In this paper,a meshfree Jacobi point interpolation(MJPI)approach for the dynamic analysis of sandwich laminated conical and cylindrical shells with varying thickness is presented.The theoretical formulations for sand...In this paper,a meshfree Jacobi point interpolation(MJPI)approach for the dynamic analysis of sandwich laminated conical and cylindrical shells with varying thickness is presented.The theoretical formulations for sandwich laminated shells with varying thickness are established using the modified variational principle within the framework of first-order shear deformation theory(FSDT).The displacement components of the sandwich shell are expanded using the MJPI shape function and Fourier series in the meridional and circumferential directions,respectively.The accuracy and reliability of the proposed MJPI shape function are validated against numerical results from published literature and the commercial simulation tool Abaqus.Finally,the effects of different parameters such as thickness gradient,thickness power index and boundary condition on the free vibration and dynamic response of the sandwich laminated shell are investigated.展开更多
Three-dimensional rock fracture induced by blasting is a highly complex problem and has received considerable attention in geotechnical engineering.The material point method is firstly applied to treat this challengin...Three-dimensional rock fracture induced by blasting is a highly complex problem and has received considerable attention in geotechnical engineering.The material point method is firstly applied to treat this challenging task.Some inherent weaknesses can be overcome by coupling the generalized interpolation material point(GIMP)and the convected particle domain interpolation technique(CPDI).For the media in the borehole,unchanged GIMP-type particles are used to guarantee a homogenous blast pressure.CPDITetrahedron type particles are employed to avoid the fake numerical fracture near the borehole for the rock material.A blasting experiment using three-dimensional single-borehole rock was simulated to examine the applicability of the coupled model under realistic loading and boundary conditions.A good agreement was achieved between the simulation and experimental results.Moreover,the mechanism of three-dimensional rock fracture was analyzed.It was concluded that rock particle size and material parameters play an important role in rock damage.The reflected tensile waves cause severe damage in the lower part of the model.Rayleigh waves occur on the top face of the rock model to induce a hoop failure band.展开更多
This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit m...This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit material point method(iMPM).The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations.Where possible,the implementation procedure closely follows standard finite element method(FEM)approaches to allow easy conversion of other FEM codes.The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM.For the first time,the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics.The proposed i GIMP was tested and compared with i MPM and analytical solutions via a 1 D column compression problem.Results highlighted the superiority of the i GIMP approach in reducing stress oscillations,thereby improving computational accuracy.Then,elasto-plastic slope stabilities and rigid footing problems were considered,further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility.Results showed that the proposed i GIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.展开更多
An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in th...An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating repro- ducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.展开更多
Recently,the radial point interpolation meshfree method has gained popularity owing to its advantages in large deformation and discontinuity problems,however,the accuracy of this method depends on many factors and the...Recently,the radial point interpolation meshfree method has gained popularity owing to its advantages in large deformation and discontinuity problems,however,the accuracy of this method depends on many factors and their influences are not fully investigated yet.In this work,three main factors,i.e.,the shape parameters,the influence domain size,and the nodal distribution,on the accuracy of the radial point interpolation method(RPIM)are systematically studied and conclusive results are obtained.First,the effect of shape parameters(R,q)of the multi-quadric basis function on the accuracy of RPIM is examined via global search.A new interpolation error index,closely related to the accuracy of RPIM,is proposed.The distribution of various error indexes on the R q plane shows that shape parameters q[1.2,1.8]and R[0,1.5]can give good results for general 3-D analysis.This recommended range of shape parameters is examined by multiple benchmark examples in 3D solid mechanics.Second,through numerical experiments,an average of 30 40 nodes in the influence domain of a Gauss point is recommended for 3-D solid mechanics.Third,it is observed that the distribution of nodes has significant effect on the accuracy of RPIM although it has little effect on the accuracy of interpolation.Nodal distributions with better uniformity give better results.Furthermore,how the influence domain size and nodal distribution affect the selection of shape parameters and how the nodal distribution affects the choice of influence domain size are also discussed.展开更多
