scholarly journals Performance of a Three-Substep Time Integration Method on Structural Nonlinear Seismic Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Jinyue Zhang ◽  
Lei Shi ◽  
Tianhao Liu ◽  
De Zhou ◽  
Weibin Wen
Keyword(s):  
Nonlinear Dynamic ◽  
Integration Method ◽  
Seismic Analysis ◽  
Time Integration ◽  
Implicit Time ◽  
Numerical Dissipation ◽  
Dynamic Problems ◽  
Element Analysis ◽  
Time Integration Method ◽  
Period Elongation

In this work, a study of a three substeps’ implicit time integration method called the Wen method for nonlinear finite element analysis is conducted. The calculation procedure of the Wen method for nonlinear analysis is proposed. The basic algorithmic property analysis shows that the Wen method has good performance on numerical dissipation, amplitude decay, and period elongation. Three nonlinear dynamic problems are analyzed by the Wen method and other competitive methods. The result comparison indicates that the Wen method is feasible and efficient in the calculation of nonlinear dynamic problems. Theoretical analysis and numerical simulation illustrate that the Wen method has desirable solution accuracy and can be a good candidate for nonlinear dynamic problems.

scholarly journals An Improved Time Integration Method Based on Galerkin Weak Form with Controllable Numerical Dissipation

2021 ◽  
Vol 11 (4) ◽  
pp. 1932
Author(s):  
Weixuan Wang ◽  
Qinyan Xing ◽  
Qinghao Yang
Keyword(s):  
High Frequency ◽  
Integration Method ◽  
Time Integration ◽  
Low Frequency ◽  
Weak Form ◽  
High Accuracy ◽  
Numerical Dissipation ◽  
Frequency Range ◽  
Time Integration Method ◽  
Numerical Damping

Based on the newly proposed generalized Galerkin weak form (GGW) method, a two-step time integration method with controllable numerical dissipation is presented. In the first sub-step, the GGW method is used, and in the second sub-step, a new parameter is introduced by using the idea of a trapezoidal integral. According to the numerical analysis, it can be concluded that this method is unconditionally stable and its numerical damping is controllable with the change in introduced parameters. Compared with the GGW method, this two-step scheme avoids the fast numerical dissipation in a low-frequency range. To highlight the performance of the proposed method, some numerical problems are presented and illustrated which show that this method possesses superior accuracy, stability and efficiency compared with conventional trapezoidal rule, the Wilson method, and the Bathe method. High accuracy in a low-frequency range and controllable numerical dissipation in a high-frequency range are both the merits of the method.

scholarly journals Impact of difference between explicit and implicit second-order time integration schemes on isotropic/anisotropic steady incompressible turbulence field

2021 ◽  
Vol 2090 (1) ◽  
pp. 012145
Author(s):  
Ryuma Honda ◽  
Hiroki Suzuki ◽  
Shinsuke Mochizuki
Keyword(s):  
Kinetic Energy ◽  
Energy Conservation ◽  
Integration Method ◽  
Time Integration ◽  
Second Order ◽  
Implicit Time ◽  
Explicit Time Integration ◽  
Time Integration Method ◽  
Implicit Time Integration ◽  
Time Integration Methods

Abstract This study presents the impact of the difference between the implicit and explicit time integration methods on a steady turbulent flow field. In contrast to the explicit time integration method, the implicit time integration method may produce significant kinetic energy conservation error because the widely used spatial difference method for discretizing the governing equations is explicit with respect to time. In this study, the second-order Crank-Nicolson method is used as the implicit time integration method, and the fourth-order Runge-Kutta, second-order Runge-Kutta and second-order Adams-Bashforth methods are used as explicit time integration methods. In the present study, both isotropic and anisotropic steady turbulent fields are analyzed with two values of the Reynolds number. The turbulent kinetic energy in the steady turbulent field is hardly affected by the kinetic energy conservation error. The rms values of static pressure fluctuation are significantly sensitive to the kinetic energy conservation error. These results are examined by varying the time increment value. These results are also discussed by visualizing the large scale turbulent vortex structure.

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.

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