scholarly journals A Precise and Stiffly Stable Time Integration Method for Dynamic Analysis

2003 ◽  
Vol 46 (2) ◽  
pp. 492-499 ◽  
Author(s):  
Takeshi FUJIKAWA ◽  
Etsujiro IMANISHI ◽  
Takao NANJYO ◽  
Naoki SUGANO
Keyword(s):  
Dynamic Analysis ◽  
Integration Method ◽  
Time Integration ◽  
Time Integration Method

F-5-1-1 A precise and stiffly stable time integration method for dynamic analysis

2002 ◽  
Vol 2002 (0) ◽  
pp. 407-413
Author(s):  
Takeshi Fujikawa ◽  
Etsujiro Imanishi ◽  
Takao Nanjo ◽  
Naoki Sugano
Keyword(s):  
Dynamic Analysis ◽  
Integration Method ◽  
Time Integration ◽  
Time Integration Method

Dynamic Analysis of Slender Rods

1982 ◽  
Vol 104 (4) ◽  
pp. 302-306 ◽  
Author(s):  
D. L. Garrett
Keyword(s):  
Dynamic Analysis ◽  
Integration Method ◽  
Time Integration ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Element Model ◽  
Elastic Rod ◽  
Time Integration Method ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

A new three-dimensional finite element model of an inextensible elastic rod with equal principal stiffnesses is presented. The model permits large deflections and finite rotations and accounts for tension variation along its length. Its use in static analysis is described and a time integration method for dynamic analysis is developed. Accuracy of the spatial discretization and stability of the time integration method are demonstrated by comparison of numerical results with exact solutions for certain nonlinear 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.

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