In this paper,the authors propose a method of three-dimensional(3D)magnetotelluric(MT)forward modeling algorithm based on the meshfree and finite element coupling method.The model is discretized by regular nodes in th...In this paper,the authors propose a method of three-dimensional(3D)magnetotelluric(MT)forward modeling algorithm based on the meshfree and finite element coupling method.The model is discretized by regular nodes in the central area,and the radial point interpolation method(RPIM)based on the global weakness is utilized to construct the meshfree shape function.The Governing equations in each background gird are solved by Gaussian integration.In the extended area where the points are sparsely distributed,to avoid the instability of the meshfree method,finite element method(FEM)with regular grids is used to solve the governing equation.Finally,the meshfree and finite element governing equations are coupled by the continuity of the field at the interfaces,and the direct solution technique is used to realize the 3D MT forward modeling.Numerical experiments of several typical electrical models are used to verify the effectiveness of the method.展开更多
A meshless local radial point interpolation method （LRPIM） for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using ...A meshless local radial point interpolation method （LRPIM） for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using a locally weighted residual method. It uses a radial basis function （RBF） coupled with a polynomial basis function as a trial function,and uses the quartic spline function as a test function of the weighted residual method. The shape function has the properties of the Kronecker delta function,and no additional treatment is done to impose essen-tial boundary conditions. The Newmark method for solving the dynamic problem is adopted in computation. Effects of sizes of the quadrature sub-domain and influence domain on the dynamic properties are investigated. The numerical results show that the presented method can give quite accurate results for the elastic dynamic problem of the moderately thick plate.展开更多
Combining the radial point interpolation method （RPIM）, the dual reciprocity method （DRM） and the hybrid boundary node method （HBNM）, a dual reciprocity hybrid radial boundary node method （DHRBNM） is proposed ...Combining the radial point interpolation method （RPIM）, the dual reciprocity method （DRM） and the hybrid boundary node method （HBNM）, a dual reciprocity hybrid radial boundary node method （DHRBNM） is proposed for linear elasticity. Compared to DHBNM, RPIM is exploited to replace the moving least square （MLS） in DHRBNM, and it gets rid of the deficiency of MLS approximation, in which shape functions lack the delta function property, the boundary condition can not be applied easily and directly and it＇s computational expense is high. Besides, different approximate functions are discussed in DRM to get the interpolation property, in which the accuracy and efficiency for different basis functions are compared. Then RPIM is also applied in DRM to replace the conical function interpolation, which can greatly improve the accuracy of the present method. To demonstrate the effectiveness of the present method, DHBNM is applied for comparison, and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM.展开更多
Laminated composite materials are widely implemented in several engineering constructions. For its relative light weight, these materials are suitable for aerospace, military, marine, and automotive structural applica...Laminated composite materials are widely implemented in several engineering constructions. For its relative light weight, these materials are suitable for aerospace, military, marine, and automotive structural applications. To obtain safe and economical structures, the modelling analysis accuracy is highly relevant. Since meshless methods in the recent years achieved a remarkable progress in computational mechanics, the present work uses one of the most flexible and stable interpolation meshless technique available in the literature—the Radial Point Interpolation Method(RPIM).Here, a 2 D approach is considered to numerically analyse composite laminated beams. Both the meshless formulation and the equilibrium equations ruling the studied physical phenomenon are presented with detail. Several benchmark beam examples are studied and the results are compared with exact solutions available in the literature and the results obtained from a commercial finite element software. The results show the efficiency and accuracy of the proposed numeric technique.展开更多
Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain anal...Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain analytic solutions. So it is necessary to give numerical solutions. The reproducing kernel particle （RKP） method is based on the Carlerkin Meshless method. According to the Sobolev space and Fourier transform, the RKP shape function is mathematically proved in this paper.展开更多
Sensitivity analysis of composite laminated plates with bonding imperfection is carried out based on the radial point interpolation method （RPIM） in a Hamilton system. A set of hybrid governing equations of response...Sensitivity analysis of composite laminated plates with bonding imperfection is carried out based on the radial point interpolation method （RPIM） in a Hamilton system. A set of hybrid governing equations of response and sensitivity quantities is reduced using the spring-layer model and the modified Hellinger-Reissner （H-R） variational principle. The analytical method （AM）, the semi-analytical method （SAM）, and the finite difference method （FDM） are used for sensitivity analysis based on the reduced set of hybrid governing equations. A major advantage of the hybrid governing equations is that the convolution algorithm is avoided in sensitivity analysis. In addition, sensitivity analysis using this set of hybrid governing equations can obtain response values and sensitivity coefficients simultaneously, and accounts for bonding imperfection of composite laminated plates.展开更多
For many years finite element method(FEM)was the chosen numerical method for the analysis of composite structures.However,in the last 20 years,the scientific community has witnessed the birth and development of severa...For many years finite element method(FEM)was the chosen numerical method for the analysis of composite structures.However,in the last 20 years,the scientific community has witnessed the birth and development of several meshless methods,which are more flexible and equally accurate numerical methods.The meshless method used in this work is the natural neighbour radial point interpolation method(NNRPIM).In order to discretize the problem domain,the NNRPIM only requires an unstructured nodal distribution.Then,using the Voronoi mathematical concept,it enforces the nodal connectivity and constructs the background integration mesh.The NNRPIM shape functions are constructed using the radial point interpolation technique.In this work,the displacement field of composite laminated plates is defined by high-order shear deformation theories.In the end,several antisymmetric cross-ply laminates were analysed and the NNRPIM solutions were compared with the literature.The obtained results show the efficiency and accuracy of the NNRPIM formulation.展开更多
In this paper, we consider two interpolations of Birkhoff-type with integer-order derivative. The Birkhoff interpolation is related with collocation method for the corresponding initial or boundary value problems of d...In this paper, we consider two interpolations of Birkhoff-type with integer-order derivative. The Birkhoff interpolation is related with collocation method for the corresponding initial or boundary value problems of differential equations. The solvability of the interpolation problems is proved. For Gauss-type interpolating points, error of interpolation approximation is deduced. Also, we give efficient algorithms to implement the concerned interpolations.展开更多
Java language is widely used in a variety of development platforms to develop all kinds of application software for its simple and efficient.The programming language owning platform independent is adopted to solve the...Java language is widely used in a variety of development platforms to develop all kinds of application software for its simple and efficient.The programming language owning platform independent is adopted to solve the image flicker,sound loading and other issues by the threading technology,multimedia technology,graphics and point by point comparison techniques.Dynamic real⁃time process simulation is implemented and a two⁃dimensional network of CNC machining simulation system is developed while Java applet application is as a carrier.The simulation results show that the system has a friendly interface and fast calculation speed,and platform portability has a certain practicality and application value.展开更多
