The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is m...The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is mainly used for finite element analysis at present,and the effectiveness of the surrogate material model has been fully confirmed.However,there are some accuracy problems when dealing with boundary elements using the surrogate material model,which will affect the topology optimization results.In this study,a boundary element reconstruction(BER)model is proposed based on the surrogate material model under the MMC topology optimization framework to improve the accuracy of topology optimization.The proposed BER model can reconstruct the boundary elements by refining the local meshes and obtaining new nodes in boundary elements.Then the density of boundary elements is recalculated using the new node information,which is more accurate than the original model.Based on the new density of boundary elements,the material properties and volume information of the boundary elements are updated.Compared with other finite element analysis methods,the BER model is simple and feasible and can improve computational accuracy.Finally,the effectiveness and superiority of the proposed method are verified by comparing it with the optimization results of the original surrogate material model through several numerical examples.展开更多
To address the issue that traditional finite element methods cannot fully consider the semi-infinite earth strata and have lower solution accuracy,a new equivalent force model for induced deformation during oil and ga...To address the issue that traditional finite element methods cannot fully consider the semi-infinite earth strata and have lower solution accuracy,a new equivalent force model for induced deformation during oil and gas reservoir development is derived from the perspective of semi-infinite strata.A brand-new volume boundary element numerical method solution has been developed and verified and tested.The influences of internal flow and flow boundary of the reservoir on strata deformation are equivalent to the impacts on strata deformation when external forces act at the interior and boundary of the reservoir,respectively.Calculation methods for the flow equivalent force and boundary equivalent force are provided.The deformation solution at any point in the strata can be obtained through the convolution of flow equivalent forces,boundary equivalent forces and Green’s functions.After discretization,the deformation solution at any point in the strata can be obtained by multiplying the grid boundary equivalent forces,grid flow equivalent forces with their corresponding grid boundary sources and grid volume sources respectively,and then summing them up.This numerical method is termed the Volumetric Boundary Element Method(VBEM).Compared with traditional commercial simulators,VBEM fully considers the effects of reservoir flow boundaries,pore pressure gradient fields within the reservoir,and fluid mass changes within pores on formation deformation.It eliminates the need for meshing outside the reservoir,achieves significantly improved solution accuracy,and provides a new technical framework for simulating deformation induced by reservoir development.展开更多
Hydraulic fracturing plays a critical role in enhancing shale gas production in deep shale reservoirs.Conventional hydraulic fracturing simulation methods rely on prefabricated grids,which can be hindered by the chall...Hydraulic fracturing plays a critical role in enhancing shale gas production in deep shale reservoirs.Conventional hydraulic fracturing simulation methods rely on prefabricated grids,which can be hindered by the challenge of being computationally overpowered.This study proposes an efficient fracturing simulator to analyze fracture morphology during hydraulic fracturing processes in deep shale gas reservoirs.The simulator integrates the boundary element displacement discontinuity method and the finite volume method to model the fluid-solid coupling process by employing a pseudo-3D fracture model to calculate the fracture height.In particular,the Broyden iteration method was introduced to improve the computational efficiency and model robustness;it achieved a 46.6%reduction in computation time compared to the Newton-Raphson method.The influences of horizontal stress differences,natural fracture density,and natural fracture angle on the modified zone of the reservoir were simulated,and the following results were observed.(1)High stress difference reservoirs have smaller stimulated reservoir area than low stress difference reservoirs.(2)A higher natural fracture angle resulted in larger modification zones at low stress differences,while the effect of a natural fracture angle at high stress differences was not significant.(3)High-density and long natural fracture zones played a significant role in enhancing the stimulated reservoir area.These findings are critical for comprehending the impact of geological parameters on deep shale reservoirs.展开更多
