Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the random...Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the randomness of structural parameters,working condition and vibration environment are considered for fatigue life predication and reliability assessment.First,the lowcycle fatigue problem is modelled as stochastic static system with random parameters,while the high-cycle fatigue problem is considered as stochastic dynamic system under random excitations.Then,to deal with the two failure modes,the novel Direct Probability Integral Method(DPIM)is proposed,which is efficient and accurate for solving stochastic static and dynamic systems.The probability density functions of accumulated damage and fatigue life of turbine blade for low-cycle and high-cycle fatigue problems are achieved,respectively.Furthermore,the time–frequency hybrid method is advanced to enhance the computational efficiency for governing equation of system.Finally,the results of typical examples demonstrate high accuracy and efficiency of the proposed method by comparison with Monte Carlo simulation and other methods.It is indicated that the DPIM is a unified method for predication of random fatigue life for low-cycle and highcycle fatigue problems.The rotational speed,density,fatigue strength coefficient,and fatigue plasticity index have a high sensitivity to fatigue reliability of engine turbine blade.展开更多
In this work,a new methodology is presented to mainly solve the fluid–solid interaction(FSI)equation.This methodology combines the advantages of the Newmark precise integral method(NPIM)and the dual neural network(DN...In this work,a new methodology is presented to mainly solve the fluid–solid interaction(FSI)equation.This methodology combines the advantages of the Newmark precise integral method(NPIM)and the dual neural network(DNN)method.The NPIM is employed to modify the exponential matrix and loading vector based on the DNN integral method.This involves incorporating the basic assumption of the Newmark-βmethod into the dynamic equation and eliminating the acceleration term from the dynamic equilibrium equation.As a result,the equation is reduced to a first-order linear equation system.Subsequently,the PIM is applied to integrate the system step by step within the NPIM.The DNN method is adopted to solve the inhomogeneous term through fitting the integrand and the original function with a pair of neural networks,and the integral term is solved using the Newton–Leibniz formula.Numerical examples demonstrate that the proposed methodology significantly improves computing efficiency and provides sufficient precision compared to the DNN method.This is particularly evident when analyzing large-scale structures under blast loading conditions.展开更多
Due to the difficulties in obtaining large deformation mining subsidence using differential Interferometric Synthetic Aperture Radar （D-InSAR） alone, a new algorithm was proposed to extract large deformation mining ...Due to the difficulties in obtaining large deformation mining subsidence using differential Interferometric Synthetic Aperture Radar （D-InSAR） alone, a new algorithm was proposed to extract large deformation mining subsidence using D-InSAR technique and probability integral method. The details of the algorithm are as follows：the control points set, containing correct phase unwrapping points on the subsidence basin edge generated by D-InSAR and several observation points （near the maximum subsidence and inflection points）, was established at first; genetic algorithm （GA） was then used to optimize the parameters of probability integral method; at last, the surface subsidence was deduced according to the optimum parameters. The results of the experiment in Huaibei mining area, China, show that the presented method can generate the correct mining subsidence basin with a few surface observations, and the relative error of maximum subsidence point is about 8.3%, which is much better than that of conventional D-InSAR （relative error is 68.0%）.展开更多
On the basis of three geological models and several orebody boundaries, a method of grid subdivision and integral has been proposed to calculate and evaluate the resources of cobalt-rich crusts on the seamounts in the...On the basis of three geological models and several orebody boundaries, a method of grid subdivision and integral has been proposed to calculate and evaluate the resources of cobalt-rich crusts on the seamounts in the central Pacific Ocean. The formulas of this method are deduced and the interface of program module is designed. The method is carried out in the software ＂Auto mapping system of submarine topography and geomorphology MBChart＂. This method and program will possibly become a potential tool to calculate the resources of seamounts and determine the target diggings for China＇ s next Five-year Plan.展开更多
Considering the variable cross section thickness of longitudinal profiled plate and the dynamic reductions of straightening rolls,an analytical model combining curvature integral method with linear decreasing straight...Considering the variable cross section thickness of longitudinal profiled plate and the dynamic reductions of straightening rolls,an analytical model combining curvature integral method with linear decreasing straightening scheme was proposed to investigate the longitudinal profiled plate straightening process.Moreover,the calculation flow and solution algorithm of longitudinal profiled plate straightening process were presented.To verify the proposed model,calculated straightening forces were compared with the measured values,and very good agreements were achieved.Then,the reduction,contact angle,reverse bending curvature,residual curvature,straightening force and straightening moment of longitudinal profiled plate in the straightening process were calculated and analyzed,and the calculated results show that the curvature integral method can be used to reveal the mechanism of longitudinal profiled plate straightening.展开更多
