The solution to heat transfer problems in two-dimensional heterogeneous media is attended based on the scaled boundary finite element method(SBFEM)coupled with equilibrated basis functions(EqBFs).The SBFEM reduces the...The solution to heat transfer problems in two-dimensional heterogeneous media is attended based on the scaled boundary finite element method(SBFEM)coupled with equilibrated basis functions(EqBFs).The SBFEM reduces the model order by scaling the boundary solution onto the inner element.To this end,tri-lateral elements are emanated from a scaling center,followed by the development of a semi-analytical solution along the radial direction and a finite element solution along the circumferential/boundary direction.The discretization is thus limited to the boundaries of the model,and the semi-analytical radial solution is found through the solution of an eigenvalue problem,which restricts the methods’applicability to heterogeneous media.In this research,we first extracted the SBFEM formulation considering the heterogeneity of the media.Then,we replaced the semi-analytical radial solution with the EqBFs and removed the eigenvalue solution step from the SBFEM.The varying coefficients of the partial differential equation(PDE)resulting from the heterogeneity of the media are replaced by a finite series in the radial and circumferential directions of the element.A weighted residual approach is applied to the radial equation.The equilibrated radial solution series is used in the new formulation of the SBFEM.展开更多
This study examines the hydrodynamic performance of short-crested wave interaction with a new porous cylindrical structure by using the scaled boundary finite element method （SBFEM）, which is a semi-analytical techn...This study examines the hydrodynamic performance of short-crested wave interaction with a new porous cylindrical structure by using the scaled boundary finite element method （SBFEM）, which is a semi-analytical technique combining the advantages of the finite element method and the boundary element method and with its own special features as well. The cylindrical structure consists of dual arc-shaped porous outer cylinders circumscribing an impermeable inner cylinder. A central feature of the newly extended method is that two virtual outer cylinders extending the arc-shaped porous outer cylinders with the same centre are introduced and variable porous-effect parameters are also introduced for the two virtual cylinders, so that the final SBFEM quation still can be handled in a closed-form analytical manner in the radial direction and by a finite element approximation in the circumferential direction. The entire computational domain is divided into two bounded and one unbounded domains, and a variational principle formulation is used to derive the SBFEM equation in each sub-domain. The velocity potential in bounded and unbounded domains is formulated using sets of Bessel and Hankel functions respectively, and the unknown coefficients are determined from the matching conditions. The results of numerical verification show that the approach discretises only the outermost virtual cylinder with surface finite-elements and fewer elements are required to obtain very accurate results.Influences of the incident wave parameters and structural configurations on the hydrodynamics are examined.展开更多
Based on the modified scale boundary finite element method and continued fraction solution,a high-order doubly asymptotic transmitting boundary(DATB)is derived and extended to the simulation of vector wave propagation...Based on the modified scale boundary finite element method and continued fraction solution,a high-order doubly asymptotic transmitting boundary(DATB)is derived and extended to the simulation of vector wave propagation in complex layered soils.The high-order DATB converges rapidly to the exact solution throughout the entire frequency range and its formulation is local in the time domain,possessing high accuracy and good efficiency.Combining with finite element method,a coupled model is constructed for time-domain analysis of underground station-layered soil interaction.The coupled model is divided into the near and far field by the truncated boundary,of which the near field is modelled by FEM while the far field is modelled by the high-order DATB.The coupled model is implemented in an open source finite element software,OpenSees,in which the DATB is employed as a super element.Numerical examples demonstrate that results of the coupled model are stable,accurate and efficient compared with those of the extended mesh model and the viscous-spring boundary model.Besides,it has also shown the fitness for long-time seismic response analysis of underground station-layered soil interaction.Therefore,it is believed that the coupled model could provide a new approach for seismic analysis of underground station-layered soil interaction and could be further developed for engineering.展开更多
The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to pre...The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.展开更多
