A variationally consistent framework for the design of integrator and updates of generalized single step representations for structural dynamics

2003 ◽  
Vol 19 (8) ◽  
pp. 581-600 ◽  
Author(s):  
R. Kanapady ◽  
K. K. Tamma ◽  
X. Zhou
Keyword(s):  
Structural Dynamics ◽  
Single Step

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.

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.

An Accurate Explicit Direct Time Integration Method for Computational Structural Dynamics

1999 ◽  
Author(s):  
Bertrand Tchamwa ◽  
Ted Conway ◽  
Christian Wielgosz
Keyword(s):  
Structural Dynamics ◽  
Integration Method ◽  
Time Integration ◽  
Single Step ◽  
New Method ◽  
Phase Portraits ◽  
Structural Dynamic ◽  
Low Frequencies ◽  
Time Integration Method ◽  
Non Linear

Abstract The purpose of this paper is to introduce a new simple explicit single step time integration method with controllable high-frequency dissipation. As opposed to the methods generally used in structural dynamics, with a consistency experimentally chosen of second order, the new method is only first-order-consistent but yields smaller numerical errors in low frequencies and is therefore very efficient for structural dynamic analysis. The new method remains explicit for any structural dynamics problem, even when a non-diagonal damping matrix is used in linear structural dynamics problem or when the non-linear internal force vector is a function of velocities. Convergence and spectral properties of the new algorithm are discussed and compared to those of some well-known algorithms. Furthermore, the validity and efficiency of the new algorithm are shown in a non-linear dynamic example by comparison of phase portraits.

An Explicit Scheme for Structural Dynamics Analysis

1999 ◽  
Author(s):  
Bertrand Tchamwa ◽  
Ted Conway ◽  
Christian Wielgosz
Keyword(s):  
Structural Dynamics ◽  
Time Integration ◽  
Internal Force ◽  
Single Step ◽  
New Method ◽  
Phase Portraits ◽  
Structural Dynamic ◽  
Low Frequencies ◽  
Non Linear ◽  
Internal Force Vector

Abstract The purpose of this paper is to introduce a new simple explicit single step time integration method with controllable high-frequency dissipation. As opposed to the methods generally used in structural dynamics, with a consistency experimentally chosen of second order, the new method is only first-order-consistent but yields smaller numerical errors in low frequencies and is therefore very efficient for structural dynamic analysis. The new method remains explicit for any structural dynamics problem, even when a non-diagonal damping matrix is used in linear structural dynamics problem or when the non-linear internal force vector is a function of velocities. Convergence and spectral properties of the new algorithm are discussed and compared to those of some well-known algorithms. Furthermore, the validity and efficiency of the new algorithm are shown in a non-linear dynamic example by comparison of phase portraits.

Sign in / Sign up

Export Citation Format

Share Document