A new direct time integration method for the equations of motion in structural dynamics

2013 ◽  
Vol 94 (9) ◽  
pp. 757-774 ◽  
Author(s):  
J.T. Katsikadelis
Keyword(s):  
Structural Dynamics ◽  
Integration Method ◽  
Equations Of Motion ◽  
Time Integration ◽  
Time Integration Method

scholarly journals EVALUATION OF THE POUNDING FORCES DURING EARTHQUAKE USING EXPLICIT DYNAMIC TIME INTEGRATION METHOD

2017 ◽  
Vol 13 (3) ◽  
pp. 21-39
Author(s):  
George Bogdan Nica ◽  
Andrei Gheorghe Pricopie
Keyword(s):  
Urban Areas ◽  
Integration Method ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Time Integration ◽  
Nonlinear Behavior ◽  
Implicit Time ◽  
Time Integration Method ◽  
Nonlinear Viscoelastic ◽  
Weak Structure

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 ith+1 step is calculated based on the loads from the ith 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.

An Accurate Explicit Direct Time Integration Method for Computational Structural Dynamics

1999 ◽  
Author(s):  
Bertrand Tchamwa ◽  
Ted Conway ◽  
Christian Wielgosz
Keyword(s):  
Structural Dynamics ◽  
Integration Method ◽  
Time Integration ◽  
Single Step ◽  
New Method ◽  
Phase Portraits ◽  
Structural Dynamic ◽  
Low Frequencies ◽  
Time Integration Method ◽  
Non Linear

Abstract The purpose of this paper is to introduce a new simple explicit single step time integration method with controllable high-frequency dissipation. As opposed to the methods generally used in structural dynamics, with a consistency experimentally chosen of second order, the new method is only first-order-consistent but yields smaller numerical errors in low frequencies and is therefore very efficient for structural dynamic analysis. The new method remains explicit for any structural dynamics problem, even when a non-diagonal damping matrix is used in linear structural dynamics problem or when the non-linear internal force vector is a function of velocities. Convergence and spectral properties of the new algorithm are discussed and compared to those of some well-known algorithms. Furthermore, the validity and efficiency of the new algorithm are shown in a non-linear dynamic example by comparison of phase portraits.

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