The plane problem of a crack terminating at the interface of a bimaterial piezoelectric, and loaded on its faces, is treated. The emphasis is placed on how to transform this problem into a non-homogeneous Hilbert prob...The plane problem of a crack terminating at the interface of a bimaterial piezoelectric, and loaded on its faces, is treated. The emphasis is placed on how to transform this problem into a non-homogeneous Hilbert problem. To make the derivation tractable, the concept of the axial conjugate is introduced and related to the complex conjugate. The angle between the crack line and the interface may be arbitrary. Numerical results are given to illustrate the stress singularity at crack tip.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
Deep learning has been increasingly recognized as a promising tool in solving kinds of physical problems beyond powerful approximations. A multi-domain physics-informed neural network(mPINN) is proposed to solve the n...Deep learning has been increasingly recognized as a promising tool in solving kinds of physical problems beyond powerful approximations. A multi-domain physics-informed neural network(mPINN) is proposed to solve the non-uniform heat conduction and conjugate natural convection with the discontinuity of temperature gradient on the interface. Local radial basis function method(LRBF) is applied to compute the case without the analytical solution and is regarded as the benchmark solver.Each physical domain matches a private neural network and all neural networks are connected by the shared information of temperature and heat flux on the interface. Joint training and separate training are utilized to minimize the loss function, which usually consists of the residual of boundary conditions, interface conditions and governing equations. Joint training minimizes the sum of all losses from neural networks with one shared optimizer, while separate training owns its private optimizer. Local adaptive activation function(LAAF) is used to accelerate the convergence and acquire a lower loss value when compared with its fixed counterpart. The numerical experiments on three types of residual points, uniform, Gauss-Lobatto and random, are conducted and it can be concluded that the uniform residual points can obtain the most accurate solution than the random and Gauss-Lobatto. Joint training is more accurate than the separate training when the number of residual points is relatively small,while the separate training performs better than the joint training for the large number of residual points. Numerous test cases on multi-domain heat transfer and fluid flow show the accuracy of the proposed m PINN. Local and global heat transfer rates show good agreements with the results from LRBF. Excepting the forward problems, the thermal conductivity ratio, the constant source and the characteristic parameters of natural convection are accurately learned from sparsely distributed data points.展开更多
The present study proposes a predictive model to explore the effect of partially filled porous media on the con-jugate heat transfer characteristic of phase change material(PCM)with interfacial coupling conditions bet...The present study proposes a predictive model to explore the effect of partially filled porous media on the con-jugate heat transfer characteristic of phase change material(PCM)with interfacial coupling conditions between pure fluid region and porous region.The enthalpy-porosity method,local thermal non-equilibrium model and Darcy-Forchheimer law are comprehensively considered to describe the convective heat transfer process in porous media.The modified model is then validated by benchmark data provided by particle image velocimetry(PIV)ex-periments.The phase change behavior,heat transfer efficiency and energy storage performance are numerically investigated for different partial porous filling strategies in terms of filling content,position,height of porous foam and inclination angles of cavity.The results indicate that due to the resistance in porous region,the shear stress exerted by the main vortex(natural convection)in pure fluid region and the momentum transferred,a secondary vortex phenomenon appears in the porous region near the fluid/porous interface.Moreover,such dis-continuity of permeability and fluid-to-porous thermal conductivity results in the cusp of phase change interface at the horizontal fluid/porous boundary.Among four partial porous filling cases,the lower porous filling one has more desirable heat transfer performance,and the 3/4H lower porous filling configuration is the best solution for optimization of the latent heat thermal energy storage(LHTES)systems.For tilted cavity,the increase of inclination angle positively affects the heat transfer efficiency as well as the energy storage rate of the LHTES system,where the performance of 3/4H lower porous filling configuration is further highlighted.展开更多
Bueckner's work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials.The difficulties in separating Stroh's six complex ...Bueckner's work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials.The difficulties in separating Stroh's six complex arguments involved in the integral for the dissimilar materials are overcome and thert the explicit function representations of the integral are given and studied in detail.It is found that the pseudo-orthogonal properties of the eigenfunction expansion form(EEF)for a crack presented previously in isotropic elastic cases,in isotopic bimaterial cases,and in orthotropic cases are also valid in the present dissimilar arbitrary anisotropic cases.The relation between Bueckner's work conjugate integral and the J-integral in these cases is obtained by introducing a complementary stress- displacement state.Finally,some useful path-independent integrals and weight functions are proposed for calculating the crack tip parameters such as the stress intensity factors.展开更多
基金The Project Supported by National Natural Science Foundationthe National Education Committee Foundation for the Scholars Returning from Abroad
文摘The plane problem of a crack terminating at the interface of a bimaterial piezoelectric, and loaded on its faces, is treated. The emphasis is placed on how to transform this problem into a non-homogeneous Hilbert problem. To make the derivation tractable, the concept of the axial conjugate is introduced and related to the complex conjugate. The angle between the crack line and the interface may be arbitrary. Numerical results are given to illustrate the stress singularity at crack tip.