This study explores a sensitivity analysis method based on the boundary element method(BEM)to address the computational complexity in acoustic analysis with ground reflection problems.The advantages of BEM in acoustic...This study explores a sensitivity analysis method based on the boundary element method(BEM)to address the computational complexity in acoustic analysis with ground reflection problems.The advantages of BEM in acoustic simulations and its high computational cost in broadband problems are examined.To improve efficiency,a Taylor series expansion is applied to decouple frequency-dependent terms in BEM.Additionally,the SecondOrder Arnoldi(SOAR)model order reduction method is integrated to reduce computational costs and enhance numerical stability.Furthermore,an isogeometric sensitivity boundary integral equation is formulated using the direct differentiation method,incorporating Cauchy principal value integrals and Hadamard finite part integrals to handle singularities.The proposed method improves the computational efficiency,and the acoustic sensitivity analysis provides theoretical support for further acoustic structure optimization.展开更多
The analysis of the dynamics of surface girders is of great importance in the design of engineering structures such as steel welded bridge plane girders or concrete plate-column structures.This work is an extension of...The analysis of the dynamics of surface girders is of great importance in the design of engineering structures such as steel welded bridge plane girders or concrete plate-column structures.This work is an extension of the classical deterministic problem of free vibrations of thin(Kirchhoff)plates.Themain aim of this work is the study of stochastic eigenvibrations of thin(Kirchhoff)elastic plates resting on internal continuous and column supports by the Boundary Element Method(BEM).This work is a continuation of previous research related to the random approach in plate analysis using the BEM.The static fundamental solution(Green’s function)is applied,coupled with a nonsingular formulation of the boundary and domain integral equations.These are derived using a modified and simplified formulation of the boundary conditions,inwhich there is no need to introduce theKirchhoff forces on a plate boundary.The role of the Kirchhoff corner forces is played by the boundary elements placed close to a single corner.Internal column or linear continuous supports are introduced using the Bezine technique,where the additional collocation points are introduced inside a plate domain.This allows for significant simplification of the BEM computational algorithm.An application of the polynomial approximations in the Least Squares Method(LSM)recovery of the structural response is done.The probabilistic analysis will employ three independent computational approaches:semi-analytical method(SAM),stochastic perturbation technique(SPT),and Monte-Carlo simulations.Numerical investigations include the fundamental eigenfrequencies of an elastic,thin,homogeneous,and isotropic plate.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
The finite element artificial transmitting boundary method is employed here to treat the near field scattering of a cylindrical wave from an irregular cylinder. A comparison is made between this method and the analy...The finite element artificial transmitting boundary method is employed here to treat the near field scattering of a cylindrical wave from an irregular cylinder. A comparison is made between this method and the analytical one. And then examples are given to demonstrate the solution of several problems of the irregular object scattering. The method can not only produce clear physical pictures, but can efficiently handle many complicated scattering problems.展开更多
In this paper, an identification method to estimate the unbalances is introduced, which is based on the boundary element method (BEM). By using the vibration response measured at some points on the flexible rotor the ...In this paper, an identification method to estimate the unbalances is introduced, which is based on the boundary element method (BEM). By using the vibration response measured at some points on the flexible rotor the unbalances can be identified conveniently. Therefore, the rotor can be balanced without test runs.展开更多
The stochastic boundary element method(SBEM)is developed in this paper for 3D problems with body forces and reliability analysis of engineering structures.The integral equations of SBEM are established by the approach...The stochastic boundary element method(SBEM)is developed in this paper for 3D problems with body forces and reliability analysis of engineering structures.The integral equations of SBEM are established by the approach of partial derivation with respect to stochastic variables,considering the yield limit,rotation speeds and material density to be the fundamental stochastic variables.Through analyzing a numerical example and a turbo-disk of an aeroengine,the results show that the method developed is successful.展开更多
The matrix expression for the 3 D transient dynamic boundary integral equation in Laplace transform space is obtained and the degenerative element method has been implemented to treat the kernel function over the sin...The matrix expression for the 3 D transient dynamic boundary integral equation in Laplace transform space is obtained and the degenerative element method has been implemented to treat the kernel function over the singular element. In the computer program BEMTDY the Koizumi′s numerical inversion method is used and three examples of the 3 D vibrated foundation under harmonic forces and the influence with both adjacent foundations are studied.展开更多
