A mesh-free method is presented to investigate the static bending properties of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates.The curvature of the plate is directly interpolated with the nod...A mesh-free method is presented to investigate the static bending properties of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates.The curvature of the plate is directly interpolated with the nodal deflections due to the higher-order continuity property of the moving leastsquares approximation,establishing a mesh-free computational scheme where the nodal deflections are the only unknowns.The convergence and efficiency of the proposed method are studied based on a homogeneous square plate.The FG-CNTRC plates are modeled with continuously varying Young’s moduli along the thickness direction according to the volume fraction of the carbon nanotubes(CNTs).Detailed studies have been conducted on the effects of different boundary conditions,CNT volume fractions,geometric shapes,and width-to-thickness ratios on bending behavior.CNT efficiency parameters are introduced to account for load transfer between the nanotubes and the matrix,treating the nanocomposites as orthotropic materials.However,in the actual structure,arranging the CNTs in the desired direction is more difficult compared to other fibers.Therefore,in the present study,CNTs in the composites are considered to be arranged randomly,resulting in the composite properties being treated as isotropic.The study includes second-order derivatives of deflections,and the finite element method typically requires C1 continuity for interpolation,which introduces challenges in building elements and constructing interpolation functions.The distinct advantage of the mesh-free method is that it requires only C0 weight functions.A mesh-free computational scheme based on moving leastsquares approximations for composite plates using Kirchhoffplate theory is established.Bending analyses of homogeneous and FG-CNTRC plates are conducted using the proposed method.Aspects such as boundary conditions,CNT volume fractions,geometric shapes,and width-to-thickness ratios are also discussed.Regular node arrangements and background meshes are adopted in the present study.Results are computed using different scalar parameters and numbers of nodes.Convergence properties for the central deflection of isotropic plates are analyzed in terms of the number of nodes and different scalar parameters.The normalized central deflection is defined and examined under various boundary conditions.展开更多
In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement...In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.展开更多
A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying dom...A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying domain integrals.Trial function is constructed by using a radial basis function （RBF） coupled with a polynomial basis function,in which the shape function possesses the kronecker delta function property.So,additional treatment is not required for imposing essential boundary conditions.Governing equations of impact problems are established and solved node by node by using an explicit time integration algorithm in a local domain,which is very similar to that of the collocation method except that numerical integration can be implemented over local domain in the present method.Numerical results for several examples show that the present method performs well in dealing with the dynamic impact problem of hyperelastic material.展开更多
In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be r...In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.展开更多
Fluid-Structure Interaction(FSI) caused by fluid impacting onto a flexible structure commonly occurs in naval architecture and ocean engineering. Research on the problem of wave-structure interaction is important to e...Fluid-Structure Interaction(FSI) caused by fluid impacting onto a flexible structure commonly occurs in naval architecture and ocean engineering. Research on the problem of wave-structure interaction is important to ensure the safety of offshore structures. This paper presents the Moving Particle Semi-implicit and Finite Element Coupled Method(MPS-FEM) to simulate FSI problems. The Moving Particle Semi-implicit(MPS) method is used to calculate the fluid domain, while the Finite Element Method(FEM) is used to address the structure domain. The scheme for the coupling of MPS and FEM is introduced first. Then, numerical validation and convergent study are performed to verify the accuracy of the solver for solitary wave generation and FSI problems. The interaction between the solitary wave and an elastic structure is investigated by using the MPS-FEM coupled method.展开更多
It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method wide...It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.展开更多
In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local different...In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature （LDQ） method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.展开更多
In this study,to simulate open channel flows,an explicit incompressible mesh-free method is employed in which the pressure field is obtained by explicitly solving the pressure Poisson equation.To capture the velocity ...In this study,to simulate open channel flows,an explicit incompressible mesh-free method is employed in which the pressure field is obtained by explicitly solving the pressure Poisson equation.To capture the velocity information in open channel flows,the source term in the pressure Poisson equation is modified while the spatial discretization of gradient and Laplacian models is based on the moving particle semi-implicit(MPS)method.The inflow boundary condition is treated by injecting fluid particles into the domain according to the inlet discharge,and the outflow condition is handled by prescribing the pressure distribution and removing the fluid particles beyond the domain.The explicit incompressible mesh-free method is then used to simulate open channel flows,including weir flow,hydraulic jump,and flow over an obstacle.In the simulations,velocity distribution and flow pattern are examined.The simulated results are compared to available experimental measurements and other numerical results.There is a good agreement between the simulated results and the experimental measurements.It shows that the explicit incompressible mesh-free method can reproduce the flow characteristics in the open channel flows.展开更多