In order to overcome the possible singularity associated with the Point Interpolation Method(PIM),the Radial Point Interpolation Method(RPIM)was proposed by G.R.Liu.Radial basis functions(RBF)was used in RPIM as basis...In order to overcome the possible singularity associated with the Point Interpolation Method(PIM),the Radial Point Interpolation Method(RPIM)was proposed by G.R.Liu.Radial basis functions(RBF)was used in RPIM as basis functions for interpolation.All these radial basis functions include shape parameters.The choice of these shape parameters has been and stays a problematic theme in RBF approximation and interpolation theory.The object of this study is to contribute to the analysis of how these shape parameters affect the accuracy of the radial PIM.The RPIM is studied based on the global Galerkin weak form performed using two integration technics:classical Gaussian integration and the strain smoothing integration scheme.The numerical performance of this method is tested on their behavior on curve fitting,and on three elastic mechanical problems with regular or irregular nodes distributions.A range of recommended shape parameters is obtained from the analysis of different error indexes and also the condition number of the matrix system.All resulting RPIM methods perform very well in term of numerical computation.The Smoothed Radial Point Interpolation Method(SRPIM)shows a higher accuracy,especially in a situation of distorted node scheme.展开更多
A novel extended traction boundary element-free method is proposed to analyze the crack problems of two-dimensional infinite magnetoelectroelastic solid.An extended traction boundary integral equation only involving C...A novel extended traction boundary element-free method is proposed to analyze the crack problems of two-dimensional infinite magnetoelectroelastic solid.An extended traction boundary integral equation only involving Cauchy singularity is firstly derived.Then,the extended dislocation densities on the crack surface are expressed as the combination of a characteristic term and unknown weight functions,and the radial point interpolation method is adopted to approximate the unknown weight functions.The numerical scheme of the extended traction boundary element-free method is further established,and an effective numerical procedure is used to evaluate the Cauchy singular integrals.Finally,the stress intensity factor,electric displacement intensity factor and magnetic induction intensity factor are computed for some selected crack problems that contain straight,curved and branched cracks,and good numerical results are obtained.At the same time,the fracture properties of these crack problems are discussed.展开更多
文摘In this paper,a meshfree Jacobi point interpolation(MJPI)approach for the dynamic analysis of sandwich laminated conical and cylindrical shells with varying thickness is presented.The theoretical formulations for sandwich laminated shells with varying thickness are established using the modified variational principle within the framework of first-order shear deformation theory(FSDT).The displacement components of the sandwich shell are expanded using the MJPI shape function and Fourier series in the meridional and circumferential directions,respectively.The accuracy and reliability of the proposed MJPI shape function are validated against numerical results from published literature and the commercial simulation tool Abaqus.Finally,the effects of different parameters such as thickness gradient,thickness power index and boundary condition on the free vibration and dynamic response of the sandwich laminated shell are investigated.
基金This research was funded by the Natural Science Foundation of Sichuan,China(No.2022NSFSC1915)the National Natural Science Foundation of China(No.U19A2098)+1 种基金State Key Laboratory of Precision Blasting and Hubei Key Laboratory of Blasting Engineering,Jianghan University(No.PBSKL2022B06)the Fundamental Research Funds for the Central Universities。
文摘Three-dimensional rock fracture induced by blasting is a highly complex problem and has received considerable attention in geotechnical engineering.The material point method is firstly applied to treat this challenging task.Some inherent weaknesses can be overcome by coupling the generalized interpolation material point(GIMP)and the convected particle domain interpolation technique(CPDI).For the media in the borehole,unchanged GIMP-type particles are used to guarantee a homogenous blast pressure.CPDITetrahedron type particles are employed to avoid the fake numerical fracture near the borehole for the rock material.A blasting experiment using three-dimensional single-borehole rock was simulated to examine the applicability of the coupled model under realistic loading and boundary conditions.A good agreement was achieved between the simulation and experimental results.Moreover,the mechanism of three-dimensional rock fracture was analyzed.It was concluded that rock particle size and material parameters play an important role in rock damage.The reflected tensile waves cause severe damage in the lower part of the model.Rayleigh waves occur on the top face of the rock model to induce a hoop failure band.
