Effects of time step in stochastic central difference method

1992 ◽  
Vol 159 (1) ◽  
pp. 182-188 ◽  
Author(s):  
S.W. Zhang ◽  
H.H. Zhao
Keyword(s):  
Difference Method ◽  
Time Step ◽  
Central Difference ◽  
Central Difference Method

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.

Computational Methods Used in the Determination of Loading Rate: Experimental and Clinical Implications

1999 ◽  
Vol 15 (4) ◽  
pp. 404-417 ◽  
Author(s):  
C. Mark Woodard ◽  
Margaret K. James ◽  
Stephen P. Messier
Keyword(s):  
Difference Method ◽  
Ground Reaction Force ◽  
Loading Rate ◽  
Reaction Force ◽  
Vertical Force ◽  
Vertical Ground Reaction Force ◽  
Central Difference ◽  
Symptomatic Knee Osteoarthritis ◽  
Central Difference Method ◽  
Vertical Ground

Our purpose was to compare methods of calculating loading rate to the first peak vertical ground reaction force during walking and provide a rationale for the selection of a loading rate algorithm in the analysis of gait in clinical and research environments. Using vertical ground reaction force data collected from 15 older adults with symptomatic knee osteoarthritis and 15 healthy controls, we: (a) calculated loading rate as the first peak vertical force divided by the time from touchdown until the first peak; (b) calculated loading rate as the slope of the least squares regression line using vertical force and time as the dependent and independent variables, respectively; (c) calculated loading rate over discrete intervals using the Central Difference method; and (d) calculated loading rate using vertical force and lime data representing 20% and 90% of the first peak vertical force. The largest loading rate, which may be of greatest clinical importance, occurred when loading rates were calculated using the fewest number of data points. The Central Difference method appeared to maximize our ability to detect differences between healthy and pathologic cohorts. Finally, there was a strong correlation between methods, suggesting that all four methods are acceptable. However, if maximizing the chances of detecting differences between groups is of primary importance, the Central Difference method appears superior.

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