| Matrix or Vector | Shape Functions | Integration Points |
|---|---|---|
| Stiffness and Damping Matrices | Equation 11–6 | None |
| Mass Matrix | None (lumped mass formulation) | None |
| Stress Stiffness Matrix | Equation 11–7 and Equation 11–8 | None |
The element is not capable of carrying bending or twist loads. The force is assumed to be constant over the entire element.
All element matrices and load vectors are described below. They are generated in the element coordinate system and are then converted to the global coordinate system. The element stiffness matrix is:
 | (13–1) |
where:
| K = element stiffness (input as K on R command) |
The element mass matrix is:
 | (13–2) |
where:
| M = total element mass (input as M on R command) |
The element damping matrix is:
 | (13–3) |
where:
| C = element damping (input as C on R command) |
The element stress stiffness matrix is:
 | (13–4) |
where:
| F = the axial force in the element (output as FORCE) |
| L = current element length (output as CLENG) |
The element load vector is:
 | (13–5) |
where:
|
|
The applied force vector is:
 | (13–6) |
where:
| F' = applied force thru surface load input using the PRES label |
The Newton-Raphson restoring force vector is:
 | (13–7) |
The element spring force is determined from
 | (13–8) |
where:
| F = element spring force (output as FORCE) |
| SA = applied stroke (output as STROKE) thru surface load input using the PRES label |
| SM = computed or measured stroke (output as MSTROKE) |
The lengths, shown in the figure at the beginning of this section, are:
| Lo = initial length (output as ILEN) |
| Lo + SM = current length (output as CLEN) |