A Taylor Series Integration Method with Coupling in Structural Dynamics

2012 ◽  
Vol 166-169 ◽  
pp. 9-13
Author(s):  
Ze Ying Guo
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Integration Method ◽  
Damping Ratio ◽  
Time Integration ◽  
Taylor Series Expansion ◽  
Time Step ◽  
Structural Dynamic ◽  
Precise Time Integration ◽  
Stability And Accuracy

Based on the coupled precise time integration method and basic assumptions of constant average acceleration method in Newmark family, implicit series solution of structural dynamic equation is put forward by introducing the Taylor series expansion. Relevant time step integration formulas were designed. Stability and accuracy of the method were analyzed. Stability analyses show that the coupling implicit method is stable when damping ratio is equal to 0, and is conditionally stable when damping ratio are other values. The results show that the accuracy of the algorithm can be controlled by choosing the number of truncation order of Taylor series expansion and is better than that of traditional scheme with the increase of time step. Number examples are given to demonstrate the validity of the proposed method.

Precise Time-Integration Method with Dimensional Expanding for Structural Dynamic Equations

AIAA Journal ◽  
2001 ◽  
Vol 39 (12) ◽  
pp. 2394-2399 ◽  
Author(s):  
Yuanxian Gu ◽  
Biaosong Chen ◽  
Hongwu Zhang ◽  
Zhenqun Guan
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Dynamic Equations ◽  
Structural Dynamic ◽  
Time Integration Method ◽  
Precise Time Integration ◽  
Precise Time

Partitioned Integration Method Based on Newmark’s Scheme for Structural Dynamic Problems

2016 ◽  
Vol 16 (01) ◽  
pp. 1640009 ◽  
Author(s):  
Chuanguo Jia ◽  
Zhou Leng ◽  
Yingmin Li ◽  
Hongliu Xia ◽  
Liping Liu
Keyword(s):  
Integration Method ◽  
Computational Cost ◽  
Low Frequency ◽  
State Variables ◽  
Time Step ◽  
Order Accuracy ◽  
Mass System ◽  
Structural Dynamic ◽  
Time Integrators ◽  
Stability And Accuracy

Systems of ordinary differential equations (ODEs) arising from transient structural dynamics very often exhibit high-frequency/low-frequency and linear/nonlinear behaviors of subsets of the state variables. With this in mind, the paper resorts to the use of different time integrators with different time steps for subsystems, which tailors each method and its time step to the solution behaviors of the corresponding subsystem. In detail, a partitioned integration method is introduced which imposes continuity of velocities at the interface to couple arbitrary Newmark schemes with different time steps in different subdomains. It is proved that the velocity continuity of the method is the primal factor of its reduction to first-order accuracy. To maintain second-order accuracy without increasing drift and computational cost, a novel method with the acceleration continuity is proposed whose velocity constraint is also ensured by means of the projection strategy. Both its stability and accuracy properties are examined through numerical analysis of a Single-degree-of-freedom (DoF) split mass system. Finally, numerical validations are conducted on Single- and Two-DoF split mass systems and a four-DoF nonlinear structure showing the feasibility of the proposed method.

Novel Partitioned Integration Method Based on Newmark's Scheme for Structural Dynamic Problems

2014 ◽  
Vol 580-583 ◽  
pp. 2996-3002 ◽  
Author(s):  
Chuan Guo Jia ◽  
Ying Min Li ◽  
Hong Liu Xia ◽  
Li Ping Liu
Keyword(s):  
Integration Method ◽  
Low Frequency ◽  
State Variables ◽  
Time Step ◽  
Mass System ◽  
Structural Dynamic ◽  
Time Integrators ◽  
Systems Of Odes ◽  
Stability And Accuracy ◽  
Projection Strategy

Systems of ODEs arising from transient structural dynamics generally exhibit high-frequency/low-frequency and linear/nonlinear behaviours of subsets of state variables. This paper resorts to the use of different time integrators with different time steps for subsystems, to tailor each method and its time step to the solution behaviour of the corresponding subsystem. Anovel partitioned integration method with the acceleration continuity is proposed whose velocity continuity is also ensured by means of the mass projection strategy. Both its stability and accuracy properties are examined through numerical analysis on Single-DoF split mass system.

scholarly journals Identification of Dynamic Loads Based on Second-Order Taylor-Series Expansion Method

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Xiaowang Li ◽  
Zhongmin Deng
Keyword(s):  
Series Expansion ◽  
Taylor Series ◽  
Time History ◽  
Taylor Series Expansion ◽  
Second Order ◽  
New Method ◽  
Dynamic Loads ◽  
Discrete Equation ◽  
System Response ◽  
Structural Dynamic

A new method based on the second-order Taylor-series expansion is presented to identify the structural dynamic loads in the time domain. This algorithm expresses the response vectors as Taylor-series approximation and then a series of formulas are deduced. As a result, an explicit discrete equation which associates system response, system characteristic, and input excitation together is set up. In a multi-input-multi-output (MIMO) numerical simulation study, sinusoidal excitation and white noise excitation are applied on a cantilever beam, respectively, to illustrate the effectiveness of this algorithm. One also makes a comparison between the new method and conventional state space method. The results show that the proposed method can obtain a more accurate identified force time history whether the responses are polluted by noise or not.

Full-Scale Bounds Estimation for the Nonlinear Transient Heat Transfer Problems with Interval Uncertainties

2021 ◽  
pp. 2150026
Author(s):  
Ruifei Peng ◽  
Haitian Yang ◽  
Yanni Xue
Keyword(s):  
Heat Transfer ◽  
Series Expansion ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Transient Heat Transfer ◽  
High Fidelity ◽  
Interval Scale ◽  
Nonlinear Transient ◽  
Transfer Problems ◽  
Derivatives Of

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

scholarly journals Weighted Measurement Fusion Particle Filter for Nonlinear Systems with Correlated Noises

Sensors ◽  
2018 ◽  
Vol 18 (10) ◽  
pp. 3242 ◽  
Author(s):  
Ke Wei Zhang ◽  
Gang Hao ◽  
Shu Li Sun
Keyword(s):  
Nonlinear Systems ◽  
Particle Filter ◽  
Series Expansion ◽  
Taylor Series ◽  
Asymptotic Optimality ◽  
Taylor Series Expansion ◽  
Full Rank ◽  
Expansion Method ◽  
Least Square ◽  
Correlated Noises

The multi-sensor information fusion particle filter (PF) has been put forward for nonlinear systems with correlated noises. The proposed algorithm uses the Taylor series expansion method, which makes the nonlinear measurement functions have a linear relationship by the intermediary function. A weighted measurement fusion PF (WMF-PF) was put forward for systems with correlated noises by applying the full rank decomposition and the weighted least square theory. Compared with the augmented optimal centralized fusion particle filter (CF-PF), it could greatly reduce the amount of calculation. Moreover, it showed asymptotic optimality as the Taylor series expansion increased. The simulation examples illustrate the effectiveness and correctness of the proposed algorithm.

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