The discretization of random fields is the first and most important step in the stochastic analysis of engineering structures with spatially dependent random parameters.The essential step of discretization is solving ...The discretization of random fields is the first and most important step in the stochastic analysis of engineering structures with spatially dependent random parameters.The essential step of discretization is solving the Fredholm integral equation to obtain the eigenvalues and eigenfunctions of the covariance functions of the random fields.The collocation method,which has fewer integral operations,is more efficient in accomplishing the task than the timeconsuming Galerkin method,and it is more suitable for engineering applications with complex geometries and a large number of elements.With the help of isogeometric analysis that preserves accurate geometry in analysis,the isogeometric collocation method can efficiently achieve the results with sufficient accuracy.An adaptive moment abscissa is proposed to calculate the coordinates of the collocation points to further improve the accuracy of the collocation method.The adaptive moment abscissae led to more accurate results than the classical Greville abscissae when using the moment parameter optimized with intelligent algorithms.Numerical and engineering examples illustrate the advantages of the proposed isogeometric collocation method based on the adaptive moment abscissae over existing methods in terms of accuracy and efficiency.展开更多
The isogeometric analysis method(IGA)is a new type of numerical method solving partial differential equations.Compared with the traditional finite element method,IGA based on geometric spline can keep the model consis...The isogeometric analysis method(IGA)is a new type of numerical method solving partial differential equations.Compared with the traditional finite element method,IGA based on geometric spline can keep the model consistency between geometry and analysis,and provide higher precision with less freedom.However,huge stiffness matrix fromthe subdivision progress still leads to the solution efficiency problems.This paper presents amultigrid method based on geometric multigrid(GMG)to solve the matrix system of IGA.This method extracts the required computational data for multigrid method fromthe IGA process,which also can be used to improve the traditional algebraic multigrid method(AGM).Based on this,a full multigrid method(FMG)based on GMG is proposed.In order to verify the validity and reliability of these methods,this paper did some test on Poisson’s equation and Reynolds’equation and compared the methods on different subdivision methods,different grid degrees of freedom,different cyclic structure degrees,and studied the convergence rate under different subdivision strategies.The results show that the proposed method is superior to the conventional algebraic multigrid method,and for the standard relaxed V-cycle iteration,the method still has a convergence speed independent of the grid size at the same degrees.展开更多
This paper presents a novel framework for stochastic analysis of linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced ...This paper presents a novel framework for stochastic analysis of linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced by combination of Proper Orthogonal Decomposition(POD)and the Radial Basis Function(RBF).In order to avoid re-meshing and retain the geometric exactness,isogeometric boundary element method(IGABEM)is employed for simulation,in which the Non-Uniform Rational B-splines(NURBS)are employed for representing the crack surfaces and discretizing dual boundary integral equations.The stress intensity factors(SIFs)are extracted by M integral method.The numerical examples simulate several cracked structures with various uncertain parameters such as load effects,materials,geometric dimensions,and the results are verified by comparison with the analytical solutions.展开更多
A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study.The key treatment involves using adjoint variable method in shape sensitiv...A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study.The key treatment involves using adjoint variable method in shape sensitivity analysis with respect to non-uniform rational basis splines control points,and in topology sensitivity analysis with respect to the artificial densities of sound absorption material.OpenMP tool in Fortran code is adopted to improve the efficiency of analysis.To consider the features and efficiencies of the two types of optimization methods,this study adopts a combined iteration scheme for the optimization process to investigate the simultaneous change of geometry shape and distribution of material to achieve better noise control.Numerical examples,such as sound barrier,simple tank,and BeTSSi submarine,are performed to validate the advantage of combined optimization in noise reduction,and to demonstrate the potential of the proposed method for engineering problems.展开更多
In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral c...In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral cells and elements are defined in parameter space,which can reproduce the geometry exactly at all the stages.In IIBNM,the improved interpolating moving leastsquare method(IIMLS)is applied for field approximation and the shape functions have the delta function property.The Lagrangian basis functions are used for field approximation in IBEM.Thus,the boundary conditions can be imposed directly in both methods.The shape functions are defined in 1D parameter space and no curve length needs to be computed.Besides,most methods for the treatment of the singular integrals in the boundary element method can be applied in IIBNM and IBEM directly.Numerical examples have demonstrated the accuracy of the proposed methods.展开更多
