Adaptive Time Integration Method for DAEs of Multibody Systems

2012 ◽  
Author(s):  
Jieyu Ding ◽  
Zhenkuan Pan
Keyword(s):  
Multibody Systems ◽  
Integration Method ◽  
Time Integration ◽  
Differential Algebraic Equations ◽  
Richardson Extrapolation ◽  
Time Interval ◽  
Time Step ◽  
Time Integration Method ◽  
Adaptive Time Integration ◽  
Adaptive Time

An adaptive time integration method is developed for the index-3 differential-algebraic equations (DAEs) of multibody systems to improve the computational efficiency as well as the accuracy of the results. Based on the modified general-α method, the adaptive time integration is presented. At each discrete time interval, the time step size is changed through Richardson extrapolation with definable computation accuracy. A rotary rod slider system is used to validate the presented adaptive time integration. The accuracy and efficiency are determined by the expected order of the accuracy in Richardson extrapolation.

A Precise and Stiffly Stable Time Integration Method for Vibration Equations

2001 ◽  
Author(s):  
Takeshi Fujikawa ◽  
Etsujiro Imanishi
Keyword(s):  
Integration Method ◽  
Time Integration ◽  
Low Frequency ◽  
Quadratic Function ◽  
Time Step ◽  
Integration Algorithm ◽  
Time Integration Method ◽  
Time Integration Algorithm ◽  
Time Integration Methods ◽  
Motion Problems

Abstract A method of time integration algorithm is presented for solving stiff vibration and motion problems. It is absolutely stable, numerically dissipative, and much accurate than other dissipative time integration methods. It achieves high-frequency dissipation, while minimizing unwanted low-frequency dissipation. In this method change of acceleration during time step is expressed as quadratic function including some parameters, whose appropriate values are determined through numerical investigation. Two calculation examples are demonstrated to show the usefulness of this method.

Modified precise direct time integration method for the transient response analysis of viscoelastic systems using an internal variable model

2019 ◽  
Vol 26 (3-4) ◽  
pp. 161-174
Author(s):  
Taufeeq Ur Rehman Abbasi ◽  
Hui Zheng
Keyword(s):  
State Space ◽  
Integration Method ◽  
Time Integration ◽  
Internal Variable ◽  
New Method ◽  
Computational Time ◽  
Direct Integration ◽  
Computational Accuracy ◽  
Time Step ◽  
Time Integration Method

Engineering systems for different levels of energy dissipation use internal variable models, which may lead to tremendous problems in accurate analysis. This article aims to provide an alternative direct integration method for the analysis of systems involving an anelastic displacement field model. A new state-space formulation built on an augmented set of anelastic variables for asymmetric systems is developed. Then, a precise time integration method based on state-space matrix formulation is proposed by introducing a Legendre–Gauss quadrature. The new integration method in terms of numerical stability and its implementation is discussed. The effect of sensitivity of the selection of the time-step and computational time on the performance of the new method is investigated by using a multi-degree-of-freedom system. The performance of the new method is also evaluated in terms of both computational accuracy and efficiency at higher degrees of freedom by using a continuum system. It is demonstrated that the computational accuracy and efficiency of the new method on large-scale problems are higher than that of the direct integration linear displacement–velocity method.

Research in Numerical Simulation of Lager Multi-Scale Water Conveyance Tunnel Based on Mixed Time Integration Method

2012 ◽  
Vol 203 ◽  
pp. 432-437
Author(s):  
Jun Jie Zhao ◽  
Yan Zhi Yang
Keyword(s):  
Numerical Simulation ◽  
Computational Efficiency ◽  
Integration Method ◽  
Time Integration ◽  
Scale Model ◽  
Integration Time ◽  
Time Step ◽  
Detailed Model ◽  
Multi Scale ◽  
Time Integration Method

The global integration time step of multi-scale model is subject to local detailed model, resulting in lower computational efficiency. Mixed time integration method uses different integration time-step in different scale model, it can effectively avoid the above problem. Rest on a large-scale water tunnel under construction, in order to achieve the synchronization of the global and the local simulation, the paper establishes multi-scale finite element model of the tunnel, and calculate it by mixed time integration method. The final calculation and analysis show that the algorithm can guarantee the computational accuracy of multi-scale numerical simulation, and can effectively improve the computational efficiency, it can also provide references for related tunnel project.