This paper presents the contour integral method for solving the linear constant coefficient ordinary differential equations in complex plane,and obtains the uniform expressions of the general solutions.Firstly,by usin...This paper presents the contour integral method for solving the linear constant coefficient ordinary differential equations in complex plane,and obtains the uniform expressions of the general solutions.Firstly,by using Residue Theorem,the general form of the contour integral representation for the homogeneous complex differential equation is obtained,which can be degenerated to classical results in real line.As for inhomogeneous complex differential equations with constant coefficients,we construct the integral expression of the particular solution for any continuous forcing term,and give rigorous proof via Residue Theorem.Thus the general solutions of inhomogeneous complex differential equations are also given.The main purpose of this paper is to give a foundation for a complete theory of linear complex differential equations with constant coefficients by a contour integral method.The results can not only solve the inhomogeneous complex differential equation well,but also explain the forms that are difficult to be understood in the classical solutions.展开更多
In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the c...In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations. The obtained results include periodic and solitary wave solutions. The first integral method presents a wider applicability to handling nonlinear wave equations.展开更多
The stress intensity factors(SIFs)for two-dimensional cracks are extracted using the p-version finite element method(P-FEM)and the contour integral method.Several numerical experiments,e.g.,crack initiating from the e...The stress intensity factors(SIFs)for two-dimensional cracks are extracted using the p-version finite element method(P-FEM)and the contour integral method.Several numerical experiments,e.g.,crack initiating from the edge of a circular hole under an unidirectional uniform tension and two equal-length,unequal-length hole-edge cracks,respectively,at a rectangular plate,an inclined centered crack under uniaxial tension at a square plate and a pipeline crack model,are used to demonstrate the accuracy and effectiveness of the approaches.SIFs are presented for the effects of various crack lengths and length-width ratio.Numerical results are analyzed and compared with reference solutions and results obtained by the Voronoi cell finite element method,boundary element method,high-order extended finite element method(high-order XFEM)and commercial finite element software ABAQUS in the available literature.Numerical results are in good agreement with the benchmark problems and show faster convergence rate,higher accuracy and better numerical stability.展开更多
This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and e...This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces.The displacements and tractions were used as unknowns on the external boundary,while the relative crack opening displacement(RCOD)was chosen as unknowns on either side of crack surfaces to keep the single-domain merit.Only one side of the crack surfaces was concerned and needed to be discretized,thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method(DBEM).A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly,and the SIFs were evaluated by the extrapolation of the RCOD.Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.展开更多
In order to study the law of mining subsidence and ground movement, to provide the basis of coal mining under building, railway and water, we used the probability integration method to make comprehensive evaluation of...In order to study the law of mining subsidence and ground movement, to provide the basis of coal mining under building, railway and water, we used the probability integration method to make comprehensive evaluation of ground stability. Take Yingcheng Coal Mine of Jiutai as an example. Mining-induced movement and horizontal movement are analyzed on the basis of the measurement data. The resuhs of prediction can pro- vide reference and basis for prevention of coal mining subsidence and future restoration and treatment.展开更多
In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)deriva...In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)derivative.The advection-diffusion equation,which governs the transport of mass,heat,or energy through combined advection and diffusion processes,is central to modeling physical systems with nonlocal behavior.Our numerical scheme employs the LT to transform the time-dependent time-fractional PDEs into a time-independent PDE in LT domain,eliminating the need for classical time-stepping methods that often suffer from stability constraints.For spatial discretization,we employ the CSCM,where the solution is approximated using Lagrange interpolation polynomial based on the Chebyshev collocation nodes,achieving exponential convergence that outperforms the algebraic convergence rates of finite difference and finite element methods.Finally,the solution is reverted to the time domain using contour integration technique.We also establish the existence and uniqueness of the solution for the proposed problem.The performance,efficiency,and accuracy of the proposed method are validated through various fractional advection-diffusion problems.The computed results demonstrate that the proposed method has less computational cost and is highly accurate.展开更多