In this paper,a numerical simulation model of the flow field in a gearbox with an oil volume adjusting device is established for the first time to study its influence on the lubrication characteristics of a high-speed...In this paper,a numerical simulation model of the flow field in a gearbox with an oil volume adjusting device is established for the first time to study its influence on the lubrication characteristics of a high-speed electric multiple unit(EMU)gearbox.The moving particle semi-implicit(MPS)method is used to numerically simulate the internal flow field of the gearbox of the high-speed EMU under working conditions.The effects of the velocity of the high-speed EMU,the immersion depth,and the oil sump temperature on the power loss of the gears and the lubricant quantity of each bearing are studied and provide an effective tool for the quantitative evaluation of the lubrication characteristics of the gearbox.The lubrication characteristics of the gearbox under different working conditions are studied when the oil volume adjusting device is closed and opened.The results show that the oil volume adjusting device mainly changes the amount of lubricant stirred by the output gear by changing the flow rate of lubricant from the cavity pinion(Cavity P)to the cavity gear(Cavity G),and thus affects the power loss of gears and the lubricant quantity of each bearing.展开更多
Meshless or mesh-free (or shorten as MFree) methods have been proposed and achieved remarkable progress over the past few years. The idea of combining MFree methods with other existing numerical techniques such as t...Meshless or mesh-free (or shorten as MFree) methods have been proposed and achieved remarkable progress over the past few years. The idea of combining MFree methods with other existing numerical techniques such as the finite element method (FEM) and the boundary element method (BEM), is naturally of great interest in many practical applications. However, the shape functions used in some MFree methods do not have the Kronecker delta function property. In order to satisfy the combined conditions of displacement compatibility, two numerical techniques, using the hybrid displacement shape function and the modified variational form, are developed and discussed in this paper. In the first technique, the original MFree shape functions are modified to the hybrid forms that possess the Kronecker delta function property. In the second technique, the displacement compatibility is satisfied via a modified variational form based on the Lagrange multiplier method. Formulations of several coupled methods are presented. Numerical exam- ples are presented to demonstrate the effectiveness of the present coupling methods.展开更多
In this paper, a Kansa＇s method is designed to solve numerically the Monge-Ampere equation. The primitive Kansa＇s method is a meshfree method which applying the combination of some radial basis functions （such as H...In this paper, a Kansa＇s method is designed to solve numerically the Monge-Ampere equation. The primitive Kansa＇s method is a meshfree method which applying the combination of some radial basis functions （such as Hardy＇s MQ） to approximate the solution of the linear parabolic, hyperbolic and elliptic problems. But this method is deteriorated when is used to solve nonlinear partial differential equations. We approximate the solution in some local triangular subdomains by using the combination of some cubic polynomials. Then the given problems can be computed in each subdomains independently. We prove the stability and convergence of the new method for the elliptic Monge-Ampere equation. Finally, some numerical experiments are presented to demonstrate the theoretical results.展开更多
We propose a mesh-free method to solve the full Stokes equation for modeling the glacier dynamics with nonlinear rheology.Inspired by the Deep-Ritz method proposed in[13],we first formulate the solution to the non-New...We propose a mesh-free method to solve the full Stokes equation for modeling the glacier dynamics with nonlinear rheology.Inspired by the Deep-Ritz method proposed in[13],we first formulate the solution to the non-Newtonian Stokes equation as the minimizer of a variational problem with boundary constraints.Then,we approximate its solution space by a deep neural network.The loss function for training the neural network is a relaxed version of the variational form,in which penalty terms are used to present soft constraints due to mixed boundary conditions.Instead of introducing mesh grids or basis functions to evaluate the loss function,our method only requires uniform sampling from the physical domain and boundaries.Furthermore,we introduce a re-normalization technique in the neural network to address the significant variation in the scaling of real-world problems.Finally,we illustrate the performance of our method by several numerical experiments,including a 2D model with the analytical solution,the Arolla glacier model with realistic scaling and a 3D model with periodic boundary conditions.Numerical results show that our proposed method is efficient in solving the non-Newtonian mechanics arising from glacier modeling with nonlinear rheology.展开更多
基金supported by the National Natural Science Foundation of China(No.52374110)Key scientific and technological projects of Henan province(No.242102320337)Basic Research Fund of Zhongyuan University of Technology(No.K2022QN008).
