Problem Description

This example uses a single degree of freedom structure to test the behavior of a multi-linear elastic (no hysteresis) link element. Multi-linear elastic forcedeformation characteristics are defined for the link element. A nonlinear static analysis is used to push the link element to a negative 12 inch displacement. Then a second nonlinear load case is started from the final conditions of the first load case and used to push the link element to a positive 12 inch displacement, a 24 inch push. The link force at the end of each load case is compared with the defined link force-deformation characteristics. In addition the entire forcedeformation history for each load case is graphically compared with the defined link force-deformation characteristics.
This model consists of a two-joint multi-linear link element that is fixed at one end and free at the other end. As shown in the following figure, the link is modeled in the XZ plane and is oriented such that its length (and thus its local 1 axis) is parallel to the global Z axis. The link element length is arbitrarily chosen as ten inches.
The only active degree of freedom in the model is Uz. Similarly, the only degree of freedom in the linear link element with nonzero properties is the U1 (axial) degree of freedom.
A unit load is applied in the positive Z direction at joint 2. This load is used in the displacement-controlled static nonlinear analysis.

Link Properties

The link force-deformation characteristics are defined as shown in the table to the right. This table is plotted in the following figure. The solid line in the force-deformation plot is the data actually included in the table. The dotted lines in the plot show how this model extrapolates the provided data to reach the desired deformations. In general, for the multi-linear link, the slope given by the last two specified points on the positive deformation axis is extrapolated to infinite positive deformation. Similarly, the slope given by the last two specified points on the negative deformation axis is extrapolated to infinite negative deformation.

Load Case Definitions

Two displacement-controlled nonlinear static load cases are used in this example. They are named NLSTAT1 and NLSTAT2.
NLSTAT1 starts from zero initial conditions and pushes the link out to a negative 12 inch deformation.
NLSTAT2 starts from the conditions at the end of NLSTAT1 and pushes the link from a negative 12 inch deformation to a positive 12 inch deformation.

Tested Features

Multi-linear links
Displacement-controlled nonlinear static analysis

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