The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be d...The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.展开更多
This paper takes the analysis of economical land use in the design of oil field stations as the research object.Firstly,it elaborates the significance of saving land.Then combined with the"Fire Prevention Code of...This paper takes the analysis of economical land use in the design of oil field stations as the research object.Firstly,it elaborates the significance of saving land.Then combined with the"Fire Prevention Code of Petrol Chemical Enterprise Design",the paper analyzes and studies the safety and economical use of the general drawing design of the oil field stations for reference.展开更多
In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solu...In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solution and the DMP-preserving property.Numerical experiments show that the nonlinear iteration numbers of the scheme in[24]increase rapidly when the interfacial coefficients decrease to zero.In contrast,the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero,which reveals that the unified scheme is more robust than the scheme in[24].The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.展开更多
With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and enriched.However,there has been little theoretical wo...With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and enriched.However,there has been little theoretical work focusing on neural networks in solving interface problems.In this paper,we perform a convergence analysis of physics-informed neural networks(PINNs)for solving second-order elliptic interface problems.Specifically,we consider PINNs with domain decomposition technologies and introduce gradient-enhanced strategies on the interfaces to deal with boundary and interface jump conditions.It is shown that the neural network sequence obtained by minimizing a Lipschitz regularized loss function converges to the unique solution to the interface problem in H2 as the number of samples increases.Numerical experiments are provided to demonstrate our theoretical analysis.展开更多
基金This work was supported by the National Natural Science Foundation of China(No.19772064)by the project of CAS KJ 951-1-20
文摘The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.
文摘This paper takes the analysis of economical land use in the design of oil field stations as the research object.Firstly,it elaborates the significance of saving land.Then combined with the"Fire Prevention Code of Petrol Chemical Enterprise Design",the paper analyzes and studies the safety and economical use of the general drawing design of the oil field stations for reference.
基金National Natural Science Foundation of China(11971069,12071045)Foundation of CAEP(CX20210042)Science Challenge Project(No.TZ2016002).
文摘In this paper,we present a unified finite volume method preserving discrete maximum principle(DMP)for the conjugate heat transfer problems with general interface conditions.We prove the existence of the numerical solution and the DMP-preserving property.Numerical experiments show that the nonlinear iteration numbers of the scheme in[24]increase rapidly when the interfacial coefficients decrease to zero.In contrast,the nonlinear iteration numbers of the unified scheme do not increase when the interfacial coefficients decrease to zero,which reveals that the unified scheme is more robust than the scheme in[24].The accuracy and DMP-preserving property of the scheme are also veri ed in the numerical experiments.
基金the National Natural Science Foundation of China(Grant Nos.11771435,22073110 and 12171466).
文摘With the remarkable empirical success of neural networks across diverse scientific disciplines,rigorous error and convergence analysis are also being developed and enriched.However,there has been little theoretical work focusing on neural networks in solving interface problems.In this paper,we perform a convergence analysis of physics-informed neural networks(PINNs)for solving second-order elliptic interface problems.Specifically,we consider PINNs with domain decomposition technologies and introduce gradient-enhanced strategies on the interfaces to deal with boundary and interface jump conditions.It is shown that the neural network sequence obtained by minimizing a Lipschitz regularized loss function converges to the unique solution to the interface problem in H2 as the number of samples increases.Numerical experiments are provided to demonstrate our theoretical analysis.
