scholarly journals Theory and Implementation of a Two-Step Unconditionally Stable Explicit Integration Algorithm for Vibration Analysis of Structures

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Li Changqing ◽  
Jie Junping ◽  
Jiang Lizhong ◽  
T. Y. Yang
Keyword(s):  
Vibration Analysis ◽  
Time History ◽  
Superior Performance ◽  
Explicit Integration ◽  
Third Order ◽  
Integration Algorithm ◽  
Unconditionally Stable ◽  
History Analysis ◽  
Integration Algorithms ◽  
Explicit Integration Algorithm

Time history analysis is becoming the routine process to quantify the response of the structure under dynamic loads. In this paper, a novel two-step unconditionally stable explicit integration algorithm, named Unconditional Stable Two-Step Explicit Displacement Method (USTEDM), is proposed for vibration analysis of structure. USTEDM is unconditionally stable, requires low memory, produces no overshoot, and is third order accurate. The accuracy and efficiency of USTEDM are presented and compared with other commonly used integration algorithms. The result shows that the proposed algorithm has superior performance and can be used efficiently in solving vibration response of civil engineering structure.

Improved Explicit Method for Time History Analysis

2007 ◽  
Author(s):  
Shuenn-Yih Chang ◽  
Chiu-Li Huang
Keyword(s):  
Time History ◽  
Time History Analysis ◽  
Conditional Stability ◽  
Explicit Method ◽  
Explicit Integration ◽  
Unconditionally Stable ◽  
Stability Properties ◽  
Linear Elastic ◽  
History Analysis ◽  
Improved Stability

In this paper, an explicit integration method is presented. This method is shown to have the same numerical characteristics as those of the constant average acceleration method for a linear elastic system. This implies that it is unconditionally stable for linear elastic systems. However, it shows very different stability properties for nonlinear systems. In fact, it has conditionally stability for an instantaneous stiffness hardening system while it remains unconditionally stable for an instantaneous stiffness softening system. The conditional stability property is much better than for the Newmark explicit method for instantaneous stiffness hardening systems. Meanwhile, this method involves no iterative procedure in the step-by-step integration. Thus, it is very promising for time history analysis since it is explicit and has improved stability properties.

scholarly journals Stability Analysis of an Explicit Integration Algorithm with 3D Viscoelastic Artificial Boundary Elements

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Shutao Li ◽  
Jingbo Liu ◽  
Xin Bao ◽  
Yifan Jia ◽  
Lan Xiao ◽  
...  
Keyword(s):  
Stability Analysis ◽  
Near Field ◽  
Boundary Elements ◽  
Artificial Boundary ◽  
Explicit Integration ◽  
Integration Algorithm ◽  
Explicit Algorithm ◽  
Time Increment ◽  
The Stability ◽  
Explicit Integration Algorithm

Viscoelastic artificial boundary elements are one of the most commonly used artificial boundaries when solving dynamic soil-structure interactions or near-field wave propagation problems. However, due to the lack of clear and practical stability criteria for the explicit algorithm that considers the influence of viscoelastic artificial boundary elements, the determination of the stable time increment in such numerical analyses is still a challenge. In this study, we proposed a numerical stability analysis method for the explicit algorithm with a 3D viscoelastic artificial boundary element based on the idea of a subsystem. Through this method, the artificial boundary subsystem that controls the stability of the overall numerical system is determined, and the analytical solution for the stability condition of the explicit integration algorithm with 3D viscoelastic artificial boundary elements is obtained. On this basis, the maximum time increment for solving dynamic problems with viscoelastic artificial boundary elements can be determined.

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