Numerical modeling of MDOF structures with sliding supports using rigid-plastic link

Abstract

In this paper, the responses of multi-degree-of-freedom (MDOF) structures on sliding supports subjected to harmonic or random base motions are investigated. Modeling of the friction force under the foundation raft is accomplished by using a fictitious rigid link which has a rigid-perfectly plastic material. This will result in identical equations of motion for the sliding structure, both in the sliding and non-sliding (stick) phases which greatly simplifies the implementation of the method into a numerical algorithm. In this model the phase transition times are determined with high accuracy. This has two advantages: first, it prevents the so-called high-frequency oscillation of the relative velocity at the end of the sliding phase, and second, the time steps can be selected so that each falls exactly within one phase of motion. In this case, the stiffness matrix of the structure remains constant throughout each phase and thus any method for solving the non-linear differential equations of motion (e.g. Newmark method) can be used without iteration. The proposed method, besides its simplicity, is numerically very efficient and considerably reduces the required analysis time compared with most of the other methods.