文摘A mesh-free method is presented to investigate the static bending properties of functionally graded carbon nanotube-reinforced composite(FG-CNTRC)plates.The curvature of the plate is directly interpolated with the nodal deflections due to the higher-order continuity property of the moving leastsquares approximation,establishing a mesh-free computational scheme where the nodal deflections are the only unknowns.The convergence and efficiency of the proposed method are studied based on a homogeneous square plate.The FG-CNTRC plates are modeled with continuously varying Young’s moduli along the thickness direction according to the volume fraction of the carbon nanotubes(CNTs).Detailed studies have been conducted on the effects of different boundary conditions,CNT volume fractions,geometric shapes,and width-to-thickness ratios on bending behavior.CNT efficiency parameters are introduced to account for load transfer between the nanotubes and the matrix,treating the nanocomposites as orthotropic materials.However,in the actual structure,arranging the CNTs in the desired direction is more difficult compared to other fibers.Therefore,in the present study,CNTs in the composites are considered to be arranged randomly,resulting in the composite properties being treated as isotropic.The study includes second-order derivatives of deflections,and the finite element method typically requires C1 continuity for interpolation,which introduces challenges in building elements and constructing interpolation functions.The distinct advantage of the mesh-free method is that it requires only C0 weight functions.A mesh-free computational scheme based on moving leastsquares approximations for composite plates using Kirchhoffplate theory is established.Bending analyses of homogeneous and FG-CNTRC plates are conducted using the proposed method.Aspects such as boundary conditions,CNT volume fractions,geometric shapes,and width-to-thickness ratios are also discussed.Regular node arrangements and background meshes are adopted in the present study.Results are computed using different scalar parameters and numbers of nodes.Convergence properties for the central deflection of isotropic plates are analyzed in terms of the number of nodes and different scalar parameters.The normalized central deflection is defined and examined under various boundary conditions.
基金Project supported by the Natural Science Foundation of Zhejiang Province,China (Grant No. Y6110007)
文摘In this paper,we analyse the equal width（EW） wave equation by using the mesh-free reproducing kernel particle Ritz（kp-Ritz） method.The mesh-free kernel particle estimate is employed to approximate the displacement field.A system of discrete equations is obtained through the application of the Ritz minimization procedure to the energy expressions.The effectiveness of the kp-Ritz method for the EW wave equation is investigated by numerical examples in this paper.
基金supported by the National Natural Science Foundation of China(No.10902038)
文摘A mesh-free method based on local Petrov-Galerkin formulation is presented to solve dynamic impact problems of hyperelastic material.In the present method,a simple Heaviside test function is chosen for simplifying domain integrals.Trial function is constructed by using a radial basis function （RBF） coupled with a polynomial basis function,in which the shape function possesses the kronecker delta function property.So,additional treatment is not required for imposing essential boundary conditions.Governing equations of impact problems are established and solved node by node by using an explicit time integration algorithm in a local domain,which is very similar to that of the collocation method except that numerical integration can be implemented over local domain in the present method.Numerical results for several examples show that the present method performs well in dealing with the dynamic impact problem of hyperelastic material.
基金supported by the National Natural Science Foundation of China (No.12172154)the 111 Project (No.B14044)+1 种基金the Natural Science Foundation of Gansu Province (No.23JRRA1035)the Natural Science Foundation of Anhui University of Finance and Economics (No.ACKYC20043).