In this work, the Direct Numerical Simulation(DNS) and Oil-Film Interferometry(OFI)technique are used to investigate the hypersonic boundary layer transition induced by single and double roughness elements at Mach num...In this work, the Direct Numerical Simulation(DNS) and Oil-Film Interferometry(OFI)technique are used to investigate the hypersonic boundary layer transition induced by single and double roughness elements at Mach number 5. For single roughness, the DNS results showed that both horseshoe vortices and hairpin vortices caused by shear layer instability can affect the boundary layer instability. The generation of the near-wall unstable structure is the key point of boundary layer transition behind the roughness element. At the downstream of the roughness element, the interaction between horseshoe vortices and hairpin vortices will spread in the spanwise direction.For double roughness elements, the effect of the spacing between roughness elements on the transition is studied. It is found that the case of higher spacing between roughness elements is more effective for inducing transition than the lower one. The interaction between two adjacent roughness elements can suppress the evolution of horseshoe vortices in the downstream and trigger the instability of shear layer. Thus, the transition will be suppressed accordingly.展开更多
The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （B...The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （BEFM）, combining the boundary integral equation （BIE） method with the IMLS method, the improved boundary element-free method （IBEFM） for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker ~ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker 5 function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.展开更多
This study examines the design provisions of the Chinese GB 50011-2010 code for seismic design of buildings for the special boundary elements of T-shaped reinforced concrete walls and proposes an improved design metho...This study examines the design provisions of the Chinese GB 50011-2010 code for seismic design of buildings for the special boundary elements of T-shaped reinforced concrete walls and proposes an improved design method. Comparison of the design provisions of the GB 50011-2010 code and those of the American code ACI 318-14 indicates a possible deficiency in the T-shaped wall design provisions in GB 50011-2010. A case study of a typical T-shaped wall designed in accordance with GB 50011-2010 also indicates the insufficient extent of the boundary element at the non-flange end and overly conservative design of the flange end boundary element. Improved designs for special boundary elements ofT-shaped walls are developed using a displacement-based method. The proposed design formulas produce a longer boundary element at the non-flange end and a shorter boundary element at the flange end, relative to those of the GB 50011-2010 provisions. Extensive numerical analysis indicates that T-shaped walls designed using the proposed formulas develop inelastic drift of 0.01 for both cases of the flange in compression and in tension.展开更多
This paper presents a step-by-step procedure using the three-dimensional boundary element approach to study the behavior of semi-circular canyons under seismic shear waves. The boundary element code TDASC allows utili...This paper presents a step-by-step procedure using the three-dimensional boundary element approach to study the behavior of semi-circular canyons under seismic shear waves. The boundary element code TDASC allows utilization for various canyon geometries, evaluation of concurrent seismic waves and calculation of the ground motions on canyons due to an excitation at any arbitrary point of the incident field. Considering the widening ratio of the canyon(including prismatic, semi-prismatic and non-prismatic canyons), wave characteristics(wavelength, dimensionless period, direction) and maximum amplification pattern, the solution was applied to carry out a series of parametric studies. It was shown that canyon form can significantly affect the displacement amplification, especially at the points located on its edges. By increasing the wave dimensionless frequency(η > 1), the amplification pattern becomes more complex. On the basis of the results from a variety of considered cases, a new expression has been presented for the limiting wavelength beyond which the widening of the canyon will not have a major effect on the displacement amplification. To verify the reliability of the proposed approach, the obtained results, expressed in terms of displacement amplitude, were compared with those from the available published literature and a reasonably good agreement was observed.展开更多
This paper develops the boundary element method, the authors employ two-layered earth Green 's functions as the weighting functions of residual and derive boundary integral equations. The forward problems of point...This paper develops the boundary element method, the authors employ two-layered earth Green 's functions as the weighting functions of residual and derive boundary integral equations. The forward problems of point sources on 2 - D and 3-D structures with an influencing cover are solved by this method. The results show that this method markedly improves the original boundary element method. The features of the improved method are greater numerical accuracy and much smaller systems of equations and thus considerable savings for the storage capacity of computers, allowing us to solve the above problems with only ordinary microcomputers. The results in this paper extend the scope of applying the boundary element method while using electrical methods for geophysical prospecting.展开更多
