scholarly journals A Highly Accurate Approach for Aeroelastic System with Hysteresis Nonlinearity

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
C. C. Cui ◽  
S. X. Xie ◽  
X. C. Huang ◽  
J. K. Liu ◽  
Y. M. Chen
Keyword(s):  
Accurate Determination ◽  
Step Length ◽  
Computational Accuracy ◽  
Time Step ◽  
Aeroelastic System ◽  
Precise Integration ◽  
Runge Kutta Method ◽  
Hysteresis Nonlinearity ◽  
Major Procedure ◽  
Predictor Corrector

We propose an accurate approach, based on the precise integration method, to solve the aeroelastic system of an airfoil with a pitch hysteresis. A major procedure for achieving high precision is to design a predictor-corrector algorithm. This algorithm enables accurate determination of switching points resulting from the hysteresis. Numerical examples show that the results obtained by the presented method are in excellent agreement with exact solutions. In addition, the high accuracy can be maintained as the time step increases in a reasonable range. It is also found that the Runge-Kutta method may sometimes provide quite different and even fallacious results, though the step length is much less than that adopted in the presented method. With such high computational accuracy, the presented method could be applicable in dynamical systems with hysteresis nonlinearities.

Simulation of Transient Heat Transfer Based on Element-Free Galerkin Method and Increment-Dimensional Precise Integration Method

2012 ◽  
Vol 204-208 ◽  
pp. 4254-4259
Author(s):  
Fu Liang Mei ◽  
Gui Ling Li
Keyword(s):  
Heat Transfer ◽  
Integration Method ◽  
Step Length ◽  
Grid Size ◽  
Inverse Matrix ◽  
Coupling Method ◽  
Time Step ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Element Free

There were many issues in numerical methods of heat transfer problems such as instability at a big time step length or grid size and no-existence of inverse matrix by time-precise integration method. For sake of avoiding instability and calculating an inverse matrix, a coupling method was put forward based on EFGM and IDPIM. Formulae were deduced according to EFGM and IDPIM. Results show that the coupling method has a higher accuracy and its stability is small subjected to the time step length or grid size, and is to deserve to be popularized.

Assessment of numerical integration algorithms for nonlinear vibration of railway vehicles

2016 ◽  
Vol 231 (6) ◽  
pp. 729-739 ◽  
Author(s):  
Chao Yang ◽  
Duo Li ◽  
Tao Zhu ◽  
Shoune Xiao
Keyword(s):  
Integration Method ◽  
Railway Vehicle ◽  
Kutta Method ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Adams Method ◽  
Runge Kutta Method ◽  
Vehicle Systems ◽  
Runge Kutta ◽  
Predictor Corrector

The primary purpose of this paper was to choose appropriate time integration methods for the simulation of nonlinear railway vehicle systems. The nonlinear elements existing in railway vehicle systems were summarized, and the relevant mathematical expressions were provided. A newly developed integration method, which is the corrected explicit method of double time steps, was implemented in five typical nonlinear examples of nonlinear railway vehicle systems. The Newmark method, the Wilson-θ method, the Runge–Kutta method, the predictor-corrector Adams method, the Zhai method, and the precise integration method were also employed for comparison purpose. Finally, the scope of application of these methods was pointed out . The results show that the Newmark method and the Wilson-θ method should not be applied to nonlinear railway vehicle systems as these methods result in errors. In contrast to the predictor-corrector Adams method and the precise integration method, the Runge–Kutta method with error control (RK45) is not applicable to the non-smooth problems although the RK45 possesses high accuracy. In addition, the application of the RK45 and the predictor-corrector Adams method with error control may result in spurious tiny oscillation in the vehicle system related to nonlinear vertical wheel–rail forces. The corrected explicit method of double time steps, the Zhai method, the standard Runge–Kutta method, the precise integration method, the RK45, and the predictor-corrector Adams method which possess tight error tolerances are recommended for nonlinear railway vehicle systems according to the requirements of accuracy and computational efficiency.