The static response of two-dimensional horizontal layered piezoelectric bounded domain with side face load was investigated.In this paper,the modified scaled boundary finite element method(SBFEM)is provided as an effe...The static response of two-dimensional horizontal layered piezoelectric bounded domain with side face load was investigated.In this paper,the modified scaled boundary finite element method(SBFEM)is provided as an effective semi analytical methodology.The method is used to solve the static problem for the layered piezoelectric bounded domain.The scaling line definition extends the SBFEM to be more suitable for analyzing the multilayered piezoelectric bounded domain.It avoids the limitations of original SBFEM in modeling the horizontal layered bounded domain.The modified SBFEM governing equation with piezoelectric medium is derived by introducing Duality variable in the Hamilton system.This derivation technology makes the progress be concise.The novel displacement and electric governing equations of the modified SBFEM is given together by the first time.The node forces can be expressed as power exponent function with radial coordinate by introducing the auxiliary variable and using the eigenvalue decomposition.The novel modified SBFEM solution of layered bounded domain with piezoelectric medium is solved.The new power expansion function of layered piezoelectric medium with side face load is proposed.This technology significantly extends the application range of modified SBFEM.The novel treatment of side face load for the layered piezoelectric bounded domain is proposed.Numerical studies are conducted to demonstrate the accuracy of proposed technique in handling with the static problem of layered bounded domain with piezoelectric medium for side face load.The influence of the side face load type and depth are discussed in detail.展开更多
将W o lf和Song提出的比例边界有限元法(sca led boundary fin ite e lem en t m ethod,简称SBFEM)应用于坝-库水相互作用分析.在库水不可压缩假定的前提下推导了坝面动水压力与附加质量矩阵的基本方程.二维重力坝和三维拱坝坝面动水压...将W o lf和Song提出的比例边界有限元法(sca led boundary fin ite e lem en t m ethod,简称SBFEM)应用于坝-库水相互作用分析.在库水不可压缩假定的前提下推导了坝面动水压力与附加质量矩阵的基本方程.二维重力坝和三维拱坝坝面动水压力的算例表明,与有限元法比较,SBFEM计算精度明显提高,同时由于具有降维的特点,计算工作量也在很大程度上有所节约.还分析了库底和水面坡度变化以及水库边界形状适当变化对动水压力分布和数值大小的影响.结果表明,一般情况下水库边界的变化对动水压力的分布形状基本上不发生影响,对动水压力数值大小也影响不大.展开更多
Based on the scaled boundary finite-element method, the governing equations for the analysis of dam-reservoir interaction including the reservoir boundary absorption are developed. Coupling with the equation of dam-un...Based on the scaled boundary finite-element method, the governing equations for the analysis of dam-reservoir interaction including the reservoir boundary absorption are developed. Coupling with the equation of dam-unbounded foundation interaction, it can effectively carry out the earthquake response analysis of dameservoir-foundation system. The proposed approach has the advantages that the effect of compressibility of reservoir water as well as the energy absorption of reservoir boundary on the earthquake response of arch dams and gravity dams can be efficiently evaluated and higher accuracy can be achieved. In comparison with the methods available in the literature, the computational cost can be reduced to a great extent. It facilitates the application of earthquake response analysis of dam-reservoir-foundation system including reservoir boundary absorption to the engineering practice.展开更多
将比例边界有限元法(Scaled Boundary Finite Element Method,SBFEM)和机器学习算法相结合,基于Lamb波在含缺陷薄板结构中传播时结构的动力响应变化定量反演结构中的缺陷信息。SBFEM通过改变裂纹所在子域的比例中心位置反映不同的裂纹信...将比例边界有限元法(Scaled Boundary Finite Element Method,SBFEM)和机器学习算法相结合,基于Lamb波在含缺陷薄板结构中传播时结构的动力响应变化定量反演结构中的缺陷信息。SBFEM通过改变裂纹所在子域的比例中心位置反映不同的裂纹信息,减少了需要进行重划分的网格数量,大大提升了计算效率,能够提供足够多的反映缺陷特性的训练数据;基于极限学习机的人工神经网络机器学习模型避免了传统反分析问题求解的目标函数极小化迭代过程,能在极快的学习速度下保证缺陷反演的精度。因此,提出的缺陷反演模型大大减少了运算时间成本。若干数值算例表明:建立的反演分析模型能够根据含缺陷的薄板结构Lamb波传播时观测点的动响应信号,准确地探测出薄板结构中的开口裂纹状缺陷的位置和大小等信息,并具有很高的反演效率,且在信号含有噪声的情况下仍具有较好的鲁棒性。展开更多
文摘The solution to heat transfer problems in two-dimensional heterogeneous media is attended based on the scaled boundary finite element method(SBFEM)coupled with equilibrated basis functions(EqBFs).The SBFEM reduces the model order by scaling the boundary solution onto the inner element.To this end,tri-lateral elements are emanated from a scaling center,followed by the development of a semi-analytical solution along the radial direction and a finite element solution along the circumferential/boundary direction.The discretization is thus limited to the boundaries of the model,and the semi-analytical radial solution is found through the solution of an eigenvalue problem,which restricts the methods’applicability to heterogeneous media.In this research,we first extracted the SBFEM formulation considering the heterogeneity of the media.Then,we replaced the semi-analytical radial solution with the EqBFs and removed the eigenvalue solution step from the SBFEM.The varying coefficients of the partial differential equation(PDE)resulting from the heterogeneity of the media are replaced by a finite series in the radial and circumferential directions of the element.A weighted residual approach is applied to the radial equation.The equilibrated radial solution series is used in the new formulation of the SBFEM.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51121005 and 51138001)the China-Germany Joint Research Project (Grant No. GZ566)