The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear b...The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear boundary value problems on a two-dimensional(2D)arbitrary multi-connected domain.We apply this method to solve large deflection bending problems of complex plates with holes.Our solution method simplifies the treatment of the 2D multi-connected domain by utilizing a natural discretization approach that divides it into a series of one-dimensional(1D)intervals.This approach establishes a fundamental relationship between the highest-order derivative in the governing equation of the problem and the remaining lower-order derivatives.By combining a wavelet high accuracy integral approximation format on 1D intervals,where the convergence order remains constant regardless of the number of integration folds,with the collocation method,we obtain a system of algebraic equations that only includes discrete point values of the highest order derivative.In this process,the boundary conditions are automatically replaced using integration constants,eliminating the need for additional processing.Error estimation and numerical results demonstrate that the accuracy of this method is unaffected by the degree of nonlinearity of the equations.When solving the bending problem of multi-perforated complex-shaped plates under consideration,it is evident that directly using higher-order derivatives as unknown functions significantly improves the accuracy of stress calculation,even when the stress exhibits large gradient variations.Moreover,compared to the finite element method,the wavelet method requires significantly fewer nodes to achieve the same level of accuracy.Ultimately,the method achieves a sixth-order accuracy and resembles the treatment of one-dimensional problems during the solution process,effectively avoiding the need for the complex 2D meshing process typically required by conventional methods when solving problems with multi-connected domains.展开更多
Partial differential equations(PDE)on manifolds arise in many areas,including mathematics and many applied fields.Due to the complicated geometrical structure of the manifold,it is difficult to get efficient numerical...Partial differential equations(PDE)on manifolds arise in many areas,including mathematics and many applied fields.Due to the complicated geometrical structure of the manifold,it is difficult to get efficient numerical method to solve PDE on manifold.In the paper,we propose a method called point integral method(PIM)to solve the Poisson-type equations from point clouds.Among different kinds of PDEs,the Poisson-type equations including the standard Poisson equation and the related eigenproblem of the Laplace-Beltrami operator are one of the most important.In PIM,the key idea is to derive the integral equations which approximates the Poisson-type equations and contains no derivatives but only the values of the unknown function.This featuremakes the integral equation easy to be discretized frompoint cloud.In the paper,we explain the derivation of the integral equations,describe the point integral method and its implementation,and present the numerical experiments to demonstrate the convergence of PIM.展开更多
We present an accurate spectral integral method(SIM)for the analyses of scattering from multiple circular perfect electric conductor(PEC)cylinders.It solves the coupled surface integral equations by using the Fourier ...We present an accurate spectral integral method(SIM)for the analyses of scattering from multiple circular perfect electric conductor(PEC)cylinders.It solves the coupled surface integral equations by using the Fourier series and addition theorem to decouple the system.The SIM has exponential convergence so that the error decreases exponentially with the sample density on the surfaces,and requires only about 2–3 points per wavelength(PPW)to reach engineering accuracy defined as higher than 99%accuracy(or with an error smaller than 1%).Numerical results demonstrate that the SIM is much more accurate and efficient than the method of moments(MoM),and thus can be potentially used as the exact radiation boundary condition in the finite element and spectral element methods.展开更多
This paper deals with the boundary integral method to study the Navier-Stokes equations around a rotating obstacle. The detail of this method is that the exterior domain is truncated into a bounded domain and a new ex...This paper deals with the boundary integral method to study the Navier-Stokes equations around a rotating obstacle. The detail of this method is that the exterior domain is truncated into a bounded domain and a new exterior domain by introducing some open ball BR, and the nonlinear problem in the bounded domain and the linearized problem in the new exterior domain are considered and the approximation coupled problem is obtained. We show that the error between the solution u of Navier-Stokes equations around a rotating obstacle and the solution ue of the approximation coupled problem is O（R-1/4） in the Hl-seminorm when Iwl does not exceed some constant.展开更多
This paper presents a fourth-order Cartesian grid based boundary integral method(BIM)for heterogeneous interface problems in two and three dimensional space,where the problem interfaces are irregular and can be explic...This paper presents a fourth-order Cartesian grid based boundary integral method(BIM)for heterogeneous interface problems in two and three dimensional space,where the problem interfaces are irregular and can be explicitly given by parametric curves or implicitly defined by level set functions.The method reformulates the governing equation with interface conditions into boundary integral equations(BIEs)and reinterprets the involved integrals as solutions to some simple interface problems in an extended regular region.Solution of the simple equivalent interface problems for integral evaluation relies on a fourth-order finite difference method with an FFT-based fast elliptic solver.The structure of the coefficient matrix is preserved even with the existence of the interface.In the whole calculation process,analytical expressions of Green’s functions are never determined,formulated or computed.This is the novelty of the proposed kernel-free boundary integral(KFBI)method.Numerical experiments in both two and three dimensions are shown to demonstrate the algorithm efficiency and solution accuracy even for problems with a large diffusion coefficient ratio.展开更多