scholarly journals Solving Fractional Dynamical System with Freeplay by Combining Memory-Free Approach and Precise Integration Method

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Q. X. Liu ◽  
X. S. He ◽  
J. K. Liu ◽  
Y. M. Chen ◽  
L. C. Huang
Keyword(s):  
Integration Method ◽  
Piecewise Linear ◽  
Harmonic Excitation ◽  
Precise Integration ◽  
Linear Ordinary Differential Equations ◽  
First Order ◽  
Precise Integration Method ◽  
Runge Kutta Method ◽  
Predictor Corrector ◽  
Fractional Dynamical System

The Yuan-Agrawal (YA) memory-free approach is employed to study fractional dynamical systems with freeplay nonlinearities subjected to a harmonic excitation, by combining it with the precise integration method (PIM). By the YA method, the original equations are transformed into a set of first-order piecewise-linear ordinary differential equations (ODEs). These ODEs are further separated as three linear inhomogeneous subsystems, which are solved by PIM together with a predictor-corrector process. Numerical examples show that the results by the presented method agree well with the solutions obtained by the Runge-Kutta method and a modified fractional predictor-corrector algorithm. More importantly, the presented method has higher computational efficiency.

Application of the piecewise constant method in nonlinear dynamics of drill string

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jialin Tian ◽  
Jie Wang ◽  
Yi Zhou ◽  
Lin Yang ◽  
Changyue Fan ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Model ◽  
Dynamic Characteristics ◽  
Drill String ◽  
Vibration Velocity ◽  
Kutta Method ◽  
Time Step ◽  
Piecewise Constant ◽  
Runge Kutta Method ◽  
Runge Kutta

Abstract Aiming at the current development of drilling technology and the deepening of oil and gas exploration, we focus on better studying the nonlinear dynamic characteristics of the drill string under complex working conditions and knowing the real movement of the drill string during drilling. This paper firstly combines the actual situation of the well to establish the dynamic model of the horizontal drill string, and analyzes the dynamic characteristics, giving the expression of the force of each part of the model. Secondly, it introduces the piecewise constant method (simply known as PT method), and gives the solution equation. Then according to the basic parameters, the axial vibration displacement and vibration velocity at the test points are solved by the PT method and the Runge–Kutta method, respectively, and the phase diagram, the Poincare map, and the spectrogram are obtained. The results obtained by the two methods are compared and analyzed. Finally, the relevant experimental tests are carried out. It shows that the results of the dynamic model of the horizontal drill string are basically consistent with the results obtained by the actual test, which verifies the validity of the dynamic model and the correctness of the calculated results. When solving the drill string nonlinear dynamics, the results of the PT method is closer to the theoretical solution than that of the Runge–Kutta method with the same order and time step. And the PT method is better than the Runge–Kutta method with the same order in smoothness and continuity in solving the drill string nonlinear dynamics.

scholarly journals Three-Dimensional Elastodynamic Analysis Employing Partially Discontinuous Boundary Elements

Algorithms ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 129
Author(s):  
Yuan Li ◽  
Ni Zhang ◽  
Yuejiao Gong ◽  
Wentao Mao ◽  
Shiguang Zhang
Keyword(s):  
Side Effect ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Boundary Integral ◽  
Integration Scheme ◽  
Computational Accuracy ◽  
Time Step ◽  
Corner Points ◽  
Discontinuous Elements ◽  
The Time Domain

Compared with continuous elements, discontinuous elements advance in processing the discontinuity of physical variables at corner points and discretized models with complex boundaries. However, the computational accuracy of discontinuous elements is sensitive to the positions of element nodes. To reduce the side effect of the node position on the results, this paper proposes employing partially discontinuous elements to compute the time-domain boundary integral equation of 3D elastodynamics. Using the partially discontinuous element, the nodes located at the corner points will be shrunk into the element, whereas the nodes at the non-corner points remain unchanged. As such, a discrete model that is continuous on surfaces and discontinuous between adjacent surfaces can be generated. First, we present a numerical integration scheme of the partially discontinuous element. For the singular integral, an improved element subdivision method is proposed to reduce the side effect of the time step on the integral accuracy. Then, the effectiveness of the proposed method is verified by two numerical examples. Meanwhile, we study the influence of the positions of the nodes on the stability and accuracy of the computation results by cases. Finally, the recommended value range of the inward shrink ratio of the element nodes is provided.

