An improved time integration scheme based on uniform cubic B-splines and its application in structural dynamics

doi:10.1007/s10483-017-2207-8

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (6): 889-908.doi: https://doi.org/10.1007/s10483-017-2207-8

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An improved time integration scheme based on uniform cubic B-splines and its application in structural dynamics

Weibin WEN¹, Hongshuai LEI², Kai WEI³, Baosheng XU⁴, Shengyu DUAN², Daining FANG^1,2

1. College of Engineering, Peking University, Beijing 100871, China;
2. Beijing Institute of Technology, Beijing 100081, China;
3. State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, School of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China;
4. Key Laboratory of Applied Mechanics, Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing 100084, China

Received:2016-05-03 Revised:2016-09-27 Online:2017-06-01 Published:2017-06-01
Contact: Kai WEI E-mail:weikai@hnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Nos. 11602004 and 11602081) and the Fundamental Research Funds for the Central Universities (No. 531107040934)

Abstract

Abstract:

A time integration algorithm for structural dynamic analysis is proposed by uniform cubic B-spline functions. The proposed algorithm is successfully used to solve the dynamic response of a single degree of freedom (SDOF) system, and then is generalized for a multiple-degree of freedom (MDOF) system. Stability analysis shows that, with an adjustable algorithmic parameter, the proposed method can achieve both conditional and unconditional stabilities. Validity of the method is shown with four numerical simulations. Comparison between the proposed method and other methods shows that the proposed method possesses high computation accuracy and desirable computation efficiency.

Key words: homotopy, continuation method, bifurcation, isolated singularity, dynamical system, time integration, stability, dynamic response, B-spline

2010 MSC Number:

74Kxx
34N05

Weibin WEN, Hongshuai LEI, Kai WEI, Baosheng XU, Shengyu DUAN, Daining FANG. An improved time integration scheme based on uniform cubic B-splines and its application in structural dynamics. Applied Mathematics and Mechanics (English Edition), 2017, 38(6): 889-908.

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References

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An improved time integration scheme based on uniform cubic B-splines and its application in structural dynamics

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