This paper gives an introduction into the dissipation integral method. The general integral equations for the three-dimensional case are derived. It is found that for a practical calculation algorithm the integral mom...This paper gives an introduction into the dissipation integral method. The general integral equations for the three-dimensional case are derived. It is found that for a practical calculation algorithm the integral momentum equation and the integral energy equation are most useful. Using two different sets of mean velocity profiles the hyperbolical character of a dissipation integral method is shown. Test cases for two- and three-dimensional boundary layers are analysed and discussed. The paper concludes with a discussion of the advantages and limits of dissipation integral methods.展开更多
We present a new numerical method for solving two-dimensional Stokes flow with deformable interfaces such as dynamics of suspended drops or bubbles.The method is based on a boundary integral formulation for the interf...We present a new numerical method for solving two-dimensional Stokes flow with deformable interfaces such as dynamics of suspended drops or bubbles.The method is based on a boundary integral formulation for the interfacial velocity and is spectrally accurate in space.We analyze the singular behavior of the integrals(single-layer and double-layer integrals)appearing in the equations.The interfaces are formulated in the tangent angle and arc-length coordinates and,to reduce the stiffness of the evolution equation,the marker points are evenly distributed in arc-length by choosing a proper tangential velocity along the interfaces.Examples of Stokes flow with bubbles are provided to demonstrate the accuracy and effectiveness of the numerical method.展开更多
This work proposes a generalized boundary integral method for variable coefficients elliptic partial differential equations(PDEs),including both boundary value and interface problems.The method is kernel-free in the s...This work proposes a generalized boundary integral method for variable coefficients elliptic partial differential equations(PDEs),including both boundary value and interface problems.The method is kernel-free in the sense that there is no need to know analytical expressions for kernels of the boundary and volume integrals in the solution of boundary integral equations.Evaluation of a boundary or volume integral is replaced with interpolation of a Cartesian grid based solution,which satisfies an equivalent discrete interface problem,while the interface problem is solved by a fast solver in the Cartesian grid.The computational work involved with the generalized boundary integral method is essentially linearly proportional to the number of grid nodes in the domain.This paper gives implementation details for a secondorder version of the kernel-free boundary integral method in two space dimensions and presents numerical experiments to demonstrate the efficiency and accuracy of the method for both boundary value and interface problems.The interface problems demonstrated include those with piecewise constant and large-ratio coefficients and the heterogeneous interface problem,where the elliptic PDEs on two sides of the interface are of different types.展开更多
In order to improve rolled strip quality, precise plate shape control theory should be established. Roll flat- tening theory is an important part of the plate shape theory. To improve the accuracy of roll flattening c...In order to improve rolled strip quality, precise plate shape control theory should be established. Roll flat- tening theory is an important part of the plate shape theory. To improve the accuracy of roll flattening calculation based on semi infinite body model, especially near the two roll barrel edges, a new and more accurate roll flattening model is proposed. Based on boundary integral equation method, an analytical model for solving a finite length semi infinite body is established. The lateral surface displacement field of the finite length semi-infinite body is simulated by finite element method （FEM） and lateral surface displacement decay functions are established. Based on the boundary integral equation method, the numerical solution of the finite length semi-infinite body under the distribu ted force is obtained and an accurate roll flattening model is established. Different from the traditional semi-infinite body model, the matrix form of the new roll flattening model is established through the mathematical derivation. The result from the new model is more consistent with that by FEM especially near the edges.展开更多
基金supports of the National Natural Science Foundation of China(Nos.12032008,12102080)the Fundamental Research Funds for the Central Universities,China(No.DUT23RC(3)038)are much appreciated。
文摘Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the randomness of structural parameters,working condition and vibration environment are considered for fatigue life predication and reliability assessment.First,the lowcycle fatigue problem is modelled as stochastic static system with random parameters,while the high-cycle fatigue problem is considered as stochastic dynamic system under random excitations.Then,to deal with the two failure modes,the novel Direct Probability Integral Method(DPIM)is proposed,which is efficient and accurate for solving stochastic static and dynamic systems.The probability density functions of accumulated damage and fatigue life of turbine blade for low-cycle and high-cycle fatigue problems are achieved,respectively.Furthermore,the time–frequency hybrid method is advanced to enhance the computational efficiency for governing equation of system.Finally,the results of typical examples demonstrate high accuracy and efficiency of the proposed method by comparison with Monte Carlo simulation and other methods.It is indicated that the DPIM is a unified method for predication of random fatigue life for low-cycle and highcycle fatigue problems.The rotational speed,density,fatigue strength coefficient,and fatigue plasticity index have a high sensitivity to fatigue reliability of engine turbine blade.