文摘In this study,a wavelet multi-resolution interpolation Galerkin method(WMIGM)is proposed to solve linear singularly perturbed boundary value problems.Unlike conventional wavelet schemes,the proposed algorithm can be readily extended to special node generation techniques,such as the Shishkin node.Such a wavelet method allows a high degree of local refinement of the nodal distribution to efficiently capture localized steep gradients.All the shape functions possess the Kronecker delta property,making the imposition of boundary conditions as easy as that in the finite element method.Four numerical examples are studied to demonstrate the validity and accuracy of the proposedwavelet method.The results showthat the use ofmodified Shishkin nodes can significantly reduce numerical oscillation near the boundary layer.Compared with many other methods,the proposed method possesses satisfactory accuracy and efficiency.The theoretical and numerical results demonstrate that the order of theε-uniform convergence of this wavelet method can reach 5.
基金Supported by the National Natural Science Foundation of China(51379125,51490675,11432009,51579145)Chang Jiang Scholars Program(T2014099)+3 种基金Shanghai Excellent Academic Leaders Program(17XD1402300)Program for Professor of Special Appointment(Eastern Scholar)at Shanghai Institutions of Higher Learning(2013022)Innovative Special Project of Numerical Tank of the Ministry of Industry and Information Technology of China(2016-23/09)Lloyd’s Register Foundation for Doctoral Students
文摘Fluid-Structure Interaction(FSI) caused by fluid impacting onto a flexible structure commonly occurs in naval architecture and ocean engineering. Research on the problem of wave-structure interaction is important to ensure the safety of offshore structures. This paper presents the Moving Particle Semi-implicit and Finite Element Coupled Method(MPS-FEM) to simulate FSI problems. The Moving Particle Semi-implicit(MPS) method is used to calculate the fluid domain, while the Finite Element Method(FEM) is used to address the structure domain. The scheme for the coupling of MPS and FEM is introduced first. Then, numerical validation and convergent study are performed to verify the accuracy of the solver for solitary wave generation and FSI problems. The interaction between the solitary wave and an elastic structure is investigated by using the MPS-FEM coupled method.
基金provided by China Geological Survey with the project(Nos.DD20190707,DD20190012)the Fundamental Research Funds for China Central public research Institutes with the project(No.JKY202014)
文摘It is one of the most important part to build an accurate gravity model in geophysical exploration.Traditional gravity modelling is usually based on grid method,such as difference method and finite element method widely used.Due to self-adaptability lack of division meshes and the difficulty of high-dimensional calculation.
文摘In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature （LDQ） method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.
基金This work was supported by the Key Research and Development Program of Zhejiang Province(Grant No.2020C03082)the Visiting Researcher Fund Program of State Key Laboratory of Water Resources and Hydropower Engineering Science,Wuhan University(Grant No.2021HLG01).
文摘In this study,to simulate open channel flows,an explicit incompressible mesh-free method is employed in which the pressure field is obtained by explicitly solving the pressure Poisson equation.To capture the velocity information in open channel flows,the source term in the pressure Poisson equation is modified while the spatial discretization of gradient and Laplacian models is based on the moving particle semi-implicit(MPS)method.The inflow boundary condition is treated by injecting fluid particles into the domain according to the inlet discharge,and the outflow condition is handled by prescribing the pressure distribution and removing the fluid particles beyond the domain.The explicit incompressible mesh-free method is then used to simulate open channel flows,including weir flow,hydraulic jump,and flow over an obstacle.In the simulations,velocity distribution and flow pattern are examined.The simulated results are compared to available experimental measurements and other numerical results.There is a good agreement between the simulated results and the experimental measurements.It shows that the explicit incompressible mesh-free method can reproduce the flow characteristics in the open channel flows.
