Stability and accuracy analysis of the central difference method for real-time substructure testing

2005 ◽  
Vol 34 (7) ◽  
pp. 705-718 ◽  
Author(s):  
B. Wu ◽  
H. Bao ◽  
J. Ou ◽  
S. Tian
Keyword(s):  
Real Time ◽  
Difference Method ◽  
Accuracy Analysis ◽  
Central Difference ◽  
Central Difference Method ◽  
Stability And Accuracy

Second Order Errors Related to Geometric Nonlinearity in Explicit Central Difference Operator

2008 ◽  
Author(s):  
Don R. Metzger ◽  
Young-Suk Kim
Keyword(s):  
Difference Method ◽  
Difference Operator ◽  
Time Integration ◽  
General Nature ◽  
Time Step ◽  
Central Difference ◽  
Central Difference Method ◽  
Dynamic Structures ◽  
The Stability ◽  
Stability And Accuracy

Numerical analysis of nonlinear dynamic structures frequently makes use of the central difference method to step the transient forward in time. The method is particularly robust, accommodating material and geometric nonlinearities as well as contact surfaces and constraints of a very general nature. The implementation of the method is most usually performed according to [1], where velocity terms (or more generally rate quantities) are taken half a time step from the displacement and acceleration terms. It was recognized that a proper check of energy balance, requires that velocity must also be interpolated to the integer steps [2]. The stability and accuracy of the central difference method is well established, and decades of experience including its use in numerous commercial finite element codes confirms why it is the method of choice for explicit time integration of transients.

scholarly journals Frequency-Dependent FDTD Algorithm Using Newmark’s Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Bing Wei ◽  
Le Cao ◽  
Fei Wang ◽  
Qian Yang
Keyword(s):  
Differential Equation ◽  
Electric Field ◽  
Field Intensity ◽  
Time Domain ◽  
Difference Method ◽  
Electric Field Intensity ◽  
Polarization Vector ◽  
Solution Stability ◽  
Central Difference ◽  
Central Difference Method

According to the characteristics of the polarizability in frequency domain of three common models of dispersive media, the relation between the polarization vector and electric field intensity is converted into a time domain differential equation of second order with the polarization vector by using the conversion from frequency to time domain. Newmarkβγdifference method is employed to solve this equation. The electric field intensity to polarizability recursion is derived, and the electric flux to electric field intensity recursion is obtained by constitutive relation. Then FDTD iterative computation in time domain of electric and magnetic field components in dispersive medium is completed. By analyzing the solution stability of the above differential equation using central difference method, it is proved that this method has more advantages in the selection of time step. Theoretical analyses and numerical results demonstrate that this method is a general algorithm and it has advantages of higher accuracy and stability over the algorithms based on central difference method.

Numerical Method for Earthquake-Induced Pounding between Girder and Shear Key. I: Theory

2010 ◽  
Vol 34-35 ◽  
pp. 1402-1405
Author(s):  
Wei He
Keyword(s):  
Seismic Response ◽  
Difference Method ◽  
Equations Of Motion ◽  
Earthquake Ground Motion ◽  
Analysis Model ◽  
Central Difference ◽  
Kelvin Model ◽  
Shear Key ◽  
Analytical Perspective ◽  
Central Difference Method

Earthquake ground motion can induce out-of-phase vibrations between girders and shear keys, which can result in impact or pounding. The paper investigated pounding between girder and shear key from an analytical perspective. By introducing the initial gap in the analysis model, the elastomer stiffness played a role in the transverse vibration as well. A simplified model of bridge transverse seismic response considering girder-shear key pounding was developed. The equations of motion of the bridge response to transverse ground excitation were assembled and solved using the central difference method. Pounding was simulated using a contact force-based model—Kelvin model. Thus, the girder-shear key pounding effects and bridge transverse seismic response can be obtained by using a step-by-step direct integration the central difference method with the appropriate parameters. The proposed method is very useful in the seismic design of bridge.

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