A growing body of evidence shows that volcanism near the Permian-Triassic boundary（PTB） may be crucial in triggering the Permian–Triassic（P–Tr） mass extinction. Thus, the ash beds near the PTB in South China may...A growing body of evidence shows that volcanism near the Permian-Triassic boundary（PTB） may be crucial in triggering the Permian–Triassic（P–Tr） mass extinction. Thus, the ash beds near the PTB in South China may carry information on this event. Three volcanic ash layers, altered to clay, outcropped in the PTB beds in Zunyi Section, Guizhou Province, Southwest China. The U-Pb ages, trace elements, and Hf-isotope compositions of zircon grains from these three ash beds were analyzed using LA-ICPMS and LA-MC-ICPMS. The zircons are mainly magmatic in origin（241-279 Ma） except for two inherited/xenocrystic zircons（939 and 2 325 Ma）. The ages of these magmatic zircons indicate three episodes of magmatism which occurred around the MiddleLate Permian boundary（-261.5 Ma, MLPB）, the Wuchiapingian-Changhsingian boundary（-254.5 Ma, WCB）, and the PTB（-250.5 Ma）, respectively. The first two episodes of magmatism near the MLPB and WCB may be attributed to magmatic inheritance or re-deposition. All magmatic zircons share similar trace-element and Hf-isotope compositions. They have Y, Hf, Th and U contents and Nb/Ta ratios are typical of zircons from silicic calc-alkaline magmas. These zircons also exhibit enriched Hf-isotope compositions with _（εHf）（t） values of-11.4 to ＋0.2, which suggests that the three magmatic episodes involved melting of the continental crust. The more enriched Hf-isotope composition （_（εHf）（t）=-11.4--4.8） of Bed ZY13（-250.5 Ma） implies more input of ancient crustal material in the magma. Integration of the Hf-isotope and trace-element compositions of magmatic zircons suggest that these three episodes of magmatism may take place along the convergent continent margin in or near southwestern South China as a result of the closure of the Palaeo-Tethys Ocean.展开更多
For higher accuracy in simulating the transformation of three dimensional waves, in consideration of the advantages of constant panels and linear elements, a combined boundary elements is applied in this research. The...For higher accuracy in simulating the transformation of three dimensional waves, in consideration of the advantages of constant panels and linear elements, a combined boundary elements is applied in this research. The method can be used to remove the transverse vibration due to the accumulation of computational errors. A combined boundary condition of sponge layer and Sommerfeld radiation condition is used to remove the reflected waves from the computing domain. By following the water particle on the water surface, the third order Stokes wave transform is simulated by the numerical wave flume technique. The computed results are in good agreement with theoretical ones.展开更多
We presented a boundary element method using the approximate analytical Green＇s function given by Sanchez-Sesma et al. Coordinate transform is introduced to extend the method to deal with the model with constant-grad...We presented a boundary element method using the approximate analytical Green＇s function given by Sanchez-Sesma et al. Coordinate transform is introduced to extend the method to deal with the model with constant-gradient velocity along oblique direction. The method is validated by comparing the numerical results with other independent methods. This method provides a useful tool for analyzing local site effects. We computed seismic response for two series of models. The results in both frequency and time domains are analyzed and show complex amplification patterns. The fundamental mode of resonance is dependent not only on the velocity at the free surface but also on the velocity distribution of the whole basin. For the higher modes of vibration the heterogeneous basin also has its own characteristic.展开更多
Dempster-Shafer evidence theory, also called the theory of belief function, is widely used for uncertainty modeling and reasoning. However, when the size and number of focal elements are large, the evidence combinatio...Dempster-Shafer evidence theory, also called the theory of belief function, is widely used for uncertainty modeling and reasoning. However, when the size and number of focal elements are large, the evidence combination will bring a high computational complexity. To address this issue,various methods have been proposed including the implementation of more efficient combination rules and the simplifications or approximations of Basic Belief Assignments(BBAs). In this paper,a novel principle for approximating a BBA into a simpler one is proposed, which is based on the degree of non-redundancy for focal elements. More non-redundant focal elements are kept in the approximation while more redundant focal elements in the original BBA are removed first. Three types of degree of non-redundancy are defined based on three different definitions of focal element distance, respectively. Two different implementations of this principle for BBA approximations are proposed including a batch and an iterative type. Examples, experiments, comparisons and related analyses are provided to validate proposed approximation approaches.展开更多
基金supported by the Science and Technology Research Project of Henan Province(242102241055)the Industry-University-Research Collaborative Innovation Base on Automobile Lightweight of“Science and Technology Innovation in Central Plains”(2024KCZY315)the Opening Fund of State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment(GZ2024A03-ZZU).