文摘This study examines the hydrodynamic performance of short-crested wave interaction with a new porous cylindrical structure by using the scaled boundary finite element method （SBFEM）, which is a semi-analytical technique combining the advantages of the finite element method and the boundary element method and with its own special features as well. The cylindrical structure consists of dual arc-shaped porous outer cylinders circumscribing an impermeable inner cylinder. A central feature of the newly extended method is that two virtual outer cylinders extending the arc-shaped porous outer cylinders with the same centre are introduced and variable porous-effect parameters are also introduced for the two virtual cylinders, so that the final SBFEM quation still can be handled in a closed-form analytical manner in the radial direction and by a finite element approximation in the circumferential direction. The entire computational domain is divided into two bounded and one unbounded domains, and a variational principle formulation is used to derive the SBFEM equation in each sub-domain. The velocity potential in bounded and unbounded domains is formulated using sets of Bessel and Hankel functions respectively, and the unknown coefficients are determined from the matching conditions. The results of numerical verification show that the approach discretises only the outermost virtual cylinder with surface finite-elements and fewer elements are required to obtain very accurate results.Influences of the incident wave parameters and structural configurations on the hydrodynamics are examined.
基金This research investigation was supported by the National Natural Science Foundation of China(Grant No.51678248 and Grant No.51878296)the Fundamental Research Funds for the Central Universities.And sincere thanks also to State Key Lab of Subtropical Building Science,South China University of Technology under Grant No.2017KB15 and the Open Research Fund of State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin under Grant No.IWHRSKL-KF201818.
文摘Based on the modified scale boundary finite element method and continued fraction solution,a high-order doubly asymptotic transmitting boundary(DATB)is derived and extended to the simulation of vector wave propagation in complex layered soils.The high-order DATB converges rapidly to the exact solution throughout the entire frequency range and its formulation is local in the time domain,possessing high accuracy and good efficiency.Combining with finite element method,a coupled model is constructed for time-domain analysis of underground station-layered soil interaction.The coupled model is divided into the near and far field by the truncated boundary,of which the near field is modelled by FEM while the far field is modelled by the high-order DATB.The coupled model is implemented in an open source finite element software,OpenSees,in which the DATB is employed as a super element.Numerical examples demonstrate that results of the coupled model are stable,accurate and efficient compared with those of the extended mesh model and the viscous-spring boundary model.Besides,it has also shown the fitness for long-time seismic response analysis of underground station-layered soil interaction.Therefore,it is believed that the coupled model could provide a new approach for seismic analysis of underground station-layered soil interaction and could be further developed for engineering.
基金Supported by the Key Program of National Natural Science Foundation of China(No.51138001)the Science Fund for Creative Research Groups of National Natural Science Foundation of China(No.51121005)+2 种基金the Fundamental Research Funds for the Central Universities(DUT13LK16)the Young Scientists Fund of National Natural Science Foundation of China(No.51109134)China Postdoctoral Science Foundation(No.2011M500814)
文摘The prediction of dynamic crack propagation in brittle materials is still an important issue in many engineering fields. The remeshing technique based on scaled boundary finite element method(SBFEM) is extended to predict the dynamic crack propagation in brittle materials. The structure is firstly divided into a number of superelements, only the boundaries of which need to be discretized with line elements. In the SBFEM formulation, the stiffness and mass matrices of the super-elements can be coupled seamlessly with standard finite elements, thus the advantages of versatility and flexibility of the FEM are well maintained. The transient response of the structure can be calculated directly in the time domain using a standard time-integration scheme. Then the dynamic stress intensity factor(DSIF) during crack propagation can be solved analytically due to the semi-analytical nature of SBFEM. Only the fine mesh discretization for the crack-tip super-element is needed to ensure the required accuracy for the determination of stress intensity factor(SIF). According to the predicted crack-tip position, a simple remeshing algorithm with the minimum mesh changes is suggested to simulate the dynamic crack propagation. Numerical examples indicate that the proposed method can be effectively used to deal with the dynamic crack propagation in a finite sized rectangular plate including a central crack. Comparison is made with the results available in the literature, which shows good agreement between each other.
