Parallel 3D simulation of structural dynamic problem by using explicit discontinuous time integration method

2001 ◽  
Author(s):  
Jin Cho ◽  
Kuk Ji ◽  
Seung Kim ◽  
Jeong Kim
Keyword(s):  
Dynamic Problem ◽  
Integration Method ◽  
Time Integration ◽  
3D Simulation ◽  
Structural Dynamic ◽  
Time Integration 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

scholarly journals A Time Integration Method Based on Galerkin Weak Form for Nonlinear Structural Dynamics

2019 ◽  
Vol 9 (15) ◽  
pp. 3076
Author(s):  
Qinyan Xing ◽  
Qinghao Yang ◽  
Weixuan Wang
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Weak Form ◽  
Numerical Dissipation ◽  
Integration Scheme ◽  
Structural Dynamic ◽  
Time Integration Method ◽  
Nonlinear Structural ◽  
Nonlinear Dynamic Equations ◽  
Step Algorithm

This paper presents a step-by-step time integration method for transient solutions of nonlinear structural dynamic problems. Taking the second-order nonlinear dynamic equations as the model problem, this self-starting one-step algorithm is constructed using the Galerkin finite element method (FEM) and Newton–Raphson iteration, in which it is recommended to adopt time elements of degree m = 1,2,3. Based on the mathematical and numerical analysis, it is found that the method can gain a convergence order of 2m for both displacement and velocity results when an ordinary Gauss integral is implemented. Meanwhile, with reduced Gauss integration, the method achieves unconditional stability. Furthermore, a feasible integration scheme with controllable numerical damping has been established by modifying the test function and introducing a special integral rule. Representative numerical examples show that the proposed method performs well in stability with controllable numerical dissipation, and its computational efficiency is superior as well.

Further Insights Into Time-Integration Method Based on Bernstein Polynomials and Bezier Curve for Structural Dynamics

2019 ◽  
Vol 19 (10) ◽  
pp. 1950113
Author(s):  
Mohammad Mahdi Malakiyeh ◽  
Saeed Shojaee ◽  
Saleh Hamzehei-Javaran ◽  
Behrooz Tadayon
Keyword(s):  
Integration Method ◽  
Bernstein Polynomials ◽  
Time Integration ◽  
Bézier Curve ◽  
Implicit Time ◽  
Bezier Curve ◽  
Structural Dynamic ◽  
Numerical Examples ◽  
Time Integration Method ◽  
Low Dissipation

In [M. M. Malakiyeh, S. Shojaee and S. Hamzehei-Javaran, Development of a direct time integration method based on Bezier curve and 5th-order Berstein basis function, Comput. Struct. 194 (2108) 15–31] an unconditionally stable implicit time-integration method using the Bezier curve was proposed for solving structural dynamic problems. In this study, a new class of the previous algorithm is presented by using the Bernstein polynomials and the Bezier curve as the interpolation functions for solving the equations of motion with the possibility of using large time steps. The spectral radius, period elongation, amplitude decay and overshooting of the present method are investigated and compared with some other methods. To show the high-performance, robustness and validity of this method, five numerical examples are presented. The theoretical analysis and numerical examples show that the proposed method has low dissipation in the lower modes and high dissipation in the higher modes in comparison with the other methods reported in the literature.

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.

A new time integration method in structural dynamics using the Taylor series

1998 ◽  
Vol 212 (7) ◽  
pp. 567-575
Author(s):  
S M Wang ◽  
R A Shenoi ◽  
L B Zhao
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Structural Response ◽  
Simultaneous Equation ◽  
Dynamic Responses ◽  
Implicit Methods ◽  
Explicit Integration ◽  
Structural Dynamic ◽  
Order Of Accuracy ◽  
Time Integration Method

The paper presents a new method of time integration for structural dynamic responses. In comparison with well-known methods, it is advantageous in several aspects. It satisfies the governing equations in continuous intervals rather than at discrete time instants (collocation, SSpj) or in average form (weighted, GNpj). It approximates the structural response with user-controllable order of accuracy. It automatically controls the convergence and accuracy so that a correct answer can be assured via auto-adjusted stepping and expansion terms. As far as the accuracy of velocity and acceleration is concerned, the method is much better since rapid convergence can be obtained with ease. Like the explicit integration method, this approach does not demand solution of simultaneous equation sets, yet it can be used with a time increment much larger than that of the implicit methods.

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