文摘The moving morphable component(MMC)topology optimization method,as a typical explicit topology optimization method,has been widely concerned.In the MMC topology optimization framework,the surrogate material model is mainly used for finite element analysis at present,and the effectiveness of the surrogate material model has been fully confirmed.However,there are some accuracy problems when dealing with boundary elements using the surrogate material model,which will affect the topology optimization results.In this study,a boundary element reconstruction(BER)model is proposed based on the surrogate material model under the MMC topology optimization framework to improve the accuracy of topology optimization.The proposed BER model can reconstruct the boundary elements by refining the local meshes and obtaining new nodes in boundary elements.Then the density of boundary elements is recalculated using the new node information,which is more accurate than the original model.Based on the new density of boundary elements,the material properties and volume information of the boundary elements are updated.Compared with other finite element analysis methods,the BER model is simple and feasible and can improve computational accuracy.Finally,the effectiveness and superiority of the proposed method are verified by comparing it with the optimization results of the original surrogate material model through several numerical examples.
基金Supported by the China National Natural Science Foundation Project(52274048)Beijing Natural Science Foundation Project(3222037)。
文摘To address the issue that traditional finite element methods cannot fully consider the semi-infinite earth strata and have lower solution accuracy,a new equivalent force model for induced deformation during oil and gas reservoir development is derived from the perspective of semi-infinite strata.A brand-new volume boundary element numerical method solution has been developed and verified and tested.The influences of internal flow and flow boundary of the reservoir on strata deformation are equivalent to the impacts on strata deformation when external forces act at the interior and boundary of the reservoir,respectively.Calculation methods for the flow equivalent force and boundary equivalent force are provided.The deformation solution at any point in the strata can be obtained through the convolution of flow equivalent forces,boundary equivalent forces and Green’s functions.After discretization,the deformation solution at any point in the strata can be obtained by multiplying the grid boundary equivalent forces,grid flow equivalent forces with their corresponding grid boundary sources and grid volume sources respectively,and then summing them up.This numerical method is termed the Volumetric Boundary Element Method(VBEM).Compared with traditional commercial simulators,VBEM fully considers the effects of reservoir flow boundaries,pore pressure gradient fields within the reservoir,and fluid mass changes within pores on formation deformation.It eliminates the need for meshing outside the reservoir,achieves significantly improved solution accuracy,and provides a new technical framework for simulating deformation induced by reservoir development.
文摘Hydraulic fracturing plays a critical role in enhancing shale gas production in deep shale reservoirs.Conventional hydraulic fracturing simulation methods rely on prefabricated grids,which can be hindered by the challenge of being computationally overpowered.This study proposes an efficient fracturing simulator to analyze fracture morphology during hydraulic fracturing processes in deep shale gas reservoirs.The simulator integrates the boundary element displacement discontinuity method and the finite volume method to model the fluid-solid coupling process by employing a pseudo-3D fracture model to calculate the fracture height.In particular,the Broyden iteration method was introduced to improve the computational efficiency and model robustness;it achieved a 46.6%reduction in computation time compared to the Newton-Raphson method.The influences of horizontal stress differences,natural fracture density,and natural fracture angle on the modified zone of the reservoir were simulated,and the following results were observed.(1)High stress difference reservoirs have smaller stimulated reservoir area than low stress difference reservoirs.(2)A higher natural fracture angle resulted in larger modification zones at low stress differences,while the effect of a natural fracture angle at high stress differences was not significant.(3)High-density and long natural fracture zones played a significant role in enhancing the stimulated reservoir area.These findings are critical for comprehending the impact of geological parameters on deep shale reservoirs.
基金supported by the Shanxi Scholarship Council of China(Grant No.2023-036)the Natural Science Foundation of Shanxi Province(Grant No.202303021222020).
文摘This study explores a sensitivity analysis method based on the boundary element method(BEM)to address the computational complexity in acoustic analysis with ground reflection problems.The advantages of BEM in acoustic simulations and its high computational cost in broadband problems are examined.To improve efficiency,a Taylor series expansion is applied to decouple frequency-dependent terms in BEM.Additionally,the SecondOrder Arnoldi(SOAR)model order reduction method is integrated to reduce computational costs and enhance numerical stability.Furthermore,an isogeometric sensitivity boundary integral equation is formulated using the direct differentiation method,incorporating Cauchy principal value integrals and Hadamard finite part integrals to handle singularities.The proposed method improves the computational efficiency,and the acoustic sensitivity analysis provides theoretical support for further acoustic structure optimization.
