Link01 – Linear Link with Ramp Loading

Problem Description

In this example a ramp load is applied to an undamped single degree of freedom structure. The ramp loading has a finite rise time (ramp time), tr, but remains constant thereafter. The displacements of the structure at two selected times are compared with hand calculated results based on theory presented in Chopra 1995. The output times used for comparison are selected such that one is less than tr and the other is greater than tr. The following properties are assumed for the model:

From those two properties the expected period of the structure, T, is calculated as:

The analysis is performed using two different ramp loading rise times, tr, in two different load cases. In case A, tr is equal to the period of the structure, tr = T = π. In case B, tr is equal to one-half the period of the structure, tr = T/2 = π/2. This model consists of a two-joint linear link element that is fixed at one end and free at the other end. As shown in the figure on the following page, 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. The mass, m, and the ramp loading, p(t), are applied to the joint at the free end of the link, which is joint 2 in the figure.

Tested Features

•  Linear links
•  Modal load case for eigenvectors
•  Modal time history load case
•  Direct integration time history load case
•  Ramp loading