基金This research was supported by Grants Nos.51409038,51421064,51138001 and 51308307 from the National Natural Science Foundation of ChinaGrant No.GZ1406 from the Open Foundation of State Key Laboratory of Structural Analysis for Industrial Equipment,Grant No.DUT15RC(4)23 from the fundamental research funds for the central universities,and Grant No.YL1610 from the Youth Foundation of State Key Laboratory of Coastal and Offshore Engineering for which the authors are grateful.
文摘The static response of two-dimensional horizontal layered piezoelectric bounded domain with side face load was investigated.In this paper,the modified scaled boundary finite element method(SBFEM)is provided as an effective semi analytical methodology.The method is used to solve the static problem for the layered piezoelectric bounded domain.The scaling line definition extends the SBFEM to be more suitable for analyzing the multilayered piezoelectric bounded domain.It avoids the limitations of original SBFEM in modeling the horizontal layered bounded domain.The modified SBFEM governing equation with piezoelectric medium is derived by introducing Duality variable in the Hamilton system.This derivation technology makes the progress be concise.The novel displacement and electric governing equations of the modified SBFEM is given together by the first time.The node forces can be expressed as power exponent function with radial coordinate by introducing the auxiliary variable and using the eigenvalue decomposition.The novel modified SBFEM solution of layered bounded domain with piezoelectric medium is solved.The new power expansion function of layered piezoelectric medium with side face load is proposed.This technology significantly extends the application range of modified SBFEM.The novel treatment of side face load for the layered piezoelectric bounded domain is proposed.Numerical studies are conducted to demonstrate the accuracy of proposed technique in handling with the static problem of layered bounded domain with piezoelectric medium for side face load.The influence of the side face load type and depth are discussed in detail.
文摘将W o lf和Song提出的比例边界有限元法(sca led boundary fin ite e lem en t m ethod,简称SBFEM)应用于坝-库水相互作用分析.在库水不可压缩假定的前提下推导了坝面动水压力与附加质量矩阵的基本方程.二维重力坝和三维拱坝坝面动水压力的算例表明,与有限元法比较,SBFEM计算精度明显提高,同时由于具有降维的特点,计算工作量也在很大程度上有所节约.还分析了库底和水面坡度变化以及水库边界形状适当变化对动水压力分布和数值大小的影响.结果表明,一般情况下水库边界的变化对动水压力的分布形状基本上不发生影响,对动水压力数值大小也影响不大.
基金National Natural Science Foundation of China (Grant No. 90510018)
文摘Based on the scaled boundary finite-element method, the governing equations for the analysis of dam-reservoir interaction including the reservoir boundary absorption are developed. Coupling with the equation of dam-unbounded foundation interaction, it can effectively carry out the earthquake response analysis of dameservoir-foundation system. The proposed approach has the advantages that the effect of compressibility of reservoir water as well as the energy absorption of reservoir boundary on the earthquake response of arch dams and gravity dams can be efficiently evaluated and higher accuracy can be achieved. In comparison with the methods available in the literature, the computational cost can be reduced to a great extent. It facilitates the application of earthquake response analysis of dam-reservoir-foundation system including reservoir boundary absorption to the engineering practice.
文摘将比例边界有限元法(Scaled Boundary Finite Element Method,SBFEM)和机器学习算法相结合,基于Lamb波在含缺陷薄板结构中传播时结构的动力响应变化定量反演结构中的缺陷信息。SBFEM通过改变裂纹所在子域的比例中心位置反映不同的裂纹信息,减少了需要进行重划分的网格数量,大大提升了计算效率,能够提供足够多的反映缺陷特性的训练数据;基于极限学习机的人工神经网络机器学习模型避免了传统反分析问题求解的目标函数极小化迭代过程,能在极快的学习速度下保证缺陷反演的精度。因此,提出的缺陷反演模型大大减少了运算时间成本。若干数值算例表明:建立的反演分析模型能够根据含缺陷的薄板结构Lamb波传播时观测点的动响应信号,准确地探测出薄板结构中的开口裂纹状缺陷的位置和大小等信息,并具有很高的反演效率,且在信号含有噪声的情况下仍具有较好的鲁棒性。
