Constrain nodes displacements in 3D

Figure 10 shows a mesh with nelx = 2, nely = 2, nelz = 1, and how the nodes are numbered.

Figure 10: 3D mesh with numbered nodes.

It’s passed a list of dictionaries. There are two options for constrain nodes displacements:

• Constrain nodes displacements by column

• Constrain nodes displacements by coordinate

Hint

It’s possible combine and use both options.

Constrain nodes displacements by coordinate

The dictionary has the following keys:

• “x_coord”: coordinate in X-axis.

• “y_coord”: coordinate in Y-axis.

• “z_coord”: coordinate in Z-axis.

• “constrain_disp_x”: indicates if the node displacement is contraint in X-direction.

  • If 1 constrain the node displacement in the X-direction.

  • If 0 don’t constrain the node displacement in the X-direction.

• “constrain_disp_y”: indicates if the node displacement is contraint in Y-direction.

  • If 1 constrain the node displacement in the Y-direction.

  • If 0 don’t constrain the node displacement in the Y-direction.

• “constrain_disp_z”: indicates if the node displacement is contraint in Z-direction.

  • If 1 constrain the node displacement in the Z-direction.

  • If 0 don’t constrain the node displacement in the Z-direction.

In the example is constrained the node displacement at coordinateS (1, 0.5, 0.3) and (1, 0.5, 0).

restri_matrix = [{"x_coord":1, "y_coord":0.5, "z_coord":0.3, "constrain_disp_x":1, "constrain_disp_y":1, "constrain_disp_z":1}, \
                 {"x_coord":1, "y_coord":0.5, "z_coord":0, "constrain_disp_x":1, "constrain_disp_y":1, "constrain_disp_z":1}]

The resulting mesh is shown in figure 11.

Figure 11: Mesh with nodes at coordinates (1, 0.5, 0.3) and (1, 0.5, 0).

Constrain nodes displacements by column

The dictionary has the following keys:

• “coord”: coordinate.

• “axis”: Direction that the node displacement is constraint. It can be: 1 (X-Axis), 2 (Y-Axis) or 3 (Z-Axis).

• “eps”: Margin of error.

• “constrain_disp_x”: indicates if the node displacement is contraint in X-direction.

  • If 1 constrain the node displacement in the X-direction.

  • If 0 don’t constrain the node displacement in the X-direction.

• “constrain_disp_y”: indicates if the node displacement is contraint in Y-direction.

  • If 1 constrain the node displacement in the Y-direction.

  • If 0 don’t constrain the node displacement in the Y-direction.

• “constrain_disp_z”: indicates if the node displacement is contraint in Z-direction.

  • If 1 constrain the node displacement in the Z-direction.

  • If 0 don’t constrain the node displacement in the Z-direction.

In the example is constrained the X displacement of the nodes in the plane Z = 0.3.

restri_matrix = [{"coord":0.3, "axis":3, "eps":0.001, "constrain_disp_x":1, "constrain_disp_y":0, "constrain_disp_z":0}]

The resulting mesh is shown in figure 12.

Figure 12: Nodes in the plane Z = 0.3.