T2D2

2D Linear Truss

• Number of Nodes: 2

• Number of DoFs: 2 (Translation, Translation)

• DoF Label: U1, U2

Syntax

element T2D2 (1) (2) (3) (4) (5) [6] [7] [8] [9]
# (1) int, unique element tag
# (2) int, node i
# (3) int, node j
# (4) int, material tag
# (5) double, cross sectional area
# [6] bool string, nonlinear geometry switch, default: false
# [7] bool string, if to update sectional area, default: false
# [8] bool string, if to use log strain, default: false
# [9] double, flexural rigidity, positive to activate Euler buckling limit, default: -1.0

Remarks

1. The corotational formulation is implemented, turn on the nonlinear geometry switch to use it.

2. According to different implementations of details, either a constant area or a constant volume assumption is adopted. If the volume is constant, the cross-sectional area would be updated based on $A=\dfrac{A_0L_0}{L}$.

3. The computation of strain can be altered from engineering strain (by default) to log strain.

4. By turning on all three switches, full nonlinearity can be achieved.

Euler Buckling Limit

[added in version 2.8]

The parameter [9] allows one to define a positive flexural rigidity $EI$ that will be used to compute the Euler buckling load. When [9] is negative, the check is disabled.

The truss element matches a pinned-pinned condition, for which the Euler buckling load is given by

$$P_{cr}=\dfrac{\pi^2EI}{L^2}$$

where $L$ is the length of the truss element.

For a given positive $EI$, $P_{cr}$ can be computed using only the $L$, regardless of the used material model. The computed axial resistance will be compared to $P_{cr}$ and an error will be issued if the axial resistance (in compression) exceeds $P_{cr}$.

This is a theoretical upper bound, the design value requires an additional reduction.