Direct integration methods with integral model for dynamic systems

Hexiang, Lu; Yu, Hongjie; Chunhang, Qiu

doi:10.1007/bf02437882

Cited by 2 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is worth mentioning that some research on this kind of time integrations is available. These studies show the performances of the predictor-corrector techniques for both linear and non-linear analyses (Chung and Hulbert, 1994;Hulbert and Chung, 1996;He-xiang et al, 2001).…”

Section: Introductionmentioning

confidence: 97%

Stability and accuracy of non-linear dynamic analysis using time integration algorithms

Rezaiee‐Pajand¹,

Sarafrazi²

2012

Proceedings of the Institution of Civil Engineers - Structures

View full text Add to dashboard Cite

The stability and accuracy of two families of time integration algorithms are investigated in this study. The paper has three intended goals. The first one is to find the precise properties of the implicit higher-order accuracy methods. The capabilities of the family members are found both by analytical and numerical procedures. The second goal is to find the well-defined characteristics of the predictor–corrector methods. For application purposes, the best order of each family is introduced by this investigation. Numerical results show that the stability properties of the implicit high-order accuracy and predictor–corrector methods are approximately the same. As a third goal, a modified dynamic relaxation method is also developed for non-linear dynamic analyses. This is a robust scheme that uses less memory and requires less computational effort, in comparison with the previous version of dynamic relaxation method.

show abstract

Section: Introductionmentioning

confidence: 97%

Stability and accuracy of non-linear dynamic analysis using time integration algorithms

Rezaiee‐Pajand¹,

Sarafrazi²

2012

Proceedings of the Institution of Civil Engineers - Structures

View full text Add to dashboard Cite

show abstract

“…To satisfy the pursuit for high accurate solutions, higher-order algorithms [24][25][26][27][28][29][30][31][32] were developed. The series algorithms, such as the Taylor series algorithm and the Lie series algorithm, are classical higher-order algorithms, which cannot be unconditionally stable when the accuracy order is more than two [25].…”

Section: Introductionmentioning

confidence: 99%

An Improved Higher-Order Time Integration Algorithm for Structural Dynamics

Ji¹,

Xing²

2021

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

Based on the weighted residual method, a single-step time integration algorithm with higher-order accuracy and unconditional stability has been proposed, which is superior to the second-order accurate algorithms in tracking long-term dynamics. For improving such a higher-order accurate algorithm, this paper proposes a two sub-step higher-order algorithm with unconditional stability and controllable dissipation. In the proposed algorithm, a time step interval [t k , t k + h] where h stands for the size of a time step is divided into two sub-stepsA non-dissipative fourth-order algorithm is used in the first sub-step to ensure low-frequency accuracy and a dissipative third-order algorithm is employed in the second sub-step to filter out the contribution of high-frequency modes. Besides, two approaches are used to design the algorithm parameter γ . The first approach determines γ by maximizing low-frequency accuracy and the other determines γ for quickly damping out highfrequency modes. The present algorithm uses ρ ∞ to exactly control the degree of numerical dissipation, and it is third-order accurate when 0 ≤ ρ ∞ < 1 and fourth-order accurate when ρ ∞ = 1. Furthermore, the proposed algorithm is self-starting and easy to implement. Some illustrative linear and nonlinear examples are solved to check the performances of the proposed two sub-step higher-order algorithm.

show abstract

Direct integration methods with integral model for dynamic systems

Cited by 2 publications

References 0 publications

Stability and accuracy of non-linear dynamic analysis using time integration algorithms

Stability and accuracy of non-linear dynamic analysis using time integration algorithms

An Improved Higher-Order Time Integration Algorithm for Structural Dynamics

Contact Info

Product

Resources

About