tests with EBC's compute deformations and forces in a clamped beam with a node-local coordinate system (fundamental test of transformation mechanism). The constraint is specified in the node local system of node 5 (see figure below). The beam is modeled by linear beam elements.

Geometry of clamped beam with prescribed displacement

Figure 123. Geometry of clamped beam with prescribed displacement


The y-displacement of node 5 is the one prescribed. The test checks that the node-local transformation is performed properly:

  • The global dof 1 of node 5 must be equal to v.

  • The branch global dof 2 of node 5 must be equal to v.

The node local transformation tests with master-slave nodes compute deformations and forces in a simply supported beam with a node-local coordinate system either in the master node 3 of branch 1 or the slave node1 of branch 2 (fundamental test of transformation mechanism). The beam is modeled by linear beam elements.

Geometry of simply supported beam

Figure 124. Geometry of simply supported beam


The y-displacement of node 3 (branch 1) is checked both in the global system and the branch local system. Note that the master node 's local coordinate system is the computational system!