基金funded by research grant OPUS no.2021/41/B/ST8/02432 entitled Probabilistic entropy in engineering computations sponsored by The National Science Center in Polandthe Institute of Structural Analysis of Poznan University of Technology in the framework of the internal research grant 0411/SBAD/0010.
文摘The analysis of the dynamics of surface girders is of great importance in the design of engineering structures such as steel welded bridge plane girders or concrete plate-column structures.This work is an extension of the classical deterministic problem of free vibrations of thin(Kirchhoff)plates.Themain aim of this work is the study of stochastic eigenvibrations of thin(Kirchhoff)elastic plates resting on internal continuous and column supports by the Boundary Element Method(BEM).This work is a continuation of previous research related to the random approach in plate analysis using the BEM.The static fundamental solution(Green’s function)is applied,coupled with a nonsingular formulation of the boundary and domain integral equations.These are derived using a modified and simplified formulation of the boundary conditions,inwhich there is no need to introduce theKirchhoff forces on a plate boundary.The role of the Kirchhoff corner forces is played by the boundary elements placed close to a single corner.Internal column or linear continuous supports are introduced using the Bezine technique,where the additional collocation points are introduced inside a plate domain.This allows for significant simplification of the BEM computational algorithm.An application of the polynomial approximations in the Least Squares Method(LSM)recovery of the structural response is done.The probabilistic analysis will employ three independent computational approaches:semi-analytical method(SAM),stochastic perturbation technique(SPT),and Monte-Carlo simulations.Numerical investigations include the fundamental eigenfrequencies of an elastic,thin,homogeneous,and isotropic plate.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
文摘The finite element artificial transmitting boundary method is employed here to treat the near field scattering of a cylindrical wave from an irregular cylinder. A comparison is made between this method and the analytical one. And then examples are given to demonstrate the solution of several problems of the irregular object scattering. The method can not only produce clear physical pictures, but can efficiently handle many complicated scattering problems.
文摘In this paper, an identification method to estimate the unbalances is introduced, which is based on the boundary element method (BEM). By using the vibration response measured at some points on the flexible rotor the unbalances can be identified conveniently. Therefore, the rotor can be balanced without test runs.
文摘The stochastic boundary element method(SBEM)is developed in this paper for 3D problems with body forces and reliability analysis of engineering structures.The integral equations of SBEM are established by the approach of partial derivation with respect to stochastic variables,considering the yield limit,rotation speeds and material density to be the fundamental stochastic variables.Through analyzing a numerical example and a turbo-disk of an aeroengine,the results show that the method developed is successful.
文摘The matrix expression for the 3 D transient dynamic boundary integral equation in Laplace transform space is obtained and the degenerative element method has been implemented to treat the kernel function over the singular element. In the computer program BEMTDY the Koizumi′s numerical inversion method is used and three examples of the 3 D vibrated foundation under harmonic forces and the influence with both adjacent foundations are studied.
基金the China Scholarship Council(CSC)the Aeronautics Science Foundation of China(No.20163252037)+2 种基金the China Postdoctoral Science Foundation(No.2017M610325)the Natural Science Foundation of Jiangsu Province of China(No.BK20170771)the Fundamental Research Funds for the Central Universities of China(No.NP2017202)for their support
文摘In this work, the Direct Numerical Simulation(DNS) and Oil-Film Interferometry(OFI)technique are used to investigate the hypersonic boundary layer transition induced by single and double roughness elements at Mach number 5. For single roughness, the DNS results showed that both horseshoe vortices and hairpin vortices caused by shear layer instability can affect the boundary layer instability. The generation of the near-wall unstable structure is the key point of boundary layer transition behind the roughness element. At the downstream of the roughness element, the interaction between horseshoe vortices and hairpin vortices will spread in the spanwise direction.For double roughness elements, the effect of the spacing between roughness elements on the transition is studied. It is found that the case of higher spacing between roughness elements is more effective for inducing transition than the lower one. The interaction between two adjacent roughness elements can suppress the evolution of horseshoe vortices in the downstream and trigger the instability of shear layer. Thus, the transition will be suppressed accordingly.