基金the National Natural Science Foundation of China(Nos.41807223 and 51908175)the Fundamental Research Funds for the Central Universities(No.B210202096)+1 种基金the Natural Science Foundation of Guangdong Province(No.2018A030310346)the Water Conservancy Science and Technology Innovation Project of Guangdong Province(No.2020-11),China。
文摘This paper presents a quasi-static implicit generalized interpolation material point method(i GIMP)with B-bar approach for large deformation geotechnical problems.The i GIMP algorithm is an extension of the implicit material point method(iMPM).The global stiffness matrix is formed explicitly and the Newton-Raphson iterative method is used to solve the equilibrium equations.Where possible,the implementation procedure closely follows standard finite element method(FEM)approaches to allow easy conversion of other FEM codes.The generalized interpolation function is assigned to eliminate the inherent cell crossing noise within conventional MPM.For the first time,the B-bar approach is used to overcome volumetric locking in standard GIMP method for near-incompressible non-linear geomechanics.The proposed i GIMP was tested and compared with i MPM and analytical solutions via a 1 D column compression problem.Results highlighted the superiority of the i GIMP approach in reducing stress oscillations,thereby improving computational accuracy.Then,elasto-plastic slope stabilities and rigid footing problems were considered,further illustrating the ability of the proposed method to overcome volumetric locking due to incompressibility.Results showed that the proposed i GIMP with B-bar approach can be used to simulate geotechnical problems with large deformations.
基金supported by the National Natural Science Foundation of China(Grant No.11171208)the Natural Science Foundation of Shanxi Province,China(Grant No.2013011022-6)
文摘An interpolating reproducing kernel particle method for two-dimensional （2D） scatter points is introduced. It elim- inates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating repro- ducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.
基金Project(2010CB732103)supported by the National Basic Research Program of ChinaProject(51179092)supported by the National Natural Science Foundation of ChinaProject(2012-KY-02)supported by the State Key Laboratory of Hydroscience and Engineering,China
文摘Recently,the radial point interpolation meshfree method has gained popularity owing to its advantages in large deformation and discontinuity problems,however,the accuracy of this method depends on many factors and their influences are not fully investigated yet.In this work,three main factors,i.e.,the shape parameters,the influence domain size,and the nodal distribution,on the accuracy of the radial point interpolation method(RPIM)are systematically studied and conclusive results are obtained.First,the effect of shape parameters(R,q)of the multi-quadric basis function on the accuracy of RPIM is examined via global search.A new interpolation error index,closely related to the accuracy of RPIM,is proposed.The distribution of various error indexes on the R q plane shows that shape parameters q[1.2,1.8]and R[0,1.5]can give good results for general 3-D analysis.This recommended range of shape parameters is examined by multiple benchmark examples in 3D solid mechanics.Second,through numerical experiments,an average of 30 40 nodes in the influence domain of a Gauss point is recommended for 3-D solid mechanics.Third,it is observed that the distribution of nodes has significant effect on the accuracy of RPIM although it has little effect on the accuracy of interpolation.Nodal distributions with better uniformity give better results.Furthermore,how the influence domain size and nodal distribution affect the selection of shape parameters and how the nodal distribution affects the choice of influence domain size are also discussed.
基金Supported by Project of National Natural Science Foundation of China(No.42074120).
文摘In this paper,the authors propose a method of three-dimensional(3D)magnetotelluric(MT)forward modeling algorithm based on the meshfree and finite element coupling method.The model is discretized by regular nodes in the central area,and the radial point interpolation method(RPIM)based on the global weakness is utilized to construct the meshfree shape function.The Governing equations in each background gird are solved by Gaussian integration.In the extended area where the points are sparsely distributed,to avoid the instability of the meshfree method,finite element method(FEM)with regular grids is used to solve the governing equation.Finally,the meshfree and finite element governing equations are coupled by the continuity of the field at the interfaces,and the direct solution technique is used to realize the 3D MT forward modeling.Numerical experiments of several typical electrical models are used to verify the effectiveness of the method.