The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built b...The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built by subdivision surfaces,and meantime the basis functions of subdivision surfaces are employed to discretize the boundary integral equations for heat conduction analysis.Moreover,the radial integration method is adopted to transform the additional domain integrals caused by variable coefficients to the boundary integrals.Several numerical examples are provided to demonstrate the correctness and advantages of the proposed algorithm in the integration of CAD and numerical analysis.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
Accurate quantification of the uncertainty in the mechanical characteristics of dielectric solids is crucial for advancing their application in high-precision technological domains,necessitating the development of rob...Accurate quantification of the uncertainty in the mechanical characteristics of dielectric solids is crucial for advancing their application in high-precision technological domains,necessitating the development of robust com-putational methods.This paper introduces a Conditional Generation Adversarial Network Isogeometric Analysis(CGAN-IGA)to assess the uncertainty of dielectric solids’mechanical characteristics.IGA is utilized for the precise computation of electric potentials in dielectric,piezoelectric,and flexoelectric materials,leveraging its advantage of integrating seamlessly with Computer-Aided Design(CAD)models to maintain exact geometrical fidelity.The CGAN method is highly efficient in generating models for piezoelectric and flexoelectric materials,specifically adapting to targeted design requirements and constraints.Then,the CGAN-IGA is adopted to calculate the electric potential of optimum models with different parameters to accelerate uncertainty quantification processes.The accuracy and feasibility of this method are verified through numerical experiments presented herein.展开更多
In this paper,a generalized nth-order perturbation method based on the isogeometric boundary element method is proposed for the uncertainty analysis of broadband structural acoustic scattering problems.The Burton-Mill...In this paper,a generalized nth-order perturbation method based on the isogeometric boundary element method is proposed for the uncertainty analysis of broadband structural acoustic scattering problems.The Burton-Miller method is employed to solve the problem of non-unique solutions that may be encountered in the external acoustic field,and the nth-order discretization formulation of the boundary integral equation is derived.In addition,the computation of loop subdivision surfaces and the subdivision rules are introduced.In order to confirm the effectiveness of the algorithm,the computed results are contrasted and analyzed with the results under Monte Carlo simulations(MCs)through several numerical examples.展开更多
Isogeometric collocation method(IGC)shows high computational efficiency compared with isogeometric Galerkin method(IGG)when solving partial differential equations(PDEs).However,few studies about IGC have focused on mu...Isogeometric collocation method(IGC)shows high computational efficiency compared with isogeometric Galerkin method(IGG)when solving partial differential equations(PDEs).However,few studies about IGC have focused on multi-sided physical domains.In this paper,the authors propose a new IGC method based on toric parameterization(IGCT)for the multi-sided planar physical domains.Due to the high order continuity of toric basis functions,the IGCT method shows more accurate numerical approximation.Moreover,the authors generalize the adaptive w-refinement method into IGCT(IGCT-w),in which the weights of basis functions in physical domains are optimized independently for geometry representation.The numerical accuracy of IGCT-w is significantly improved by an order of magnitude in comparison with IGCT method.To save the computational cost of IGCT-w,the authors devise a selection of weights scheme according to relative residuals.Finally,several numerical examples demonstrate the effectiveness and robustness of the proposed method.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.U22A6001 and 52375273)Major Project of Science and Technology Innovation 2030(Grant No.2021ZD0113100)Zhejiang Provincial Natural Science Foundation of China(Grant No.LZ24E050005)。
文摘The discretization of random fields is the first and most important step in the stochastic analysis of engineering structures with spatially dependent random parameters.The essential step of discretization is solving the Fredholm integral equation to obtain the eigenvalues and eigenfunctions of the covariance functions of the random fields.The collocation method,which has fewer integral operations,is more efficient in accomplishing the task than the timeconsuming Galerkin method,and it is more suitable for engineering applications with complex geometries and a large number of elements.With the help of isogeometric analysis that preserves accurate geometry in analysis,the isogeometric collocation method can efficiently achieve the results with sufficient accuracy.An adaptive moment abscissa is proposed to calculate the coordinates of the collocation points to further improve the accuracy of the collocation method.The adaptive moment abscissae led to more accurate results than the classical Greville abscissae when using the moment parameter optimized with intelligent algorithms.Numerical and engineering examples illustrate the advantages of the proposed isogeometric collocation method based on the adaptive moment abscissae over existing methods in terms of accuracy and efficiency.