基金Project supported by the National Natural Science Foundation of China (Grant No 10871124)Innovation Program of Shanghai Municipal Education Commission (Grant No 09ZZ99)Shanghai Leading Academic Discipline Project (Grant No J50103)
文摘The interpolating moving least-squares （IMLS） method is discussed first in this paper. And the formulae of the IMLS method obtained by Lancaster are revised. Then on the basis of the boundary element-free method （BEFM）, combining the boundary integral equation （BIE） method with the IMLS method, the improved boundary element-free method （IBEFM） for two-dimensional potential problems is presented, and the corresponding formulae of the IBEFM are obtained. In the BEFM, boundary conditions are applied directly, but the shape function in the MLS does not satisfy the property of the Kronecker ~ function. This is a problem of the BEFM, and must be solved theoretically. In the IMLS method, when the shape function satisfies the property of the Kronecker 5 function, then the boundary conditions, in the meshless method based on the IMLS method, can be applied directly. Then the IBEFM, based on the IMLS method, is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be applied directly and easily, thus it gives a greater computational precision. Some numerical examples are presented to demonstrate the method.
基金International Science&Technology Cooperation Program of China under Grant No.2014DFA70950Tsinghua University Initiative Scientific Research Program under Grant No.2012THZ02-1National Natural Science Foundation of China under Grant No.91315301
文摘This study examines the design provisions of the Chinese GB 50011-2010 code for seismic design of buildings for the special boundary elements of T-shaped reinforced concrete walls and proposes an improved design method. Comparison of the design provisions of the GB 50011-2010 code and those of the American code ACI 318-14 indicates a possible deficiency in the T-shaped wall design provisions in GB 50011-2010. A case study of a typical T-shaped wall designed in accordance with GB 50011-2010 also indicates the insufficient extent of the boundary element at the non-flange end and overly conservative design of the flange end boundary element. Improved designs for special boundary elements ofT-shaped walls are developed using a displacement-based method. The proposed design formulas produce a longer boundary element at the non-flange end and a shorter boundary element at the flange end, relative to those of the GB 50011-2010 provisions. Extensive numerical analysis indicates that T-shaped walls designed using the proposed formulas develop inelastic drift of 0.01 for both cases of the flange in compression and in tension.
文摘This paper presents a step-by-step procedure using the three-dimensional boundary element approach to study the behavior of semi-circular canyons under seismic shear waves. The boundary element code TDASC allows utilization for various canyon geometries, evaluation of concurrent seismic waves and calculation of the ground motions on canyons due to an excitation at any arbitrary point of the incident field. Considering the widening ratio of the canyon(including prismatic, semi-prismatic and non-prismatic canyons), wave characteristics(wavelength, dimensionless period, direction) and maximum amplification pattern, the solution was applied to carry out a series of parametric studies. It was shown that canyon form can significantly affect the displacement amplification, especially at the points located on its edges. By increasing the wave dimensionless frequency(η > 1), the amplification pattern becomes more complex. On the basis of the results from a variety of considered cases, a new expression has been presented for the limiting wavelength beyond which the widening of the canyon will not have a major effect on the displacement amplification. To verify the reliability of the proposed approach, the obtained results, expressed in terms of displacement amplitude, were compared with those from the available published literature and a reasonably good agreement was observed.
文摘This paper develops the boundary element method, the authors employ two-layered earth Green 's functions as the weighting functions of residual and derive boundary integral equations. The forward problems of point sources on 2 - D and 3-D structures with an influencing cover are solved by this method. The results show that this method markedly improves the original boundary element method. The features of the improved method are greater numerical accuracy and much smaller systems of equations and thus considerable savings for the storage capacity of computers, allowing us to solve the above problems with only ordinary microcomputers. The results in this paper extend the scope of applying the boundary element method while using electrical methods for geophysical prospecting.