scholarly journals Regional Associations of Cortical Thickness With Gait Variability: The Tasmanian Study of Cognition and Gait

2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 232-233
Author(s):  
Oshadi Jayakody ◽  
Monique Breslin ◽  
Richard Beare ◽  
Velandai Srikanth ◽  
Helena Blumen ◽  
...  
Keyword(s):  
Cortical Thickness ◽  
Step Length ◽  
Gait Variability ◽  
Thickness Ratio ◽  
Sensory Function ◽  
Time Variability ◽  
Step Width ◽  
Time Step ◽  
Cortical Regions ◽  
Regional Associations

Abstract Gait variability is a marker of cognitive decline. However, there is limited understanding of the cortical regions associated with gait variability. We examined associations between regional cortical thickness and gait variability in a population-based sample of older people without dementia. Participants (n=350, mean age 71.9±7.1) were randomly selected from the electoral roll. Variability in step time, step length, step width and double support time (DST) were calculated as the standard deviation of each measure, obtained from the GAITRite walkway. MRI scans were processed through FreeSurfer to obtain cortical thickness of 68 regions. Bayesian regression was used to determine regional associations of mean cortical thickness and thickness ratio (regional thickness/overall mean thickness) with gait variability. Smaller overall cortical thickness was only associated with greater step width and step time variability. Smaller mean thickness in widespread regions important for sensory, cognitive and motor functions were associated with greater step width and step time variability. In contrast, smaller thickness in a few frontal and temporal regions were associated with DST variability and the right cuneus was associated with step length variability. Smaller thickness ratio in frontal and temporal regions important for motor planning, execution and sensory function and, greater thickness ratio in the anterior cingulate was associated with greater variability in all measures. Examining individual cortical regions is important in understanding the relationship between gray matter and gait variability. Cortical thickness ratio highlights that smaller regional thickness relative to global thickness may be important for the consistency of gait.

Application of Symplectic Partitioned Runge-Kutta Method and Total-Field Scattered-Field Formulation to Simulation of GPR Data

2014 ◽  
Vol 926-930 ◽  
pp. 2777-2780
Author(s):  
Hong Yuan Fang ◽  
Jian Li ◽  
Jia Li
Keyword(s):  
Scattered Field ◽  
Measured Signal ◽  
Total Field ◽  
Time Step ◽  
Absorbing Boundary ◽  
Runge Kutta Method ◽  
Actual Field ◽  
Ground Penetrating ◽  
Radar Wave ◽  
Difference Time

The second-order Lobatto IIIA-IIIB symplectic partitioned RungeKutta (SPRK) method, combining with the first-order Mur absorbing boundary condition, is developed for the simulation of ground penetrating radar wave propagation in layered pavement structure. For 2-dimetional case, a significant advantage of this method is that only two functions need to be calculated at each time step. The total-field/scattered-field technique is used for plane wave excitation. Numerical examples are presented to verify the accuracy and efficiency of the proposed algorithm. The results illustrate that the reflected signal calculated by the SPRK method is in good agreement with that obtained using the finite difference time domain (FDTD) scheme, but the CPU time consumed by proposed algorithm is reduce about 20% of the FDTD scheme. In addition, an actual field test is conducted to evaluate the further performance of the SPRK method. It is found that the simulated waveform fits well with the measured signal in many aspects, especially in the peak amplitude and time delay.

