The fuzzy control algorithms used commonly at present are all regarded as some interpolation functions, which is in essence equivalent to discrete response functions to be fitted. This means that fuzzy control method ...The fuzzy control algorithms used commonly at present are all regarded as some interpolation functions, which is in essence equivalent to discrete response functions to be fitted. This means that fuzzy control method is similar to finite element method in mathematical physics, which is a kind of direct manner or numerical method in control systems.展开更多
An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions ...An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms satisfying different conditions are employed to generate a number of formulations. Performances of the new schemes are tested against well-known numerical integrators for selected test cases with quite satisfactory results. Convergence and stability issues of the new formulations are not addressed as the treatment of these aspects requires a separate work. The general approach introduced herein opens a wide vista for producing virtually unlimited number of formulations.展开更多
The multiscale method provides an effective approach for the numerical analysis of heterogeneous viscoelastic materials by reducing the degree of freedoms(DOFs).A basic framework of the Multiscale Scaled Boundary Fini...The multiscale method provides an effective approach for the numerical analysis of heterogeneous viscoelastic materials by reducing the degree of freedoms(DOFs).A basic framework of the Multiscale Scaled Boundary Finite Element Method(MsSBFEM)was presented in our previous works,but those works only addressed two-dimensional problems.In order to solve more realistic problems,a three-dimensional MsSBFEM is further developed in this article.In the proposed method,the octree SBFEM is used to deal with the three-dimensional calculation for numerical base functions to bridge small and large scales,the three-dimensional image-based analysis can be conveniently conducted in small-scale and coarse nodes can be flexibly adjusted to improve the computational accuracy.Besides,the Temporally Piecewise Adaptive Algorithm(TPAA)is used to maintain the computational accuracy of multiscale analysis by adaptive calculation in time domain.The results of numerical examples show that the proposed method can significantly reduce the DOFs for three-dimensional viscoelastic analysis with good accuracy.For instance,the DOFs can be reduced by 9021 times compared with Direct Numerical Simulation(DNS)with an average error of 1.87%in the third example,and it is very effective in dealing with three-dimensional complex microstructures directly based on images without any geometric modelling process.展开更多
A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter fa...A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter family of solutions in exact form, with all the coefficients determined in rational numbers. Comparative studies are pursued to investigate the effects due to changes of base parameters on （i） the accuracy of the theoretically predicted wave properties and （ii） the rate of convergence of perturbation expansion. Two important results are found by comparisons between the theoretical predictions based on a set of parameters separately adopted for expansion in turn. First, the accuracy and the convergence of the perturbation expansions, appraised versus the exact solution provided by an earlier paper [1] as the standard reference, are found to depend, quite sensitively, on changes in base parameter. The resulting variations in the solution are physically displayed in various wave properties with differences found dependent on which property （e.g. the wave amplitude, speed, its profile, excess mass, momentum, and energy）, on what range in value of the base, and on the rank of the order n in the expansion being addressed. Secondly, regarding convergence, the present perturbation series is found definitely asymptotic in nature, with the relative error δ （n） （the relative mean-square difference between successive orders n of wave elevations） reaching a minimum, δm at a specific order, n = n both depending on the base adopted, e.g. nm,α= 11-12 based on parameter α （wave amplitude）, nm,δ = 15 on δ （amplitude-speed square ratio）, and nm.ε= 17 on ε （ wave number squared）. The asymptotic range is brought to completion by the highest order of n = 18 reached in this work.展开更多
With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and re...With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.展开更多
We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without res...We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale characters.The key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary conditions.The boundary conditions are chosen to extract more accurate boundary information in the local problem.We consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base functions.Numerical examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.展开更多
文摘The fuzzy control algorithms used commonly at present are all regarded as some interpolation functions, which is in essence equivalent to discrete response functions to be fitted. This means that fuzzy control method is similar to finite element method in mathematical physics, which is a kind of direct manner or numerical method in control systems.