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supported by the National Natural Science Foundation of China (Grant Nos. 12102331 and 52130603)
文摘Deep learning has been increasingly recognized as a promising tool in solving kinds of physical problems beyond powerful approximations. A multi-domain physics-informed neural network(mPINN) is proposed to solve the non-uniform heat conduction and conjugate natural convection with the discontinuity of temperature gradient on the interface. Local radial basis function method(LRBF) is applied to compute the case without the analytical solution and is regarded as the benchmark solver.Each physical domain matches a private neural network and all neural networks are connected by the shared information of temperature and heat flux on the interface. Joint training and separate training are utilized to minimize the loss function, which usually consists of the residual of boundary conditions, interface conditions and governing equations. Joint training minimizes the sum of all losses from neural networks with one shared optimizer, while separate training owns its private optimizer. Local adaptive activation function(LAAF) is used to accelerate the convergence and acquire a lower loss value when compared with its fixed counterpart. The numerical experiments on three types of residual points, uniform, Gauss-Lobatto and random, are conducted and it can be concluded that the uniform residual points can obtain the most accurate solution than the random and Gauss-Lobatto. Joint training is more accurate than the separate training when the number of residual points is relatively small,while the separate training performs better than the joint training for the large number of residual points. Numerous test cases on multi-domain heat transfer and fluid flow show the accuracy of the proposed m PINN. Local and global heat transfer rates show good agreements with the results from LRBF. Excepting the forward problems, the thermal conductivity ratio, the constant source and the characteristic parameters of natural convection are accurately learned from sparsely distributed data points.
基金support from the National Natural Science Foundation of China(Grant No.:52006039)Natural Science Foundation of Guangdong Province(Grant No.:2022A1515010602)+1 种基金Guangzhou Science and Technology Plan Project(Grant No.:202201010575)Guangdong Provincial Key Laboratory of Distributed Energy Systems(Grant No.:2020B1212060075).
文摘The present study proposes a predictive model to explore the effect of partially filled porous media on the con-jugate heat transfer characteristic of phase change material(PCM)with interfacial coupling conditions between pure fluid region and porous region.The enthalpy-porosity method,local thermal non-equilibrium model and Darcy-Forchheimer law are comprehensively considered to describe the convective heat transfer process in porous media.The modified model is then validated by benchmark data provided by particle image velocimetry(PIV)ex-periments.The phase change behavior,heat transfer efficiency and energy storage performance are numerically investigated for different partial porous filling strategies in terms of filling content,position,height of porous foam and inclination angles of cavity.The results indicate that due to the resistance in porous region,the shear stress exerted by the main vortex(natural convection)in pure fluid region and the momentum transferred,a secondary vortex phenomenon appears in the porous region near the fluid/porous interface.Moreover,such dis-continuity of permeability and fluid-to-porous thermal conductivity results in the cusp of phase change interface at the horizontal fluid/porous boundary.Among four partial porous filling cases,the lower porous filling one has more desirable heat transfer performance,and the 3/4H lower porous filling configuration is the best solution for optimization of the latent heat thermal energy storage(LHTES)systems.For tilted cavity,the increase of inclination angle positively affects the heat transfer efficiency as well as the energy storage rate of the LHTES system,where the performance of 3/4H lower porous filling configuration is further highlighted.
基金The project supported by the National Natural Science Foundation of China and the Graduate School of Xi'an Jiaotong University
文摘Bueckner's work conjugate integral customarily adopted for linear elastic materials is established for an interface crack in dissimilar anisotropic materials.The difficulties in separating Stroh's six complex arguments involved in the integral for the dissimilar materials are overcome and thert the explicit function representations of the integral are given and studied in detail.It is found that the pseudo-orthogonal properties of the eigenfunction expansion form(EEF)for a crack presented previously in isotropic elastic cases,in isotopic bimaterial cases,and in orthotropic cases are also valid in the present dissimilar arbitrary anisotropic cases.The relation between Bueckner's work conjugate integral and the J-integral in these cases is obtained by introducing a complementary stress- displacement state.Finally,some useful path-independent integrals and weight functions are proposed for calculating the crack tip parameters such as the stress intensity factors.
