A new family of explicit time integration methods for linear and non-linear structural dynamics

1994 ◽  
Vol 37 (23) ◽  
pp. 3961-3976 ◽  
Author(s):  
Jintai Chung ◽  
Jang Moo Lee
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Integration Methods ◽  
Explicit Time Integration ◽  
New Family ◽  
Non Linear ◽  
Time Integration Methods

A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method

1993 ◽  
Vol 60 (2) ◽  
pp. 371-375 ◽  
Author(s):  
J. Chung ◽  
G. M. Hulbert
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Low Frequency ◽  
Numerical Dissipation ◽  
Integration Algorithm ◽  
Integration Methods ◽  
New Family ◽  
Time Integration Methods ◽  
Improved Performance ◽  
Dynamics Problems

A new family of time integration algorithms is presented for solving structural dynamics problems. The new method, denoted as the generalized-α method, possesses numerical dissipation that can be controlled by the user. In particular, it is shown that the generalized-α method achieves high-frequency dissipation while minimizing unwanted low-frequency dissipation. Comparisons are given of the generalized-α method with other numerically dissipative time integration methods; these results highlight the improved performance of the new algorithm. The new algorithm can be easily implemented into programs that already include the Newmark and Hilber-Hughes-Taylor-α time integration methods.

Optimization of a Class of n-Sub-Step Time Integration Methods for Structural Dynamics

2021 ◽  
Author(s):  
Yi Ji ◽  
Yufeng Xing
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Single Step ◽  
Numerical Dissipation ◽  
Integration Methods ◽  
Stiffness Matrices ◽  
Difference Formula ◽  
Different Types ◽  
Time Integration Methods ◽  
Methods Numerical

This paper develops a family of optimized [Formula: see text]-sub-step time integration methods for structural dynamics, in which the generalized trapezoidal rule is used in the first [Formula: see text] sub-steps, and the last sub-step employs [Formula: see text]-point backward difference formula. The proposed methods can achieve second-order accuracy and unconditional stability, and their degree of numerical dissipation can range from zero to one. Also, the proposed methods can achieve the identical effective stiffness matrices for all sub-steps, reducing computational costs in the analysis of linear systems. Using the spectral analysis, optimized algorithmic parameters are presented, ensuring that the proposed methods can accurately calculate different types of dynamic problems such as wave propagation, stiff and nonlinear systems. Besides, with the increase in the number of sub-steps, the accuracy of the proposed methods can be enhanced without extra workload compared with single-step methods. Numerical experiments show that the proposed methods perform better in different dynamic systems.

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