A new family of generalized-α time integration algorithms without overshoot for structural dynamics

2008 ◽  
Vol 37 (12) ◽  
pp. 1389-1409 ◽  
Author(s):  
Yu KaiPing
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
New Family ◽  
Integration Algorithms

A New Family of Higher-Order Time Integration Algorithms for the Analysis of Structural Dynamics

2017 ◽  
Vol 84 (7) ◽  
Author(s):  
Wooram Kim ◽  
J. N. Reddy
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Higher Order ◽  
Weighted Residual Method ◽  
New Family ◽  
Equal Degree ◽  
Fundamental Limitations ◽  
Mixed Formulations ◽  
Dependent Variables ◽  
Integration Algorithms

For the development of a new family of implicit higher-order time integration algorithms, mixed formulations that include three time-dependent variables (i.e., the displacement, velocity, and acceleration vectors) are developed. Equal degree Lagrange type interpolation functions in time are used to approximate the dependent variables in the mixed formulations, and the time finite element method and the modified weighted-residual method are applied to the velocity–displacement and velocity–acceleration relations of the mixed formulations. Weight parameters are introduced and optimized to achieve preferable attributes of the time integration algorithms. Specific problems of structural dynamics are used in the numerical examples to discuss some fundamental limitations of the well-known second-order accurate algorithms as well as to demonstrate advantages of using the developed higher-order algorithms.

An Improved Time Integration Algorithm: A Collocation Time Finite Element Approach

2017 ◽  
Vol 17 (02) ◽  
pp. 1750024 ◽  
Author(s):  
Wooram Kim ◽  
J. N. Reddy
Keyword(s):  
Finite Element ◽  
Time Integration ◽  
Integration Algorithm ◽  
Finite Element Approach ◽  
New Family ◽  
Integration Schemes ◽  
Time Integration Algorithm ◽  
Time Integration Schemes ◽  
Element Approach ◽  
Integration Algorithms

A time collocation finite element approach is employed to develop one- and two-step time integration schemes with algorithmic dissipation control capability. The newly developed time integration schemes are combined to obtain a new family of time integration algorithms using the concept employed by Baig and Bathe. The newly developed algorithm can effectively control the algorithmic dissipation by relating the collocation parameters with the spectral radius in the high frequency limit. The new algorithm provides better accuracy compared with the generalized-[Formula: see text] method for highly dissipative cases and includes the Baig and Bathe method within its family as a special case.

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.

New Explicit Integration Algorithms with Controllable Numerical Dissipation for Structural Dynamics

2018 ◽  
Vol 18 (03) ◽  
pp. 1850044 ◽  
Author(s):  
Xiaoqiong Du ◽  
Dixiong Yang ◽  
Jilei Zhou ◽  
Xiaoliang Yan ◽  
Yongliang Zhao ◽  
...  
Keyword(s):  
Nonlinear Systems ◽  
Time Integration ◽  
Dynamic Responses ◽  
Discrete Control ◽  
Numerical Dissipation ◽  
Explicit Integration ◽  
Structural Dynamic ◽  
New Family ◽  
Recursive Formulas ◽  
Integration Algorithms

This paper presents a new family of explicit time integration algorithms with controllable numerical dissipation for structural dynamic problems by utilizing the discrete control theory. Firstly, the equilibrium equation of the implicit Yu-[Formula: see text] algorithm is adopted, and the recursive formulas of velocity and displacement for the explicit CR algorithm are used in the algorithms. Then, the transfer function and characteristic equation of the algorithms with integration coefficients are obtained by the [Formula: see text] transformation. Furthermore, their integration coefficients are derived according to the poles condition. It was indicated that the proposed algorithms possess the advantages of second-order accuracy, self-starting, and unconditional stability for linear systems and nonlinear systems with softening stiffness. The numerical dissipation of the algorithms is controlled by the spectral radius at infinity [Formula: see text]. It was also shown that the proposed algorithms have the same poles as the Yu-[Formula: see text] algorithm, and thus the same numerical properties. Compared with the implicit Yu-[Formula: see text] algorithm, the proposed algorithms are explicit in terms of both the displacement and velocity formulas. Finally, the effectiveness of the proposed algorithms in reducing the undesired participation of higher modes for solving the dynamic responses of linear and nonlinear systems has been demonstrated.

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