基金supported by the National 973 Scientific and Technological Innovation Project (No. 2004CB719402)National Natural Science Foundation of China (No. 10672055)+3 种基金Key Project of NSFC (No. 60635020)Natural Science Foundation for Out standing Youth of China (No. 50625519)Hunan Provincial Natural Science Foundation of China (No. 07JJ6002)Scientific Research Fund of Hunan Provincial Education Department of China (No. 08C230)
文摘A meshless local radial point interpolation method （LRPIM） for solving elastic dy-namic problems of moderately thick plates is presented in this paper. The discretized system equation of the plate is obtained using a locally weighted residual method. It uses a radial basis function （RBF） coupled with a polynomial basis function as a trial function,and uses the quartic spline function as a test function of the weighted residual method. The shape function has the properties of the Kronecker delta function,and no additional treatment is done to impose essen-tial boundary conditions. The Newmark method for solving the dynamic problem is adopted in computation. Effects of sizes of the quadrature sub-domain and influence domain on the dynamic properties are investigated. The numerical results show that the presented method can give quite accurate results for the elastic dynamic problem of the moderately thick plate.
基金Project supported by the National Basic Research Program of China (No. 2010CB732006)the CAS/SAFEA International Partnership Program for Creative Research Teams (No. KZCX2-YW-T12)the National Natural Science Foundation of China (No. 11002154)
文摘Combining the radial point interpolation method （RPIM）, the dual reciprocity method （DRM） and the hybrid boundary node method （HBNM）, a dual reciprocity hybrid radial boundary node method （DHRBNM） is proposed for linear elasticity. Compared to DHBNM, RPIM is exploited to replace the moving least square （MLS） in DHRBNM, and it gets rid of the deficiency of MLS approximation, in which shape functions lack the delta function property, the boundary condition can not be applied easily and directly and it＇s computational expense is high. Besides, different approximate functions are discussed in DRM to get the interpolation property, in which the accuracy and efficiency for different basis functions are compared. Then RPIM is also applied in DRM to replace the conical function interpolation, which can greatly improve the accuracy of the present method. To demonstrate the effectiveness of the present method, DHBNM is applied for comparison, and some numerical examples of 2-D elasticity problems show that the present method is much more effective than DHBNM.
基金the funding provided by Ministério da Ciência,Tecnologia e Ensino Superior--Fundaca para a Ciência e a Tecnologia(Portugal)(Grants SFRH/BPD/75072/2010,SFRH/BPD/111020/2015)the inter-institutional projects from LAETA(Grant UID/EMS/50022/2013)+1 种基金the funding of Project NORTE-010145-FEDER-000022-SciTech-Science and Technology for Competitive and Sustainable Industriescofinanced by Programa Operacional Regional do Norte(Grant NORTE2020),through Fundo Europeu de Desenvolvimento Regional(FEDER)
文摘Laminated composite materials are widely implemented in several engineering constructions. For its relative light weight, these materials are suitable for aerospace, military, marine, and automotive structural applications. To obtain safe and economical structures, the modelling analysis accuracy is highly relevant. Since meshless methods in the recent years achieved a remarkable progress in computational mechanics, the present work uses one of the most flexible and stable interpolation meshless technique available in the literature—the Radial Point Interpolation Method(RPIM).Here, a 2 D approach is considered to numerically analyse composite laminated beams. Both the meshless formulation and the equilibrium equations ruling the studied physical phenomenon are presented with detail. Several benchmark beam examples are studied and the results are compared with exact solutions available in the literature and the results obtained from a commercial finite element software. The results show the efficiency and accuracy of the proposed numeric technique.
文摘Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain analytic solutions. So it is necessary to give numerical solutions. The reproducing kernel particle （RKP） method is based on the Carlerkin Meshless method. According to the Sobolev space and Fourier transform, the RKP shape function is mathematically proved in this paper.
基金Project supported by the National Natural Science Foundation of China (No. 60979001)the Major Project of Civil Aviation University of China (No. CAUC2009ZD0101)
文摘Sensitivity analysis of composite laminated plates with bonding imperfection is carried out based on the radial point interpolation method （RPIM） in a Hamilton system. A set of hybrid governing equations of response and sensitivity quantities is reduced using the spring-layer model and the modified Hellinger-Reissner （H-R） variational principle. The analytical method （AM）, the semi-analytical method （SAM）, and the finite difference method （FDM） are used for sensitivity analysis based on the reduced set of hybrid governing equations. A major advantage of the hybrid governing equations is that the convolution algorithm is avoided in sensitivity analysis. In addition, sensitivity analysis using this set of hybrid governing equations can obtain response values and sensitivity coefficients simultaneously, and accounts for bonding imperfection of composite laminated plates.