基金supported by the National Natural Science Foundation of China(Grant Nos.12072288,U2241274,and 12272319).
文摘In this work,a new methodology is presented to mainly solve the fluid–solid interaction(FSI)equation.This methodology combines the advantages of the Newmark precise integral method(NPIM)and the dual neural network(DNN)method.The NPIM is employed to modify the exponential matrix and loading vector based on the DNN integral method.This involves incorporating the basic assumption of the Newmark-βmethod into the dynamic equation and eliminating the acceleration term from the dynamic equilibrium equation.As a result,the equation is reduced to a first-order linear equation system.Subsequently,the PIM is applied to integrate the system step by step within the NPIM.The DNN method is adopted to solve the inhomogeneous term through fitting the integrand and the original function with a pair of neural networks,and the integral term is solved using the Newton–Leibniz formula.Numerical examples demonstrate that the proposed methodology significantly improves computing efficiency and provides sufficient precision compared to the DNN method.This is particularly evident when analyzing large-scale structures under blast loading conditions.
基金Project (BK20130174) supported by the Basic Research Project of Jiangsu Province (Natural Science Foundation) Project (1101109C) supported by Jiangsu Planned Projects for Postdoctoral Research Funds,China+1 种基金Project (201325) supported by the Key Laboratory of Geo-informatics of State Bureau of Surveying and Mapping,ChinaProject (SZBF2011-6-B35) supported by the Priority Academic Program Development of Jiangsu Higher Education Institutions,China
文摘Due to the difficulties in obtaining large deformation mining subsidence using differential Interferometric Synthetic Aperture Radar （D-InSAR） alone, a new algorithm was proposed to extract large deformation mining subsidence using D-InSAR technique and probability integral method. The details of the algorithm are as follows：the control points set, containing correct phase unwrapping points on the subsidence basin edge generated by D-InSAR and several observation points （near the maximum subsidence and inflection points）, was established at first; genetic algorithm （GA） was then used to optimize the parameters of probability integral method; at last, the surface subsidence was deduced according to the optimum parameters. The results of the experiment in Huaibei mining area, China, show that the presented method can generate the correct mining subsidence basin with a few surface observations, and the relative error of maximum subsidence point is about 8.3%, which is much better than that of conventional D-InSAR （relative error is 68.0%）.
基金This study was supported by Projects under contract Nos DY105 China's 0cean-03-01-01 and DY105-03-01-07the National Natural Science Foundation of China under contract No.40506017the Youth Foundation of Marine High-tech Project of China under contract No.2002AA616010.
文摘On the basis of three geological models and several orebody boundaries, a method of grid subdivision and integral has been proposed to calculate and evaluate the resources of cobalt-rich crusts on the seamounts in the central Pacific Ocean. The formulas of this method are deduced and the interface of program module is designed. The method is carried out in the software ＂Auto mapping system of submarine topography and geomorphology MBChart＂. This method and program will possibly become a potential tool to calculate the resources of seamounts and determine the target diggings for China＇ s next Five-year Plan.
基金The authors are grateful for the supports of the National Key Research and Development Program of China(No.2017YFB0306404)Key Project of Hebei Education Department(No.ZD2018203).
文摘Considering the variable cross section thickness of longitudinal profiled plate and the dynamic reductions of straightening rolls,an analytical model combining curvature integral method with linear decreasing straightening scheme was proposed to investigate the longitudinal profiled plate straightening process.Moreover,the calculation flow and solution algorithm of longitudinal profiled plate straightening process were presented.To verify the proposed model,calculated straightening forces were compared with the measured values,and very good agreements were achieved.Then,the reduction,contact angle,reverse bending curvature,residual curvature,straightening force and straightening moment of longitudinal profiled plate in the straightening process were calculated and analyzed,and the calculated results show that the curvature integral method can be used to reveal the mechanism of longitudinal profiled plate straightening.
