The internal temperature of cast-in-place concrete bridges undergoes strong variations during the construction as a result of environmental factors.In order to determine precisely such variations,the present study rel...The internal temperature of cast-in-place concrete bridges undergoes strong variations during the construction as a result of environmental factors.In order to determine precisely such variations,the present study relies on the finite element method,used to model the bridge box girder section and simulate the internal temperature distribution during construction.The numerical results display good agreement with measured temperature values.It is shown that when the external temperature is higher,and the internal and external temperature difference is relatively small,the deviation of the fitting line from existing specifications(Chinese specification,American specification,New Zealand specification)is relatively large and vice versa.展开更多
The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive m...The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.展开更多
In this paper, a novel class of exponential Fourier collocation methods （EFCMs） is presented for solving systems of first-order ordinary differential equations. These so-called exponential Fourier collocation method...In this paper, a novel class of exponential Fourier collocation methods （EFCMs） is presented for solving systems of first-order ordinary differential equations. These so-called exponential Fourier collocation methods are based on the variation-of-constants formula, incorporating a local Fourier expansion of the underlying problem with collocation meth- ods. We discuss in detail the connections of EFCMs with trigonometric Fourier colloca- tion methods （TFCMs）, the well-known Hamiltonian Boundary Value Methods （HBVMs）, Gauss methods and Radau IIA methods. It turns out that the novel EFCMs are an es- sential extension of these existing methods. We also analyse the accuracy in preserving the quadratic invariants and the Hamiltonian energy when the underlying system is a Hamiltonian system. Other properties of EFCMs including the order of approximations and the convergence of fixed-point iterations are investigated as well. The analysis given in this paper proves further that EFCMs can achieve arbitrarily high order in a routine manner which allows us to construct higher-order methods for solving systems of first- order ordinary differential equations conveniently. We also derive a practical fourth-order EFCM denoted by EFCM（2,2） as an illustrative example. The numerical experiments using EFCM（2,2） are implemented in comparison with an existing fourth-order HBVM, an energy-preserving collocation method and a fourth-order exponential integrator in the literature. The numerical results demonstrate the remarkable efficiency and robustness of the novel EFCM（2,2）.展开更多
基金supported by National Natural Science Foundation of China(Grant No.51778314).
文摘The internal temperature of cast-in-place concrete bridges undergoes strong variations during the construction as a result of environmental factors.In order to determine precisely such variations,the present study relies on the finite element method,used to model the bridge box girder section and simulate the internal temperature distribution during construction.The numerical results display good agreement with measured temperature values.It is shown that when the external temperature is higher,and the internal and external temperature difference is relatively small,the deviation of the fitting line from existing specifications(Chinese specification,American specification,New Zealand specification)is relatively large and vice versa.
文摘The purpose of this paper is to introduce and study the semi-groups of nonlinear contractions in probabilistic normed spaces and to establish the Crandall-Liggett's exponential formula for some kind of accretive mappings in probabilistic normed spaces. As applications, these results are utilized to study the Cauchy problem for a kind of differential inclusions with accretive mappings in probabilistic normed spaces.
文摘In this paper, a novel class of exponential Fourier collocation methods （EFCMs） is presented for solving systems of first-order ordinary differential equations. These so-called exponential Fourier collocation methods are based on the variation-of-constants formula, incorporating a local Fourier expansion of the underlying problem with collocation meth- ods. We discuss in detail the connections of EFCMs with trigonometric Fourier colloca- tion methods （TFCMs）, the well-known Hamiltonian Boundary Value Methods （HBVMs）, Gauss methods and Radau IIA methods. It turns out that the novel EFCMs are an es- sential extension of these existing methods. We also analyse the accuracy in preserving the quadratic invariants and the Hamiltonian energy when the underlying system is a Hamiltonian system. Other properties of EFCMs including the order of approximations and the convergence of fixed-point iterations are investigated as well. The analysis given in this paper proves further that EFCMs can achieve arbitrarily high order in a routine manner which allows us to construct higher-order methods for solving systems of first- order ordinary differential equations conveniently. We also derive a practical fourth-order EFCM denoted by EFCM（2,2） as an illustrative example. The numerical experiments using EFCM（2,2） are implemented in comparison with an existing fourth-order HBVM, an energy-preserving collocation method and a fourth-order exponential integrator in the literature. The numerical results demonstrate the remarkable efficiency and robustness of the novel EFCM（2,2）.