基金supported by the Natural Science Foundation of Hubei Province(CN)(Grant No.2019CFB693)the Research Foundation of the Education Department of Hubei Province(CN)(Grant No.B2019003)the open Foundation of the Key Laboratory of Metallurgical Equipment and Control of Education Ministry(CN)(Grant No.2015B14).
文摘The isogeometric analysis method(IGA)is a new type of numerical method solving partial differential equations.Compared with the traditional finite element method,IGA based on geometric spline can keep the model consistency between geometry and analysis,and provide higher precision with less freedom.However,huge stiffness matrix fromthe subdivision progress still leads to the solution efficiency problems.This paper presents amultigrid method based on geometric multigrid(GMG)to solve the matrix system of IGA.This method extracts the required computational data for multigrid method fromthe IGA process,which also can be used to improve the traditional algebraic multigrid method(AGM).Based on this,a full multigrid method(FMG)based on GMG is proposed.In order to verify the validity and reliability of these methods,this paper did some test on Poisson’s equation and Reynolds’equation and compared the methods on different subdivision methods,different grid degrees of freedom,different cyclic structure degrees,and studied the convergence rate under different subdivision strategies.The results show that the proposed method is superior to the conventional algebraic multigrid method,and for the standard relaxed V-cycle iteration,the method still has a convergence speed independent of the grid size at the same degrees.
基金The authors thank the financial support of National Natural Science Foundation of China(NSFC)under Grant(Nos.51904202,11902212,11901578).
文摘This paper presents a novel framework for stochastic analysis of linear elastic fracture problems.Monte Carlo simulation(MCs)is adopted to address the multi-dimensional uncertainties,whose computation cost is reduced by combination of Proper Orthogonal Decomposition(POD)and the Radial Basis Function(RBF).In order to avoid re-meshing and retain the geometric exactness,isogeometric boundary element method(IGABEM)is employed for simulation,in which the Non-Uniform Rational B-splines(NURBS)are employed for representing the crack surfaces and discretizing dual boundary integral equations.The stress intensity factors(SIFs)are extracted by M integral method.The numerical examples simulate several cracked structures with various uncertain parameters such as load effects,materials,geometric dimensions,and the results are verified by comparison with the analytical solutions.
基金This study was financially supported by the National Natural Science Foundation of China(NSFC)under Grant No.11772322the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No.XDB22040502.
文摘A combined shape and topology optimization algorithm based on isogeometric boundary element method for 3D acoustics is developed in this study.The key treatment involves using adjoint variable method in shape sensitivity analysis with respect to non-uniform rational basis splines control points,and in topology sensitivity analysis with respect to the artificial densities of sound absorption material.OpenMP tool in Fortran code is adopted to improve the efficiency of analysis.To consider the features and efficiencies of the two types of optimization methods,this study adopts a combined iteration scheme for the optimization process to investigate the simultaneous change of geometry shape and distribution of material to achieve better noise control.Numerical examples,such as sound barrier,simple tank,and BeTSSi submarine,are performed to validate the advantage of combined optimization in noise reduction,and to demonstrate the potential of the proposed method for engineering problems.
基金The research for this paper was supported by(1)the National Natural Science Foundation of China(Grants Nos.51708429,51708428)the Open Projects Foundation(Grant No.2017-04-GF)of State Key Laboratory for Health and Safety of Bridge Structures+1 种基金Wuhan Institute of Technology Science Found(Grant No.K201734)the science and technology projects of Wuhan Urban and Rural Construction Bureau(Grants Nos.201831,201919).