基金Supported by the National Natural Science Foundation of China(11561055)the Natural Science Foundation of Ningxia(2018AAC03057)。
文摘This paper presents the contour integral method for solving the linear constant coefficient ordinary differential equations in complex plane,and obtains the uniform expressions of the general solutions.Firstly,by using Residue Theorem,the general form of the contour integral representation for the homogeneous complex differential equation is obtained,which can be degenerated to classical results in real line.As for inhomogeneous complex differential equations with constant coefficients,we construct the integral expression of the particular solution for any continuous forcing term,and give rigorous proof via Residue Theorem.Thus the general solutions of inhomogeneous complex differential equations are also given.The main purpose of this paper is to give a foundation for a complete theory of linear complex differential equations with constant coefficients by a contour integral method.The results can not only solve the inhomogeneous complex differential equation well,but also explain the forms that are difficult to be understood in the classical solutions.
文摘In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The first integral method is used to construct the travelling wave solutions of the modified Benjamin-Bona-Mahony and the coupled Klein-Gordon equations. The obtained results include periodic and solitary wave solutions. The first integral method presents a wider applicability to handling nonlinear wave equations.
基金the firancinal support of the National Natural Science Foundation of China(Grant No:51769011)for this work,and the authors are also deeply grateful to the editors and revewerse for tbeir rigorous work and valuable comments.
文摘The stress intensity factors(SIFs)for two-dimensional cracks are extracted using the p-version finite element method(P-FEM)and the contour integral method.Several numerical experiments,e.g.,crack initiating from the edge of a circular hole under an unidirectional uniform tension and two equal-length,unequal-length hole-edge cracks,respectively,at a rectangular plate,an inclined centered crack under uniaxial tension at a square plate and a pipeline crack model,are used to demonstrate the accuracy and effectiveness of the approaches.SIFs are presented for the effects of various crack lengths and length-width ratio.Numerical results are analyzed and compared with reference solutions and results obtained by the Voronoi cell finite element method,boundary element method,high-order extended finite element method(high-order XFEM)and commercial finite element software ABAQUS in the available literature.Numerical results are in good agreement with the benchmark problems and show faster convergence rate,higher accuracy and better numerical stability.
基金This work was supported by The National Key R&D Program of China(Grant No.2017YFC0804601)the National Natural Science Foundation of China(No.51741410)Open Research Fund of State Key Laboratory of Geomechanics and Geotechnical Engineering,Institute of Rock and Soil Mechanics,Chinese Academy of Sciences(Grant No.Z017017).
文摘This paper presents a direct traction boundary integral equation method(DTBIEM)for two-dimensional crack problems of materials.The traction boundary integral equation was collocated on both the external boundary and either side of the crack surfaces.The displacements and tractions were used as unknowns on the external boundary,while the relative crack opening displacement(RCOD)was chosen as unknowns on either side of crack surfaces to keep the single-domain merit.Only one side of the crack surfaces was concerned and needed to be discretized,thus the proposed method resulted in a smaller system of algebraic equations compared with the dual boundary element method(DBEM).A new set of crack-tip shape functions was constructed to represent the strain field singularity exactly,and the SIFs were evaluated by the extrapolation of the RCOD.Numerical examples for both straight and curved cracks are given to validate the accuracy and efficiency of the presented method.
文摘In order to study the law of mining subsidence and ground movement, to provide the basis of coal mining under building, railway and water, we used the probability integration method to make comprehensive evaluation of ground stability. Take Yingcheng Coal Mine of Jiutai as an example. Mining-induced movement and horizontal movement are analyzed on the basis of the measurement data. The resuhs of prediction can pro- vide reference and basis for prevention of coal mining subsidence and future restoration and treatment.
基金extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under grant number RGP2/174/46.
文摘In this article,we develop the Laplace transform(LT)based Chebyshev spectral collocation method(CSCM)to approximate the time fractional advection-diffusion equation,incorporating the Atangana-Baleanu Caputo(ABC)derivative.The advection-diffusion equation,which governs the transport of mass,heat,or energy through combined advection and diffusion processes,is central to modeling physical systems with nonlocal behavior.Our numerical scheme employs the LT to transform the time-dependent time-fractional PDEs into a time-independent PDE in LT domain,eliminating the need for classical time-stepping methods that often suffer from stability constraints.For spatial discretization,we employ the CSCM,where the solution is approximated using Lagrange interpolation polynomial based on the Chebyshev collocation nodes,achieving exponential convergence that outperforms the algebraic convergence rates of finite difference and finite element methods.Finally,the solution is reverted to the time domain using contour integration technique.We also establish the existence and uniqueness of the solution for the proposed problem.The performance,efficiency,and accuracy of the proposed method are validated through various fractional advection-diffusion problems.The computed results demonstrate that the proposed method has less computational cost and is highly accurate.
