China
Africa
Explore chapters and articles related to this topic
Influence of some numerical integration methods applied to calculation of dynamic response
Published in Kosta Talaganov, Gunther Schmid, Computational Structural Dynamics, 2020
In order to control process of computation, some reliable software demands could be stated: Starting values problem: Initial step size and starting multistep method.Step size control: Determination of step size so as to control local error (adaptive step size changing).Order of method control: Selection and change of the order of the method to be used from the family of methods.Output: Calculation of solution values at a specified set of points (control of output).Global error control: Estimation of cumulative effect of the local errors (keep the global error within specified tolerance).Constant checking: Control and checking of results and consistency with the model.
Modelling of Nonlinear Propagation in Waveguides
Published in Andrei V. Lavrinenko, Jesper Lægsgaard, Niels Gregersen, Frank Schmidt, Thomas Søndergaard, Numerical Methods in Photonics, 2018
Andrei V. Lavrinenko, Jesper Lægsgaard, Niels Gregersen, Frank Schmidt, Thomas Søndergaard
Equation (5.42) is a first-order ODE and can as such be propagated using conventional solvers for such problems. A common variant is the fourth-order Runge–Kutta method (RK4). The advantage of this method is that it is simple to programme, has a fairly high-order accuracy, and allows for an easy implementation of adaptive stepsize, which is usually a requirement for efficient ODE solution. More advanced ODE methods exist, but RK4 is usually found to perform quite well for solving the kind of problems that tend to occur in nonlinear waveguide modelling. In MATLAB, the ODE method is implemented as a built-in function, and we will therefore not go into a discussion of the mathematics and coding of the method.
Lumped Capacity Transient Heat Transfer
Published in Randall F. Barron, Gregory F. Nellis, Cryogenic Heat Transfer, 2017
Randall F. Barron, Gregory F. Nellis
Most software include native ODE solvers that utilize techniques that are more sophisticated than those discussed in the preceding sections. Most of these native ODE solvers also utilize adaptively changing time steps. The Euler and RK4 techniques discussed in Sections 3.4.1 and 3.4.2 were implemented using a fixed duration time step. This method is not efficient because there are regions of time during the simulation where the solution is not changing substantially, and therefore, large time steps could be taken with little loss of accuracy. Adaptive step-size solutions adjust the size of the time step used based on the local truncation error.
Study on dynamic characteristic analysis of vehicle shock absorbers based on bidirectional fluid–solid coupling
Published in Engineering Applications of Computational Fluid Mechanics, 2021
Qiping Chen, Zhihui Xu, Mingming Wu, Yuan Xiao, Hao Shao
The simulation calculation solution is optimized and selected in Workbench software, to improve the effectiveness of the simulation and obtain better results. To achieve better convergences and calculation accuracies, the relaxation factor has been set as 0.65.The compressibility of the oil inside the shock absorber is ignored (Huang et al., 2013), and the friction between the shock absorber superposition valve slices and the friction between the piston rod and the guide seat are ignored (Yu et al., 2014).Only the moving grid of superposition valve slices in the core area is considered.Owing to the existence of large perturbation deformation in the superposition valve slice under stress, it was found that a penalty stiffness coefficient could solve the problem of large perturbation deformation of the superposition valve slice, so the penalty stiffness coefficient is set to (He, Long, & Xiao, 2012).An adaptive step size is adopted and efforts are made to reduce the time step size to improve the computational efficiency under the condition of convergence.
Study on cavitation phenomenon of twin-tube hydraulic shock absorber based on CFD
Published in Engineering Applications of Computational Fluid Mechanics, 2019
Qiping Chen, Mingming Wu, Sheng Kang, Yu Liu, Jiacheng Wei
In order to save computational time and get more accurate fluid simulation results, it is necessary to select the suitable solution settings in FLUENT as following: In order to improve the convergence of simulation and take account of the accuracy of simulation, the relaxation factor is 0.65.The PISO algorithm suitable for transient fluid analysis is adopted to solve the simulation, which can improve the accuracy of the simulation results (Liang, Tian, & Zhang, 2012).Only the moving mesh at the throttle plate is considered, and the moving mesh is not considered in the rest of the flow field.Flow field grids are composed of tetrahedron and hexahedron grids, which lead to errors in calculation. Different types of flow field grids which recomposed of tetrahedron and hexahedron types should be merged to avoid the computational errors and ensure the accuracy of solution information transmission, the overlap of different types of grid spatial positions should be maintained as far as possible.The adaptive step size is adopted to reduce the time step under the convergence condition to improve the computational efficiency.
Effect of porosity on buckling and vibrational characteristics of the imperfect GPLRC composite nanoshell
Published in Mechanics Based Design of Structures and Machines, 2021
Mostafa Habibi, Alireza Mohammadi, Hamed Safarpour, Majid Ghadiri
The linear and nonlinear free vibrations of an axially moving rectangular plate coupled with dense fluid having a free surface are investigated by Wang, Huang, and Li (2016). They in their work found that the nonlinear frequencies of the plate-fluid system are influenced by initial amplitude, moving speed and nonlinear coefficient. The system is solved by applying directly the method of multiple scales to the governing partial-differential equations and boundary conditions. Wang, Liang, and Guo (2013) studied the nonlinear vibrations of a thin, elastic, laminated composite circular cylindrical shell, moving in axial direction and having an internal resonance. Their solution procedure was harmonic balance to study the nonlinear dynamic responses of the multi-degrees-of-freedom system. The nonlinear steady-state responses of longitudinally traveling FGM plates immersed in liquid is investigated by Wang and Zu (2017a). The numerical solutions are carried out by utilizing an adaptive step-size fourth-order Runge-Kutta technique. In another work, the large-amplitude (geometrically nonlinear) vibrations of rotating, laminated composite circular cylindrical shells subjected to radial harmonic excitation in the neighborhood of the lowest resonances are investigated by Wang (2014). The method of harmonic balance is applied to study the forced vibration responses of the two-degrees-of-freedom system. Wang (2018) studied the electro-mechanical vibrations of functionally graded piezoelectric material (FGPM) plates carrying porosities in the translation state. The equation is further discretized to a system of ordinary differential equations using the Galerkin method, which are subsequently solved via the harmonic balance method.