Two Lie Group Formulations for Dynamic Multibody Systems With Large Rotations

2011 ◽  
Author(s):  
Olivier Bru¨ls ◽  
Martin Arnold ◽  
Alberto Cardona
Keyword(s):  
Numerical Solution ◽  
Lie Group ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Time Integration ◽  
Computational Cost ◽  
Differential Algebraic Equations ◽  
Rigid Body Dynamics ◽  
Time Step ◽  
Iteration Matrix

This paper studies the formulation of the dynamics of multibody systems with large rotation variables and kinematic constraints as differential-algebraic equations on a matrix Lie group. Those equations can then be solved using a Lie group time integration method proposed in a previous work. The general structure of the equations of motion are derived from Hamilton principle in a general and unifying framework. Then, in the case of rigid body dynamics, two particular formulations are developed and compared from the viewpoint of the structure of the equations of motion, of the accuracy of the numerical solution obtained by time integration, and of the computational cost of the iteration matrix involved in the Newton iterations at each time step. In the first formulation, the equations of motion are described on a Lie group defined as the Cartesian product of the group of translations R3 (the Euclidean space) and the group of rotations SO(3) (the special group of 3 by 3 proper orthogonal transformations). In the second formulation, the equations of motion are described on the group of Euclidean transformations SE(3) (the group of 4 by 4 homogeneous transformations). Both formulations lead to a second-order accurate numerical solution. For an academic example, we show that the formulation on SE(3) offers the advantage of an almost constant iteration matrix.

Time Integration Method With Structure-Dependent Difference Equations

2013 ◽  
Author(s):  
Shuenn-Yih Chang ◽  
Chiu-Li Huang
Keyword(s):  
High Frequency ◽  
Integration Method ◽  
Time Integration ◽  
Low Frequency ◽  
Unconditional Stability ◽  
Total Response ◽  
Time Step ◽  
Order Accuracy ◽  
Time Integration Method ◽  
Frequency Responses

A novel family of structure-dependent integration method is proposed for time integration. This family method can have the possibility of unconditional stability, second-order accuracy and the explicitness of each time step. Since it can integrate the most important advantage of an implicit method, unconditional stability, and that of an explicit method, the explicitness of each time step, a lot of computational efforts can be saved in solving an inertial type problem, where the total response is dominated by low frequency modes and high frequency responses are of no interest.

On the Dynamic Simulation of Large Nonlinear Mechanical Systems. Part 2: The Time Integration Technique and Time Response Loop

1981 ◽  
Vol 103 (4) ◽  
pp. 857-865 ◽  
Author(s):  
R. J. Cipra ◽  
J. J. Uicker
Keyword(s):  
Differential Equations ◽  
Integration Method ◽  
Numerical Technique ◽  
Nonlinear Differential Equations ◽  
Time Integration ◽  
Simulation Technique ◽  
Time Response ◽  
Integration Technique ◽  
Time Step ◽  
Time Integration Method

Part 2 presents a time integration technique for nonlinear differential equations and illustrates its use in the time response loop of the simulation technique outlined in Part 1. The time integration method for nonlinear differential equations is based upon the repetitive analytical (modal) solution of a set of equations linearized about the current operating position. This linearized set of equations may include viscous damping. The method incorporates a variable time step suited to the degree of nonlinearity and as shown in an example problem, gives comparable agreement in results with a Runge-Kutta numerical technique. The time response loop of the simulation technique uniquely combines the concepts of substructuring, system synthesis, and frequency reduction discussed in Part 1 with the time integration method presented here to form the overall simulation technique.

scholarly journals An Improved Time Integration Method Based on Galerkin Weak Form with Controllable Numerical Dissipation

2021 ◽  
Vol 11 (4) ◽  
pp. 1932
Author(s):  
Weixuan Wang ◽  
Qinyan Xing ◽  
Qinghao Yang
Keyword(s):  
High Frequency ◽  
Integration Method ◽  
Time Integration ◽  
Low Frequency ◽  
Weak Form ◽  
High Accuracy ◽  
Numerical Dissipation ◽  
Frequency Range ◽  
Time Integration Method ◽  
Numerical Damping

Based on the newly proposed generalized Galerkin weak form (GGW) method, a two-step time integration method with controllable numerical dissipation is presented. In the first sub-step, the GGW method is used, and in the second sub-step, a new parameter is introduced by using the idea of a trapezoidal integral. According to the numerical analysis, it can be concluded that this method is unconditionally stable and its numerical damping is controllable with the change in introduced parameters. Compared with the GGW method, this two-step scheme avoids the fast numerical dissipation in a low-frequency range. To highlight the performance of the proposed method, some numerical problems are presented and illustrated which show that this method possesses superior accuracy, stability and efficiency compared with conventional trapezoidal rule, the Wilson method, and the Bathe method. High accuracy in a low-frequency range and controllable numerical dissipation in a high-frequency range are both the merits of the method.

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