基金supported by the National Natural Science Foundation of China(Grant No.11925204).
文摘The challenge of solving nonlinear problems in multi-connected domains with high accuracy has garnered significant interest.In this paper,we propose a unified wavelet solution method for accurately solving nonlinear boundary value problems on a two-dimensional(2D)arbitrary multi-connected domain.We apply this method to solve large deflection bending problems of complex plates with holes.Our solution method simplifies the treatment of the 2D multi-connected domain by utilizing a natural discretization approach that divides it into a series of one-dimensional(1D)intervals.This approach establishes a fundamental relationship between the highest-order derivative in the governing equation of the problem and the remaining lower-order derivatives.By combining a wavelet high accuracy integral approximation format on 1D intervals,where the convergence order remains constant regardless of the number of integration folds,with the collocation method,we obtain a system of algebraic equations that only includes discrete point values of the highest order derivative.In this process,the boundary conditions are automatically replaced using integration constants,eliminating the need for additional processing.Error estimation and numerical results demonstrate that the accuracy of this method is unaffected by the degree of nonlinearity of the equations.When solving the bending problem of multi-perforated complex-shaped plates under consideration,it is evident that directly using higher-order derivatives as unknown functions significantly improves the accuracy of stress calculation,even when the stress exhibits large gradient variations.Moreover,compared to the finite element method,the wavelet method requires significantly fewer nodes to achieve the same level of accuracy.Ultimately,the method achieves a sixth-order accuracy and resembles the treatment of one-dimensional problems during the solution process,effectively avoiding the need for the complex 2D meshing process typically required by conventional methods when solving problems with multi-connected domains.
基金This research was partial supported by NSFC Grant(11201257 to Z.S.,11371220 to Z.S.and J.S.and 11271011 to J.S.)National Basic Research Program of China(973 Program 2012CB825500 to J.S.).
文摘Partial differential equations(PDE)on manifolds arise in many areas,including mathematics and many applied fields.Due to the complicated geometrical structure of the manifold,it is difficult to get efficient numerical method to solve PDE on manifold.In the paper,we propose a method called point integral method(PIM)to solve the Poisson-type equations from point clouds.Among different kinds of PDEs,the Poisson-type equations including the standard Poisson equation and the related eigenproblem of the Laplace-Beltrami operator are one of the most important.In PIM,the key idea is to derive the integral equations which approximates the Poisson-type equations and contains no derivatives but only the values of the unknown function.This featuremakes the integral equation easy to be discretized frompoint cloud.In the paper,we explain the derivation of the integral equations,describe the point integral method and its implementation,and present the numerical experiments to demonstrate the convergence of PIM.
文摘We present an accurate spectral integral method(SIM)for the analyses of scattering from multiple circular perfect electric conductor(PEC)cylinders.It solves the coupled surface integral equations by using the Fourier series and addition theorem to decouple the system.The SIM has exponential convergence so that the error decreases exponentially with the sample density on the surfaces,and requires only about 2–3 points per wavelength(PPW)to reach engineering accuracy defined as higher than 99%accuracy(or with an error smaller than 1%).Numerical results demonstrate that the SIM is much more accurate and efficient than the method of moments(MoM),and thus can be potentially used as the exact radiation boundary condition in the finite element and spectral element methods.
基金the National Natural Science Foundation of China(No.10901122,No.11001205)Zhejiang Provincial Natural Science Foundation of China(No.LY12A01015)
文摘This paper deals with the boundary integral method to study the Navier-Stokes equations around a rotating obstacle. The detail of this method is that the exterior domain is truncated into a bounded domain and a new exterior domain by introducing some open ball BR, and the nonlinear problem in the bounded domain and the linearized problem in the new exterior domain are considered and the approximation coupled problem is obtained. We show that the error between the solution u of Navier-Stokes equations around a rotating obstacle and the solution ue of the approximation coupled problem is O（R-1/4） in the Hl-seminorm when Iwl does not exceed some constant.
基金the National Natural Science Foundation of China(Grant No.DMS-12101553,Grant No.DMS-11771290)the Natural Science Foundation of Zhejiang Province(Grant No.LQ22A010017)+4 种基金the National Key Research and Development Program of China(Project No.2020YFA0712000)the Science Challenge Project of China(Grant No.TZ2016002)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA25000400)the National Science Foundation of America(Grant No.ECCS-1927432)also partially supported by the National Science Foundation of America(Grant No.DMS-1720420).