文摘In this paper,general interpolating isogeometric boundary node method(IIBNM)and isogeometric boundary element method(IBEM)based on parameter space are proposed for 2D elasticity problems.In both methods,the integral cells and elements are defined in parameter space,which can reproduce the geometry exactly at all the stages.In IIBNM,the improved interpolating moving leastsquare method(IIMLS)is applied for field approximation and the shape functions have the delta function property.The Lagrangian basis functions are used for field approximation in IBEM.Thus,the boundary conditions can be imposed directly in both methods.The shape functions are defined in 1D parameter space and no curve length needs to be computed.Besides,most methods for the treatment of the singular integrals in the boundary element method can be applied in IIBNM and IBEM directly.Numerical examples have demonstrated the accuracy of the proposed methods.
文摘The present work couples isogeometric analysis(IGA)and boundary element methods(BEM)for three dimensional steady heat conduction problems with variable coefficients.The Computer-Aided Design(CAD)geometries are built by subdivision surfaces,and meantime the basis functions of subdivision surfaces are employed to discretize the boundary integral equations for heat conduction analysis.Moreover,the radial integration method is adopted to transform the additional domain integrals caused by variable coefficients to the boundary integrals.Several numerical examples are provided to demonstrate the correctness and advantages of the proposed algorithm in the integration of CAD and numerical analysis.
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.
文摘Accurate quantification of the uncertainty in the mechanical characteristics of dielectric solids is crucial for advancing their application in high-precision technological domains,necessitating the development of robust com-putational methods.This paper introduces a Conditional Generation Adversarial Network Isogeometric Analysis(CGAN-IGA)to assess the uncertainty of dielectric solids’mechanical characteristics.IGA is utilized for the precise computation of electric potentials in dielectric,piezoelectric,and flexoelectric materials,leveraging its advantage of integrating seamlessly with Computer-Aided Design(CAD)models to maintain exact geometrical fidelity.The CGAN method is highly efficient in generating models for piezoelectric and flexoelectric materials,specifically adapting to targeted design requirements and constraints.Then,the CGAN-IGA is adopted to calculate the electric potential of optimum models with different parameters to accelerate uncertainty quantification processes.The accuracy and feasibility of this method are verified through numerical experiments presented herein.
基金sponsored by the Graduate Student Research and Innovation Fund of Xinyang Normal University under No.2024KYJJ012.
文摘In this paper,a generalized nth-order perturbation method based on the isogeometric boundary element method is proposed for the uncertainty analysis of broadband structural acoustic scattering problems.The Burton-Miller method is employed to solve the problem of non-unique solutions that may be encountered in the external acoustic field,and the nth-order discretization formulation of the boundary integral equation is derived.In addition,the computation of loop subdivision surfaces and the subdivision rules are introduced.In order to confirm the effectiveness of the algorithm,the computed results are contrasted and analyzed with the results under Monte Carlo simulations(MCs)through several numerical examples.
基金supported by the National Natural Science Foundation of China under Grant Nos.12071057 and 11671068the Fundamental Research Funds for the Central Universities under Grant No.DUT23LAB302。
文摘Isogeometric collocation method(IGC)shows high computational efficiency compared with isogeometric Galerkin method(IGG)when solving partial differential equations(PDEs).However,few studies about IGC have focused on multi-sided physical domains.In this paper,the authors propose a new IGC method based on toric parameterization(IGCT)for the multi-sided planar physical domains.Due to the high order continuity of toric basis functions,the IGCT method shows more accurate numerical approximation.Moreover,the authors generalize the adaptive w-refinement method into IGCT(IGCT-w),in which the weights of basis functions in physical domains are optimized independently for geometry representation.The numerical accuracy of IGCT-w is significantly improved by an order of magnitude in comparison with IGCT method.To save the computational cost of IGCT-w,the authors devise a selection of weights scheme according to relative residuals.Finally,several numerical examples demonstrate the effectiveness and robustness of the proposed method.