BIASED RANDOM WALKS, PARTIAL DIFFERENTIAL EQUATIONS AND UPDATE SCHEMES

2013 ◽  
Vol 55 (2) ◽  
pp. 93-108 ◽  
Author(s):  
JACK D. HYWOOD ◽  
KERRY A. LANDMAN
Keyword(s):  
Statistical Physics ◽  
Planck Equation ◽  
Step Length ◽  
Physical Object ◽  
Cell Diameter ◽  
Agent Based Models ◽  
Time Step ◽  
Partial Differential ◽  
Agent Based ◽  
Random Walkers

AbstractThere is much interest within the mathematical biology and statistical physics community in converting stochastic agent-based models for random walkers into a partial differential equation description for the average agent density. Here a collection of noninteracting biased random walkers on a one-dimensional lattice is considered. The usual master equation approach requires that two continuum limits, involving three parameters, namely step length, time step and the random walk bias, approach zero in a specific way. We are interested in the case where the two limits are not consistent. New results are obtained using a Fokker–Planck equation and the results are highly dependent on the simulation update schemes. The theoretical results are confirmed with examples. These findings provide insight into the importance of updating schemes to an accurate macroscopic description of stochastic local movement rules in agent-based models when the lattice spacing represents a physical object such as cell diameter.

scholarly journals Estimation of Optimal Time Step and Compare with of ODE Solver of MATLAB Package of RLC Circuit using Numerical Methods

1970 ◽  
Vol 7 (1) ◽  
pp. 67-73 ◽  
Author(s):  
Sheikh Md Rabiul Islam
Keyword(s):  
Mesh Size ◽  
Paper Analysis ◽  
Optimal Time ◽  
Time Step ◽  
Minimum Error ◽  
Optimal Output ◽  
Runge Kutta Method ◽  
Rlc Circuit ◽  
Matlab Package ◽  
Theoretical Results

In this paper analysis of a RLC circuit model that has been described optimal time step and minimize of error using numerical method. The goal is to reach the optimal time response due to the input for which optimal output response reaches a minimum error and also compared with ODE solver of MATLAB packages for the different cell (mesh) size of the RLC model. Table is constructed of the model to evaluate optimal time step and also CPU time into the simulation using MATLAB 7.6.0(R2008a).The values of register, capacitor and inductor as well as electromagnetic force are obtained through the mathematical relations of the model. The general analysis of the RLC circuit due to the optimal time step and minimum error is developed after several analysis and operations. The theoretical results show effectiveness of optimized of the model. Keywords: Optimal time step; MATLAB; Trapezoidal; Implicit Euler; Runge-Kutta method; RLC circuit. DOI: http://dx.doi.org/10.3329/diujst.v7i1.9650   Daffodil International University Journal of Science and Technology Vol.7(1) 2012 67-73

scholarly journals Algorithms for Solving Darcian Flow in Structured Porous Media

10.14311/1829 ◽  
2013 ◽  
Vol 53 (4) ◽  
Author(s):  
Michal Kuráž ◽  
Petr Mayer
Keyword(s):  
Proper Time ◽  
Time Integration ◽  
Mass Term ◽  
Step Length ◽  
Richards Equation ◽  
Parabolic Problems ◽  
Computational Domain ◽  
Wetting Front ◽  
Time Step ◽  
The Matrix

This paper presents several algorithms that were implemented in DRUtES [1], a new open source project. DRUtES is a finite element solver for coupled nonlinear parabolic problems, namely the Richards equation with the dual porosity approach (modeling the flow of liquids in a porous medium). Mass balance consistency is crucial in any hydrological balance and contaminant transportation evaluations. An incorrect approximation of the mass term greatly depreciates the results that are obtained. An algorithm for automatic time step selection is presented, as the proper time step length is crucial for achieving accuracy of the Euler time integration method. Various problems arise with poor conditioning of the Richards equation: the computational domain is clustered into subregions separated by a wetting front, and the nonlinear constitutive functions cover a high range of values, while a very simple diagonal preconditioning method greatly improves the matrix properties. The results are presented here, together with an analysis.

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