基金supported by an aid grant from Chengdu Center, China Geological Survey (No. 12120113049100-1)the National Natural Science Foundations (Nos. 40572068, 40839903 and 41272044)+1 种基金the "111" Program (No. B08030)an aid grant (No. GBL11206) from the State Key Laboratory of Biogeology and Environmental Geology, China University of Geosciences (Wuhan), China
文摘A growing body of evidence shows that volcanism near the Permian-Triassic boundary（PTB） may be crucial in triggering the Permian–Triassic（P–Tr） mass extinction. Thus, the ash beds near the PTB in South China may carry information on this event. Three volcanic ash layers, altered to clay, outcropped in the PTB beds in Zunyi Section, Guizhou Province, Southwest China. The U-Pb ages, trace elements, and Hf-isotope compositions of zircon grains from these three ash beds were analyzed using LA-ICPMS and LA-MC-ICPMS. The zircons are mainly magmatic in origin（241-279 Ma） except for two inherited/xenocrystic zircons（939 and 2 325 Ma）. The ages of these magmatic zircons indicate three episodes of magmatism which occurred around the MiddleLate Permian boundary（-261.5 Ma, MLPB）, the Wuchiapingian-Changhsingian boundary（-254.5 Ma, WCB）, and the PTB（-250.5 Ma）, respectively. The first two episodes of magmatism near the MLPB and WCB may be attributed to magmatic inheritance or re-deposition. All magmatic zircons share similar trace-element and Hf-isotope compositions. They have Y, Hf, Th and U contents and Nb/Ta ratios are typical of zircons from silicic calc-alkaline magmas. These zircons also exhibit enriched Hf-isotope compositions with _（εHf）（t） values of-11.4 to ＋0.2, which suggests that the three magmatic episodes involved melting of the continental crust. The more enriched Hf-isotope composition （_（εHf）（t）=-11.4--4.8） of Bed ZY13（-250.5 Ma） implies more input of ancient crustal material in the magma. Integration of the Hf-isotope and trace-element compositions of magmatic zircons suggest that these three episodes of magmatism may take place along the convergent continent margin in or near southwestern South China as a result of the closure of the Palaeo-Tethys Ocean.
基金National Natural Science Foundation of China(No.49876026)
文摘For higher accuracy in simulating the transformation of three dimensional waves, in consideration of the advantages of constant panels and linear elements, a combined boundary elements is applied in this research. The method can be used to remove the transverse vibration due to the accumulation of computational errors. A combined boundary condition of sponge layer and Sommerfeld radiation condition is used to remove the reflected waves from the computing domain. By following the water particle on the water surface, the third order Stokes wave transform is simulated by the numerical wave flume technique. The computed results are in good agreement with theoretical ones.
基金supported by the National Science Foundation of China(Nos. D40444002 and D40521002)National Key Basic Research Program(No.2006CB705803)
文摘We presented a boundary element method using the approximate analytical Green＇s function given by Sanchez-Sesma et al. Coordinate transform is introduced to extend the method to deal with the model with constant-gradient velocity along oblique direction. The method is validated by comparing the numerical results with other independent methods. This method provides a useful tool for analyzing local site effects. We computed seismic response for two series of models. The results in both frequency and time domains are analyzed and show complex amplification patterns. The fundamental mode of resonance is dependent not only on the velocity at the free surface but also on the velocity distribution of the whole basin. For the higher modes of vibration the heterogeneous basin also has its own characteristic.
基金the National Natural Science Foundation of China (Nos. 61671370, 61573275)Postdoctoral Science Foundation of China (No. 2016M592790)+1 种基金Postdoctoral Science Research Foundation of Shaanxi Province, China (No. 2016BSHEDZZ46)Fundamental Research Funds for the Central Universities, China (No. xjj201066)
文摘Dempster-Shafer evidence theory, also called the theory of belief function, is widely used for uncertainty modeling and reasoning. However, when the size and number of focal elements are large, the evidence combination will bring a high computational complexity. To address this issue,various methods have been proposed including the implementation of more efficient combination rules and the simplifications or approximations of Basic Belief Assignments(BBAs). In this paper,a novel principle for approximating a BBA into a simpler one is proposed, which is based on the degree of non-redundancy for focal elements. More non-redundant focal elements are kept in the approximation while more redundant focal elements in the original BBA are removed first. Three types of degree of non-redundancy are defined based on three different definitions of focal element distance, respectively. Two different implementations of this principle for BBA approximations are proposed including a batch and an iterative type. Examples, experiments, comparisons and related analyses are provided to validate proposed approximation approaches.
