Package for Machine Design

Finite Element Analysis in Structural Mechanics

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Zero nodal displacements and rotations

Zero components of nodal displacement and rotation (a homogeneous boundary condition) must be prescribed in the first load case and apply to all load cases.

In the name.i2 file, the boundary condition is assigned to the selected nodes:

AS 1 /$\dots$ /B 0 N node number list /$\dots$

or

AS 1 /$\dots$ /B 0 C component number list N node number list /$\dots$

The first form of assignment is used to prescribe all degrees of freedom at a node.

The second form of assignment is used when it is necessary to prescribe the values of only some of the degrees of freedom at a node, while the others are to remain free. The component (degree of freedom) numbers follow from the table:

NumberComponentMeaning
1 $u$ displacement in the direction of the $x$ axis $\text{[m]}$
2 $v$ displacement in the direction of the $y$ axis $\text{[m]}$
3 $w$ displacement in the direction of the $z$ axis $\text{[m]}$
4 $\alpha$ the rotation angle of the semi-loof element edge $\text{[rad]}$, see the Reference Manual
4 $\varphi_x$ the rotation angle about the $x$ axis $\text{[rad]}$, see the Reference Manual
5 $\beta$ the rotation angle of the semi-loof element edge $\text{[rad]}$, see the Reference Manual
5 $\varphi_y$ the rotation angle about the $y$ axis $\text{[rad]}$, see the Reference Manual
6 $\varphi_z$ the rotation angle about the $z$ axis $\text{[rad]}$, see the Reference Manual
Note
More than one homogeneous boundary condition may be assigned to a single node. In that case, the conditions are combined.

Example

The assignment

… /B 0 C 6 N <nodes>/ …

fixes the rotation angle $\varphi_z$, which is meaningful only for nodes belonging to beam elements. If the rotation $\varphi_z$ is not defined at one of the nodes, the program does not report an error and ignores the prescription at that node. The assignment applies to the remaining nodes.

Example

Let us consider a shell whose edge is clamped but free to slide (transverse contraction is allowed), see the figure. Nodes 21 and 25 can move freely in the direction of the $y$ axis. Node 77 is fully clamped, including the rotation angles. According to the Reference Manual, corner nodes have three degrees of freedom, of which the 1st and 3rd must be fixed. The midside node has five degrees of freedom and must be fully anchored. Making the angles $\alpha$ and $\beta$ zero at node 77 ensures zero rotation along the entire edge.

The assignment might, for example, take the form

… /B 0 N 77/B 0 C 1 3 N 21 25/ …