A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth...A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.展开更多
In this paper, the basic formulae for the semi-analytical graded FEM on FGM members are derived. Since FGM parameters vary along three space coordinates, the parameters can be integrated in mechanical equations. There...In this paper, the basic formulae for the semi-analytical graded FEM on FGM members are derived. Since FGM parameters vary along three space coordinates, the parameters can be integrated in mechanical equations. Therefore with the parameters of a given FGM plate, problems of FGM plate under various conditions can be solved. The approach uses 1D discretization to obtain 3D solutions, which is proven to be an effective numerical method for the mechanical analyses of FGM structures. Examples of FGM plates with complex shapes and various holes are presented.展开更多
Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic...Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.展开更多
To improve the grinding quality of robotic belt grinding systems for the workpieces with complex shaped surfaces, new concepts of the dexterity grinding point and the dexterity grinding space are proposed and their ma...To improve the grinding quality of robotic belt grinding systems for the workpieces with complex shaped surfaces, new concepts of the dexterity grinding point and the dexterity grinding space are proposed and their mathematical descriptions are defined. Factors influencing the dexterity grinding space are analyzed. And a method to determine the necessary dexterity grinding space is suggested. Based on particle swarm optimization （PSO） method, a strategy to optimize the grinding robot structural dimensions and position with respect to the grinding wheel is put forward to obtain the necessary dexterity grinding space. Finally, to grind an aerial engine blade, a dedicated PPPRRR （P： prismatic R： rotary） grinding robot structural dimensions and position with respect to the grinding wheel are optimized using the above strategy. According to simulation results, if the blade is placed within the dexterity grinding space, only one gripper and one grinding machine are needed to grind its complex shaped surfaces.展开更多
Unambiguous identification of the measurement methodologies is fundamental to reduce the uncertainty and support traceability of particle shape and size at the nanoscale. In this work, the critical aspects in atomic f...Unambiguous identification of the measurement methodologies is fundamental to reduce the uncertainty and support traceability of particle shape and size at the nanoscale. In this work, the critical aspects in atomic force microscopy measurements, that is, drawbacks on sample preparation, instrumental parameters, image pre-processing, size reconstruction, and tip enlargement, are discussed in reference to quantitative dimensional measurements on different kinds of nanoparticles (inorganic and biological) with different shapes (spherical, cylindrical, complex geometry). Once the cross-section profile is extracted, top-height measurements on isolated nanoparticles of any shape can be achieved with sub-nanometer accuracy. Lateral resolution is affected by the pixel size and shape of the probe, causing dilation in the atomic force microscopy image. For the reconstruction of critical sizes of inorganic non-spherical nanoparticles, a geometric approach that considers the nominal shape because of the synthesis conditions is presented and discussed.展开更多
Due to their high hardness and high strength,VC reinforced hard materials such as high vanadium high-speed steel(HVHSS)are not suitable for machining to obtain complex shape with low cost.Therefore,3D gel printing(3DG...Due to their high hardness and high strength,VC reinforced hard materials such as high vanadium high-speed steel(HVHSS)are not suitable for machining to obtain complex shape with low cost.Therefore,3D gel printing(3DGP)was employed to print HVHSS parts,using highly loaded slurry with 60%solid content as printing slurry.After printing parameters optimization,the printing sample had good surface quality,and obvious printing lines were observed.The extruded filament was in-situ cured,thus enough to maintain the designed shape.Uniform sintering shrinkage with a shrinkage rate of about 15%was obtained in the as-sintered sample with relative density of 99%.The surface roughness decreased from 6.5μm to 3.8μm.Fine carbides(<1μm)and dense microstructure were achieved.Besides,the as-sintered sample had comprehensive performance of HRC60 in hardness,3000 MPa in bend strength,and 20−26 J in impact energy.This study proposed one promising method to directly manufacture complex-shaped hard materials without subsequent machining.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11925204)the 111 Project(No.B14044)。
文摘A high-accuracy multiresolution method is proposed to solve mechanics problems subject to complex shapes or irregular domains.To realize this method,we design a new wavelet basis function,by which we construct a fifth-order numerical scheme for the approximation of multi-dimensional functions and their multiple integrals defined in complex domains.In the solution of differential equations,various derivatives of the unknown function are denoted as new functions.Then,the integral relations between these functions are applied in terms of wavelet approximation of multiple integrals.Therefore,the original equation with derivatives of various orders can be converted to a system of algebraic equations with discrete nodal values of the highest-order derivative.During the application of the proposed method,boundary conditions can be automatically included in the integration operations,and relevant matrices can be assured to exhibit perfect sparse patterns.As examples,we consider several second-order mathematics problems defined on regular and irregular domains and the fourth-order bending problems of plates with various shapes.By comparing the solutions obtained by the proposed method with the exact solutions,the new multiresolution method is found to have a convergence rate of fifth order.The solution accuracy of this method with only a few hundreds of nodes can be much higher than that of the finite element method(FEM)with tens of thousands of elements.In addition,because the accuracy order for direct approximation of a function using the proposed basis function is also fifth order,we may conclude that the accuracy of the proposed method is almost independent of the equation order and domain complexity.
