Nodal spring

The elastic attachment of a node (a spring) must be prescribed in the first load case and applies to all subsequent load cases.

In the name.i2 file, a vector is first defined using a NV set:

NV set number T 2 N node number V $k_n$ $k_t$ $\cos_{nx}$ $\cos_{ny}$ $\cos_{nz}$

or

NV set number T 3 N node number V $k_x$ $k_y$ $k_z$

or

NV set number T 4 N node number V $k_{11}$ $k_{12}$ $k_{22}$ $k_{13}$ $k_{23}$ $k_{33}$ $\dots$ $k_{1m}$ $k_{2m}$ $\dots$ $k_{mm}$

and the set thus defined is then assigned to the element that contains the node with the spring:

AS 1 /$\dots$ /N set number E element number /$\dots$

where

the global node number determines the node at which the spring is attached,
all stiffnesses $k$ are specified in $\text{N}/\text{m}$.

The first set form is used to prescribe the axial stiffness $k_n$ and the transverse stiffness $k_t$ of a spring whose axis is given by direction cosines.

The second set form is used to prescribe the stiffnesses $k_x$, $k_y$, and $k_z$ of a spring in the global system.

The third set form is used to prescribe a symmetric stiffness matrix, for example one determined as part of the analysis of a spatial piping system modeled using line elements. The length of the vector, i.e., the number of prescribed values after the key letter V, must be exactly equal to $m(m+1)/2$, where $m$ is the number of degrees of freedom of the node. The stiffnesses are written by columns, always from the first row up to and including the main diagonal (i.e., the upper triangle).

Note
If the node with the spring is shared by more than one element, the assignment is made to only (arbitrary) one of these elements.

Note
By simultaneously referencing the node number and the number of the element in which the node is located, the problem is overdetermined. This inconvenient way of specifying the data is necessitated by the fact that the spring is not treated as a separate element.

Example

Let us consider a spring at node 4953 of a beam element, which we want to prescribe using a stiffness matrix.

The NV set will have the form

NV 1 T 4 N 4953 V
   13340000  ;                column 1
  -15080000  19820000   ;             column 2
   -1149000   1406000   1299000  ;             column 3
   -5115000   6766000   -194200   3282000  ;             column 4
   -4306000   4782000   -493500   2144000   2544000  ;             column 5
   -2788000   5071000    323000   1742000    835300   2504000 ;             column 6