Link08 – Plastic Wen Link

Problem Description

This example uses a single degree of freedom structure to test the behavior of a plastic Wen link element. Bilinear force-deformation characteristics are defined for the link element along with an exponent that defines the sharpness of the transition from the initial stiffness to the yielded stiffness. A nonlinear static analysis is used to push the link element to a positive 10 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 negative 10 inch displacement, a 20 inch push. The resulting link force at various deformations is compared with the defined link force-deformation characteristics.
This model consists of a single joint, labeled joint 1, and one link element. The model is created in the XZ plane. Only the Uz degree of freedom is active for the analysis. The plastic Wen link element is modeled as a single-joint link element at joint 1. This means that one end of the link element is connected to the ground and the other end is connected to joint 1. The link element is oriented such that its positive local 2 axis is parallel to the positive global Z axis. This is not the default orientation of single joint link elements so this model’s advanced local axes assignment feature for link elements is used to orient the local axes as desired. Only U2 degree of freedom properties are defined for the link element.
Only the nonlinear properties of the link element are relevant for this example because the only load cases used are nonlinear load cases. The stiffness of the link element is 100 k/in. The yield force is 50 kips. The ratio of initial stiffness to yielded stiffness is 0.1; in other words, the yielded stiffness is 10 k/in. The yielding exponent, which controls the sharpness of the transition from the initial stiffness to the yielded stiffness, is 1.
The weight of the link is 1 kip. This is the only load acting on the link, and it is applied as a gravity load acting in the Z direction.
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 to a positive 10 inch deformation. NLSTAT2 starts from the conditions at the end of NLSTAT1 and pushes the link from a positive 10 inch deformation to a negative 10 inch deformation.

Tested Features

•  Plastic Wen links
•  Displacement-controlled nonlinear static analysis
•  Link local axis assignments
•  Link gravity load