A ROBUST TIME-INTEGRATION ALGORITHM FOR SOLVING NONLINEAR DYNAMIC PROBLEMS WITH LARGE ROTATIONS AND DISPLACEMENTS

2012 ◽  
Vol 12 (06) ◽  
pp. 1250051 ◽  
Author(s):  
SHYH-RONG KUO ◽  
J. D. YAU ◽  
Y. B. YANG
Keyword(s):  
Nonlinear Dynamic ◽  
Finite Difference Methods ◽  
Time Integration ◽  
Nonlinear Dynamic Analysis ◽  
Element Approximation ◽  
Dynamic Problems ◽  
Time Step ◽  
Integration Algorithm ◽  
Current Time ◽  
Time Integration Algorithm

An efficient time-integration algorithm for nonlinear dynamic analysis of structures is presented. By adopting the temporal discretization for time finite element approximation, very large time steps can be used by the algorithm. With an accuracy of fourth order, this technique requires only displacements and velocities to be made available at the start of the current time step for integration in state space. Using the weighted momentum principle, the problem of discontinuity caused by impulsive loads is resolved after time-integration of the applied load in external momentum. Since no knowledge is required of acceleration at the current time step, the errors caused by estimation of acceleration by previous finite-difference methods are circumvented. Moreover, an iterative procedure is included for each time step, involving the three phases of predictor, corrector, and error-checking. The effectiveness and robustness of the proposed algorithm in solving nonlinear dynamic problems is demonstrated in the numerical examples.

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.

scholarly journals An algorithm based on a new DQM with modified exponential cubic B-splines for solving hyperbolic telegraph equation in (2 + 1) dimension

2018 ◽  
Vol 7 (2) ◽  
pp. 113-125
Author(s):  
Brajesh Kumar Singh ◽  
Pramod Kumar
Keyword(s):  
Differential Quadrature Method ◽  
Time Integration ◽  
Telegraph Equation ◽  
Differential Quadrature ◽  
Quadrature Method ◽  
Time Step ◽  
Integration Algorithm ◽  
B Splines ◽  
Time Integration Algorithm ◽  
Telegraph Equations

Abstract In this paper, a new method modified exponential cubic B-Spline differential quadrature method (mExp-DQM) has been developed for space discretization together with a time integration algorithm for numeric study of (2 + 1) dimensional hyperbolic telegraph equations. The mExp-DQM (i.e., differential quadrature method with modified exponential cubic B-splines as new basis) reduces the problem into an amenable system of ordinary differential equations (ODEs), in time. The time integration SSP-RK54 algorithm has been adopted to solve the resulting system of ODEs. The proposed method is shown stable by computing the eigenvalues of the coefficients matrices while the accuracy of the method is illustrated in terms of L2 and L∞ error norms for each problem. A comparison of mExp-DQM solutions with the results of the other numerical methods has been carried out for various space sizes and time step sizes.

scholarly journals Wavelet-based Decomposition of Ground Acceleration for Efficient Calculation of Seismic Response in Elastoplastic Structures

2020 ◽  
Author(s):  
Reza Kamgar ◽  
Noorollah Majidi ◽  
Ali Heidari
Keyword(s):  
Wavelet Transform ◽  
Dynamic Analysis ◽  
Continuous Wavelet Transform ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Analysis ◽  
Continuous Wavelet ◽  
Frequency Content ◽  
Time Step ◽  
Integration Schemes ◽  
The Waves

The nonlinear dynamic analysis provides a more accurate simulation of the structural behavior against earthquakes. On the other hand, this analysis method is time-consuming since the time-step integration schemes are used to calculate the responses of the structure. Wavelet transform is also considered as one of the strong computing tools in studying the properties of the waves. The continuous wavelet transform is a time-frequency study and examines the frequency content of the waves while, the discrete wavelet transform is used to reduce sampling data and also to eliminate the noise of the waves. In this paper, the discrete and continuous wavelet transforms are used to reduce the wave sampling and therefore to reduce the required time for analysis. In this regard, eight near- and far- field earthquakes are studied. The frequency content of the earthquake is investigated by the Fourier spectrum and the continuous wavelet transform. The results show that the first five frequencies for the main earthquakes are similar to those values of earthquakes obtained by wavelet transform. Besides, it is shown that using wavelet transform for the main and decomposed earthquakes indicates that the duration of strong ground motion and the time of dominant frequency occur approximately in the same domain. Finally, it is concluded that the required calculation time reduces to about 80 % with an error less than 6 % when the main earthquake is decomposed by wavelet transform and the approximation waves are used in the nonlinear dynamic analysis.

Impact Dynamic Analysis of Horizontally Vibrated Conveyor with Coulomb Friction Modeling

2012 ◽  
Vol 619 ◽  
pp. 26-29
Author(s):  
Chao Sheng Song ◽  
Qi Ming Huang ◽  
Zhan Gao ◽  
Jie Xu
Keyword(s):  
Coulomb Friction ◽  
Impact Analysis ◽  
Time Integration ◽  
Impact Excitation ◽  
Friction Modeling ◽  
Integration Algorithm ◽  
Conveyor System ◽  
Time Integration Algorithm ◽  
And Control ◽  
The Impact

This paper introduces dynamic impact analysis as an effective technique for studying the response of horizontal vibrated conveyor with time-varying impact excitation by the falling of the scrap. A two degree-of-freedoms impact dynamic model is formulated considering the static and dynamic coulomb friction between the scrap and chute. Then the time integration algorithm was applied in the program to solve the dynamic equations. Using the proposed method, the impact effects of ideal single scrap and multiple scraps on the dynamic response of the conveyor were analyzed. Computational results reveal numerous interesting dynamic characteristics which can be used to forecast and control the vibration of the scrap and conveyor system.

Parallel Time-Integration of Flexible Multibody Dynamics Based on Newton-Waveform Method

2017 ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Multibody Dynamics ◽  
Time Integration ◽  
Flexible Multibody Dynamics ◽  
Small Scale ◽  
Time Step ◽  
Current Time ◽  
Parallel Time ◽  
Previous Time ◽  
Flexible Multibody ◽  
Multi Body

Traditionally, the time integration algorithms for multibody dynamics are in sequential. The predictions of previous time steps are necessary to get the solutions at current time step. This time-marching character impedes the application of parallel processor implementation. In this paper, the idea of computing a number of time steps concurrently is applied to flexible multi-body dynamics, which makes parallel time-integration possible. In the present method, the solution at the current time step is computed before accurate values at previous time step are available. This method is suitable for small-scale parallel analysis of flexible multibody systems.

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