基金supported by the Natural Science Foundation of Sichuan Province,China(Nos.2022NSFSC0034 and 2022NSFSC1901)the National Railway Group Science and Technology Program(No.N2021J028)+1 种基金the Independent Research and Development Projects of State Key Laboratory of Heavy Duty AC Drive Electric Locomotive Systems Integration(No.R111720H01385)the Independent Research and Development Projects of State Key Laboratory of Traction Power(No.2022TPL-T02),China。
文摘In this paper,a numerical simulation model of the flow field in a gearbox with an oil volume adjusting device is established for the first time to study its influence on the lubrication characteristics of a high-speed electric multiple unit(EMU)gearbox.The moving particle semi-implicit(MPS)method is used to numerically simulate the internal flow field of the gearbox of the high-speed EMU under working conditions.The effects of the velocity of the high-speed EMU,the immersion depth,and the oil sump temperature on the power loss of the gears and the lubricant quantity of each bearing are studied and provide an effective tool for the quantitative evaluation of the lubrication characteristics of the gearbox.The lubrication characteristics of the gearbox under different working conditions are studied when the oil volume adjusting device is closed and opened.The results show that the oil volume adjusting device mainly changes the amount of lubricant stirred by the output gear by changing the flow rate of lubricant from the cavity pinion(Cavity P)to the cavity gear(Cavity G),and thus affects the power loss of gears and the lubricant quantity of each bearing.
文摘Meshless or mesh-free (or shorten as MFree) methods have been proposed and achieved remarkable progress over the past few years. The idea of combining MFree methods with other existing numerical techniques such as the finite element method (FEM) and the boundary element method (BEM), is naturally of great interest in many practical applications. However, the shape functions used in some MFree methods do not have the Kronecker delta function property. In order to satisfy the combined conditions of displacement compatibility, two numerical techniques, using the hybrid displacement shape function and the modified variational form, are developed and discussed in this paper. In the first technique, the original MFree shape functions are modified to the hybrid forms that possess the Kronecker delta function property. In the second technique, the displacement compatibility is satisfied via a modified variational form based on the Lagrange multiplier method. Formulations of several coupled methods are presented. Numerical exam- ples are presented to demonstrate the effectiveness of the present coupling methods.
基金supported in part by the National Natural Science Foundations of China(No.11426039,11571023,11471329)partially supported by the National Natural Science Foundation of China(No.11501313)+1 种基金the Natural Science Foundation of Ningxia Province(No.NZ15005)the Science Research Project of Ningxia Higher Education(No.NGY2016059)
文摘In this paper, a Kansa＇s method is designed to solve numerically the Monge-Ampere equation. The primitive Kansa＇s method is a meshfree method which applying the combination of some radial basis functions （such as Hardy＇s MQ） to approximate the solution of the linear parabolic, hyperbolic and elliptic problems. But this method is deteriorated when is used to solve nonlinear partial differential equations. We approximate the solution in some local triangular subdomains by using the combination of some cubic polynomials. Then the given problems can be computed in each subdomains independently. We prove the stability and convergence of the new method for the elliptic Monge-Ampere equation. Finally, some numerical experiments are presented to demonstrate the theoretical results.
基金supported by the Australian Research Council under the grant DP21010309The research of Z.Zhang is supported by Hong Kong RGC grant(Projects 17300318 and 17307921)+2 种基金National Natural Science Foundation of China(Project 12171406)Seed Funding Programme for Basic Research(HKU),the outstanding young researcher award of HKU(2020-21)Seed Funding for Strategic Interdisciplinary Research Scheme 2021/22(HKU).
文摘We propose a mesh-free method to solve the full Stokes equation for modeling the glacier dynamics with nonlinear rheology.Inspired by the Deep-Ritz method proposed in[13],we first formulate the solution to the non-Newtonian Stokes equation as the minimizer of a variational problem with boundary constraints.Then,we approximate its solution space by a deep neural network.The loss function for training the neural network is a relaxed version of the variational form,in which penalty terms are used to present soft constraints due to mixed boundary conditions.Instead of introducing mesh grids or basis functions to evaluate the loss function,our method only requires uniform sampling from the physical domain and boundaries.Furthermore,we introduce a re-normalization technique in the neural network to address the significant variation in the scaling of real-world problems.Finally,we illustrate the performance of our method by several numerical experiments,including a 2D model with the analytical solution,the Arolla glacier model with realistic scaling and a 3D model with periodic boundary conditions.Numerical results show that our proposed method is efficient in solving the non-Newtonian mechanics arising from glacier modeling with nonlinear rheology.