文摘An entirely new framework is established for developing various single- and multi-step formulations for the numerical integration of ordinary differential equations. Besides polynomials, unconventional base-functions with trigonometric and exponential terms satisfying different conditions are employed to generate a number of formulations. Performances of the new schemes are tested against well-known numerical integrators for selected test cases with quite satisfactory results. Convergence and stability issues of the new formulations are not addressed as the treatment of these aspects requires a separate work. The general approach introduced herein opens a wide vista for producing virtually unlimited number of formulations.
基金NSFC Grants(12072063,11972109)Grant of State Key Laboratory of Structural Analysis for Industrial Equipment(S22403)+1 种基金National Key Research and Development Program of China(2020YFB1708304)Alexander von Humboldt Foundation(1217594).
文摘The multiscale method provides an effective approach for the numerical analysis of heterogeneous viscoelastic materials by reducing the degree of freedoms(DOFs).A basic framework of the Multiscale Scaled Boundary Finite Element Method(MsSBFEM)was presented in our previous works,but those works only addressed two-dimensional problems.In order to solve more realistic problems,a three-dimensional MsSBFEM is further developed in this article.In the proposed method,the octree SBFEM is used to deal with the three-dimensional calculation for numerical base functions to bridge small and large scales,the three-dimensional image-based analysis can be conveniently conducted in small-scale and coarse nodes can be flexibly adjusted to improve the computational accuracy.Besides,the Temporally Piecewise Adaptive Algorithm(TPAA)is used to maintain the computational accuracy of multiscale analysis by adaptive calculation in time domain.The results of numerical examples show that the proposed method can significantly reduce the DOFs for three-dimensional viscoelastic analysis with good accuracy.For instance,the DOFs can be reduced by 9021 times compared with Direct Numerical Simulation(DNS)with an average error of 1.87%in the third example,and it is very effective in dealing with three-dimensional complex microstructures directly based on images without any geometric modelling process.
基金The project partly supported by the National Natural Science Foundation of China(19925414,10474045)
文摘A unified perturbation theory is developed here for calculating solitary waves of all heights by series expansion of base flow variables in powers of a small base parameter to eighteenth order for the one-parameter family of solutions in exact form, with all the coefficients determined in rational numbers. Comparative studies are pursued to investigate the effects due to changes of base parameters on （i） the accuracy of the theoretically predicted wave properties and （ii） the rate of convergence of perturbation expansion. Two important results are found by comparisons between the theoretical predictions based on a set of parameters separately adopted for expansion in turn. First, the accuracy and the convergence of the perturbation expansions, appraised versus the exact solution provided by an earlier paper [1] as the standard reference, are found to depend, quite sensitively, on changes in base parameter. The resulting variations in the solution are physically displayed in various wave properties with differences found dependent on which property （e.g. the wave amplitude, speed, its profile, excess mass, momentum, and energy）, on what range in value of the base, and on the rank of the order n in the expansion being addressed. Secondly, regarding convergence, the present perturbation series is found definitely asymptotic in nature, with the relative error δ （n） （the relative mean-square difference between successive orders n of wave elevations） reaching a minimum, δm at a specific order, n = n both depending on the base adopted, e.g. nm,α= 11-12 based on parameter α （wave amplitude）, nm,δ = 15 on δ （amplitude-speed square ratio）, and nm.ε= 17 on ε （ wave number squared）. The asymptotic range is brought to completion by the highest order of n = 18 reached in this work.
文摘With the application of Hammer integral formulas of a continuous function on a triangular element, the numerical integral formulas of some discrete functions on the element are derived by means of decomposition and recombination of base functions. Hammer integral formulas are the special examples of those of the paper.
文摘We study the multiscale finite element method for solving multiscale elliptic problems with highly oscillating coefficients,which is designed to accurately capture the large scale behaviors of the solution without resolving the small scale characters.The key idea is to construct the multiscale base functions in the local partial differential equation with proper boundary conditions.The boundary conditions are chosen to extract more accurate boundary information in the local problem.We consider periodic and non-periodic coefficients with linear and oscillatory boundary conditions for the base functions.Numerical examples will be provided to demonstrate the effectiveness of the proposed multiscale finite element method.
