Evaluation of the Pounding Forces During Earthquake Using Explicit Dynamic Time Integration Method

Abstract

Pounding effects during earthquake is a subject of high significance for structural engineers performing in the urban areas. In this paper, two ways to account for structural pounding are used in a MATLAB code, namely classical stereomechanics approach and nonlinear viscoelastic impact element. The numerical study is performed on SDOF structures acted by ELCentro recording. While most of the studies available in the literature are related to Newmark implicit time integration method, in this study the equations of motion are numerical integrated using central finite difference method, an explicit method, having the main advantage that in the displacement at the i th +1 step is calculated based on the loads from the i th step. Thus, the collision is checked and the pounding forces are taken into account into the equation of motion in an easier manner than in an implicit integration method. First, a comparison is done using available data in the literature. Both linear and nonlinear behavior of the structures during earthquake is further investigated. Several layout scenarios are also investigated, in which one or more weak buildings are adjacent to a stiffer building. One of the main findings in this paper is related to the behavior of a weak structure located between two stiff structures.

A State Space Formulation for the Evaluation of the Pounding Forces During Earthquake

“…The values in table 1 are consistent with the data available in [9] and [11]. Proportional damping (Rayleigh) to the mass and stiffness is used.…”

“…Equations (9) and (10) will be used in eq. (8) written in state space form (11). With the notation from eq.…”

“…5. Figures 6 and 7 illustrate the comparison of the data obtained by state space approach to another explicit solver based on central difference method [11]. The numerical values of the displacement time-history are tabulated in Table 2 presented in the appendix for comparison reasons.…”

“…In this chapter the nonlinear viscoelastic impact element is employed and the values are compared with the data presented in [11]. The refference data in [11] is obtained with stereomechanics aproach as well as the nonlinear viscoleastic impact element, but with another time integration method, i.e. the finite central difference method.…”

“…The time integration method used in these studies is implicit. The previous study of Nica and Pricopie [11] presents an explicit time integration methodology based on central finite difference, and compares the data obtained using the stereomechanics approach with the ones from the nonlinear viscoelastic impact element. In this paper, two idealized SDOF structures are acted by El-Centro recording and their nonlinear response is obtained using a direct integration method of the equations in the state-space form, i.e.…”