scholarly journals Improved numerical dissipation for time integration algorithms in structural dynamics

1977 ◽  
Vol 5 (3) ◽  
pp. 283-292 ◽  
Author(s):  
Hans M. Hilber ◽  
Thomas J. R. Hughes ◽  
Robert L. Taylor
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Numerical Dissipation ◽  
Integration Algorithms

Optimization of a Class of n-Sub-Step Time Integration Methods for Structural Dynamics

2021 ◽  
Author(s):  
Yi Ji ◽  
Yufeng Xing
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Single Step ◽  
Numerical Dissipation ◽  
Integration Methods ◽  
Stiffness Matrices ◽  
Difference Formula ◽  
Different Types ◽  
Time Integration Methods ◽  
Methods Numerical

This paper develops a family of optimized [Formula: see text]-sub-step time integration methods for structural dynamics, in which the generalized trapezoidal rule is used in the first [Formula: see text] sub-steps, and the last sub-step employs [Formula: see text]-point backward difference formula. The proposed methods can achieve second-order accuracy and unconditional stability, and their degree of numerical dissipation can range from zero to one. Also, the proposed methods can achieve the identical effective stiffness matrices for all sub-steps, reducing computational costs in the analysis of linear systems. Using the spectral analysis, optimized algorithmic parameters are presented, ensuring that the proposed methods can accurately calculate different types of dynamic problems such as wave propagation, stiff and nonlinear systems. Besides, with the increase in the number of sub-steps, the accuracy of the proposed methods can be enhanced without extra workload compared with single-step methods. Numerical experiments show that the proposed methods perform better in different dynamic systems.

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.

scholarly journals A locally defined time-marching technique for structural dynamics

2018 ◽  
Vol 211 ◽  
pp. 17004
Author(s):  
Delfim Soares ◽  
Tales Vieira Sofiste ◽  
Webe João Mansur
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Single Step ◽  
Numerical Dissipation ◽  
Structural Elements ◽  
Structural Element ◽  
Time Integrators ◽  
Step Procedure ◽  
Time Marching ◽  
Dynamics Analyses

In this work, a new time marching procedure is proposed for structural dynamics analyses. In this novel technique, time integration parameters are locally defined and different values may be attributed to each structural element of the model. In addition, the time integrators are evaluated according to the properties of the elements, and the user may select in which structural elements numerical dissipation will be introduced. Since the integration parameters are locally defined as function of the structural element itself, the time marching technique adapts according to the model, providing enhanced accuracy. The method is very simple to implement and it stands as an efficient, direct, single-step procedure. It is second order accurate, unconditionally stable, truly self-starting and it allows highly controllable algorithm dissipation in the higher modes. Numerical results are presented along the paper, illustrating the good performance of the new technique.

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.

Sign in / Sign up

Export Citation Format

Share Document