基金Project supported by the National Natural Science Foundation of China (No. 10432030)
文摘In this paper, the basic formulae for the semi-analytical graded FEM on FGM members are derived. Since FGM parameters vary along three space coordinates, the parameters can be integrated in mechanical equations. Therefore with the parameters of a given FGM plate, problems of FGM plate under various conditions can be solved. The approach uses 1D discretization to obtain 3D solutions, which is proven to be an effective numerical method for the mechanical analyses of FGM structures. Examples of FGM plates with complex shapes and various holes are presented.
基金This project is supported by National Natural Science Foundation of China(No.50175031).
文摘Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.
基金National Natural Science Foundation of China （51075013） Beijing Natural Science Foundation （4102035）+1 种基金 Fundamental Research Funds for the Central Universities （YWF-10-01-A09） Research Foundation of State Key Laboratory for Manufacturing Systems Engineering （Xi＇an Jiaotong University）
文摘To improve the grinding quality of robotic belt grinding systems for the workpieces with complex shaped surfaces, new concepts of the dexterity grinding point and the dexterity grinding space are proposed and their mathematical descriptions are defined. Factors influencing the dexterity grinding space are analyzed. And a method to determine the necessary dexterity grinding space is suggested. Based on particle swarm optimization （PSO） method, a strategy to optimize the grinding robot structural dimensions and position with respect to the grinding wheel is put forward to obtain the necessary dexterity grinding space. Finally, to grind an aerial engine blade, a dedicated PPPRRR （P： prismatic R： rotary） grinding robot structural dimensions and position with respect to the grinding wheel are optimized using the above strategy. According to simulation results, if the blade is placed within the dexterity grinding space, only one gripper and one grinding machine are needed to grind its complex shaped surfaces.
文摘Unambiguous identification of the measurement methodologies is fundamental to reduce the uncertainty and support traceability of particle shape and size at the nanoscale. In this work, the critical aspects in atomic force microscopy measurements, that is, drawbacks on sample preparation, instrumental parameters, image pre-processing, size reconstruction, and tip enlargement, are discussed in reference to quantitative dimensional measurements on different kinds of nanoparticles (inorganic and biological) with different shapes (spherical, cylindrical, complex geometry). Once the cross-section profile is extracted, top-height measurements on isolated nanoparticles of any shape can be achieved with sub-nanometer accuracy. Lateral resolution is affected by the pixel size and shape of the probe, causing dilation in the atomic force microscopy image. For the reconstruction of critical sizes of inorganic non-spherical nanoparticles, a geometric approach that considers the nominal shape because of the synthesis conditions is presented and discussed.
基金Projects(2019-ZD08,2020-Z17)supported by the State Key Lab of Advanced Metals and Materials,ChinaProject(52004027)supported by the National Natural Science Foundation of China+2 种基金Project(GDOE[2019]A16)supported by the Guangdong MEPP Fund,ChinaProject(311020012)supported by the Innovation Group Project of Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai),ChinaProject(FRF-GF-20-05A)supported by the Fundamental Research Funds for the Central Universities,China。
文摘Due to their high hardness and high strength,VC reinforced hard materials such as high vanadium high-speed steel(HVHSS)are not suitable for machining to obtain complex shape with low cost.Therefore,3D gel printing(3DGP)was employed to print HVHSS parts,using highly loaded slurry with 60%solid content as printing slurry.After printing parameters optimization,the printing sample had good surface quality,and obvious printing lines were observed.The extruded filament was in-situ cured,thus enough to maintain the designed shape.Uniform sintering shrinkage with a shrinkage rate of about 15%was obtained in the as-sintered sample with relative density of 99%.The surface roughness decreased from 6.5μm to 3.8μm.Fine carbides(<1μm)and dense microstructure were achieved.Besides,the as-sintered sample had comprehensive performance of HRC60 in hardness,3000 MPa in bend strength,and 20−26 J in impact energy.This study proposed one promising method to directly manufacture complex-shaped hard materials without subsequent machining.