文摘This paper presents a fourth-order Cartesian grid based boundary integral method(BIM)for heterogeneous interface problems in two and three dimensional space,where the problem interfaces are irregular and can be explicitly given by parametric curves or implicitly defined by level set functions.The method reformulates the governing equation with interface conditions into boundary integral equations(BIEs)and reinterprets the involved integrals as solutions to some simple interface problems in an extended regular region.Solution of the simple equivalent interface problems for integral evaluation relies on a fourth-order finite difference method with an FFT-based fast elliptic solver.The structure of the coefficient matrix is preserved even with the existence of the interface.In the whole calculation process,analytical expressions of Green’s functions are never determined,formulated or computed.This is the novelty of the proposed kernel-free boundary integral(KFBI)method.Numerical experiments in both two and three dimensions are shown to demonstrate the algorithm efficiency and solution accuracy even for problems with a large diffusion coefficient ratio.
文摘This paper gives an introduction into the dissipation integral method. The general integral equations for the three-dimensional case are derived. It is found that for a practical calculation algorithm the integral momentum equation and the integral energy equation are most useful. Using two different sets of mean velocity profiles the hyperbolical character of a dissipation integral method is shown. Test cases for two- and three-dimensional boundary layers are analysed and discussed. The paper concludes with a discussion of the advantages and limits of dissipation integral methods.
基金supported by the grants NSF-DMS 0511411,0914923 and 0923111.
文摘We present a new numerical method for solving two-dimensional Stokes flow with deformable interfaces such as dynamics of suspended drops or bubbles.The method is based on a boundary integral formulation for the interfacial velocity and is spectrally accurate in space.We analyze the singular behavior of the integrals(single-layer and double-layer integrals)appearing in the equations.The interfaces are formulated in the tangent angle and arc-length coordinates and,to reduce the stiffness of the evolution equation,the marker points are evenly distributed in arc-length by choosing a proper tangential velocity along the interfaces.Examples of Stokes flow with bubbles are provided to demonstrate the accuracy and effectiveness of the numerical method.
基金supported in part by the National Science Foundation of the USA under Grant DMS-0915023is supported by the National Natural Science Foundation of China under Grants DMS-11101278 and DMS-91130012+2 种基金supported by the Young Thousand Talents Program of Chinasupported in part by National Science Committee of Taiwan under Grant 99-2115-M-007-002-MY2supported in part by National Center for Theoretical Sciences of Taiwan,too.
文摘This work proposes a generalized boundary integral method for variable coefficients elliptic partial differential equations(PDEs),including both boundary value and interface problems.The method is kernel-free in the sense that there is no need to know analytical expressions for kernels of the boundary and volume integrals in the solution of boundary integral equations.Evaluation of a boundary or volume integral is replaced with interpolation of a Cartesian grid based solution,which satisfies an equivalent discrete interface problem,while the interface problem is solved by a fast solver in the Cartesian grid.The computational work involved with the generalized boundary integral method is essentially linearly proportional to the number of grid nodes in the domain.This paper gives implementation details for a secondorder version of the kernel-free boundary integral method in two space dimensions and presents numerical experiments to demonstrate the efficiency and accuracy of the method for both boundary value and interface problems.The interface problems demonstrated include those with piecewise constant and large-ratio coefficients and the heterogeneous interface problem,where the elliptic PDEs on two sides of the interface are of different types.
基金Item Sponsored by National Natural Science Foundation of China(51075353)
文摘In order to improve rolled strip quality, precise plate shape control theory should be established. Roll flat- tening theory is an important part of the plate shape theory. To improve the accuracy of roll flattening calculation based on semi infinite body model, especially near the two roll barrel edges, a new and more accurate roll flattening model is proposed. Based on boundary integral equation method, an analytical model for solving a finite length semi infinite body is established. The lateral surface displacement field of the finite length semi-infinite body is simulated by finite element method （FEM） and lateral surface displacement decay functions are established. Based on the boundary integral equation method, the numerical solution of the finite length semi-infinite body under the distribu ted force is obtained and an accurate roll flattening model is established. Different from the traditional semi-infinite body model, the matrix form of the new roll flattening model is established through the mathematical derivation. The result from the new model is more consistent with that by FEM especially near the edges.