文摘For many years finite element method(FEM)was the chosen numerical method for the analysis of composite structures.However,in the last 20 years,the scientific community has witnessed the birth and development of several meshless methods,which are more flexible and equally accurate numerical methods.The meshless method used in this work is the natural neighbour radial point interpolation method(NNRPIM).In order to discretize the problem domain,the NNRPIM only requires an unstructured nodal distribution.Then,using the Voronoi mathematical concept,it enforces the nodal connectivity and constructs the background integration mesh.The NNRPIM shape functions are constructed using the radial point interpolation technique.In this work,the displacement field of composite laminated plates is defined by high-order shear deformation theories.In the end,several antisymmetric cross-ply laminates were analysed and the NNRPIM solutions were compared with the literature.The obtained results show the efficiency and accuracy of the NNRPIM formulation.
文摘In this paper, we consider two interpolations of Birkhoff-type with integer-order derivative. The Birkhoff interpolation is related with collocation method for the corresponding initial or boundary value problems of differential equations. The solvability of the interpolation problems is proved. For Gauss-type interpolating points, error of interpolation approximation is deduced. Also, we give efficient algorithms to implement the concerned interpolations.
文摘Java language is widely used in a variety of development platforms to develop all kinds of application software for its simple and efficient.The programming language owning platform independent is adopted to solve the image flicker,sound loading and other issues by the threading technology,multimedia technology,graphics and point by point comparison techniques.Dynamic real⁃time process simulation is implemented and a two⁃dimensional network of CNC machining simulation system is developed while Java applet application is as a carrier.The simulation results show that the system has a friendly interface and fast calculation speed,and platform portability has a certain practicality and application value.
文摘In order to overcome the possible singularity associated with the Point Interpolation Method(PIM),the Radial Point Interpolation Method(RPIM)was proposed by G.R.Liu.Radial basis functions(RBF)was used in RPIM as basis functions for interpolation.All these radial basis functions include shape parameters.The choice of these shape parameters has been and stays a problematic theme in RBF approximation and interpolation theory.The object of this study is to contribute to the analysis of how these shape parameters affect the accuracy of the radial PIM.The RPIM is studied based on the global Galerkin weak form performed using two integration technics:classical Gaussian integration and the strain smoothing integration scheme.The numerical performance of this method is tested on their behavior on curve fitting,and on three elastic mechanical problems with regular or irregular nodes distributions.A range of recommended shape parameters is obtained from the analysis of different error indexes and also the condition number of the matrix system.All resulting RPIM methods perform very well in term of numerical computation.The Smoothed Radial Point Interpolation Method(SRPIM)shows a higher accuracy,especially in a situation of distorted node scheme.
基金supported by the National Natural Science Foundation of China (10772123,11072160)Natural Science Foundation for Outstanding Young People of Hebei Province (A2009001624),China
文摘A novel extended traction boundary element-free method is proposed to analyze the crack problems of two-dimensional infinite magnetoelectroelastic solid.An extended traction boundary integral equation only involving Cauchy singularity is firstly derived.Then,the extended dislocation densities on the crack surface are expressed as the combination of a characteristic term and unknown weight functions,and the radial point interpolation method is adopted to approximate the unknown weight functions.The numerical scheme of the extended traction boundary element-free method is further established,and an effective numerical procedure is used to evaluate the Cauchy singular integrals.Finally,the stress intensity factor,electric displacement intensity factor and magnetic induction intensity factor are computed for some selected crack problems that contain straight,curved and branched cracks,and good numerical results are obtained.At the same time,the fracture properties of these crack problems are discussed.
