A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization...A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.展开更多
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
We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods...We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods mainly contain shape and topology schemes,with the former changing the surface geometric profile of the structure and the latter changing thematerial distribution topology or hole topology of the structure.In the present acoustic performance optimization,the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure,the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter,and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge.The topology and shape sensitivities of the approach are calculated using the adjoint variable method,which ensures the efficiency of the optimization.The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization.Numerical examples are given to validate the effectiveness of the presented optimization approach.展开更多
The compaction quality of subgrade filler strongly affects subgrade settlement.The main objective of this research is to analyze the macro-and micro-mechanical compaction characteristics of subgrade filler based on th...The compaction quality of subgrade filler strongly affects subgrade settlement.The main objective of this research is to analyze the macro-and micro-mechanical compaction characteristics of subgrade filler based on the real shape of coarse particles.First,an improved Viola-Jones algorithm is employed to establish a digitalized 2D particle database for coarse particle shape evaluation and discrete modeling purposes of subgrade filler.Shape indexes of 2D subgrade filler are then computed and statistically analyzed.Finally,numerical simulations are performed to quantitatively investigate the effects of the aspect ratio(AR)and interparticle friction coefficient(μ)on the macro-and micro-mechanical compaction characteristics of subgrade filler based on the discrete element method(DEM).The results show that with the increasing AR,the coarse particles are narrower,leading to the increasing movement of fine particles during compaction,which indicates that it is difficult for slender coarse particles to inhibit the migration of fine particles.Moreover,the average displacement of particles is strongly influenced by the AR,indicating that their occlusion under power relies on particle shapes.The dis-placement and velocity of fine particles are much greater than those of the coarse particles,which shows that compaction is primarily a migration of fine particles.Under the cyclic load,the interparticle friction coefficientμhas little effect on the internal structure of the sample;under the quasi-static loads,however,the increase inμwill lead to a significant increase in the porosity of the sample.This study could not only provide a novel approach to investigate the compaction mechanism but also establish a new theoretical basis for the evaluation of intelligent subgrade compaction.展开更多
To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection techniq...To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).展开更多
Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with...Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.展开更多
An effective optimization method for the shape/sizing design of composite wing structures is presented with satisfying weight-cutting results. After decoupling, a kind of two-layer cycled optimization strategy suitabl...An effective optimization method for the shape/sizing design of composite wing structures is presented with satisfying weight-cutting results. After decoupling, a kind of two-layer cycled optimization strategy suitable for these integrated shape/sizing optimization is obtained. The uniform design method is used to provide sample points, and approximation models for shape design variables. And the results of sizing optimization are construct- ed with the quadratic response surface method (QRSM). The complex method based on QRSM is used to opti- mize the shape design variables and the criteria method is adopted to optimize the sizing design variables. Compared with the conventional method, the proposed algorithm is more effective and feasible for solving complex composite optimization problems and has good efficiency in weight cutting.展开更多
Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary(around a data hole) inside the domain,...Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary(around a data hole) inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes(grid-staggering,local-nesting and piecewise continuous integration) are designed to deal with the singularity of the Green's function encountered in numerical calculations.For the externally induced part,by setting the velocity potential(or streamfunction) component to zero,the other component of the solution can be computed in two ways:(1) Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.(2) Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting(or piecewise continuous integration),the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point(or along the entire boundary).When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.展开更多
In order to present the microstructures of dynamic recrystallization(DRX) in different deformation zones of hot extruded NiTi shape memory alloy(SMA) pipe coupling,a simulation approach combining finite element method...In order to present the microstructures of dynamic recrystallization(DRX) in different deformation zones of hot extruded NiTi shape memory alloy(SMA) pipe coupling,a simulation approach combining finite element method(FEM) with cellular automaton(CA) was developed and the relationship between the macroscopic field variables and the microscopic internal variables was established.The results show that there exists a great distinction among the microstructures in different zones of pipe coupling because deformation histories of these regions are diverse.Large plastic deformation may result in fine recrystallized grains,whereas the recrystallized grains may grow very substantially if there is a rigid translation during the deformation,even if the final plastic strain is very large.As a consequence,the deformation history has a significant influence on the evolution path of the DRX as well as the final microstructures of the DRX,including the morphology,the mean grain size and the recrystallization fraction.展开更多
The goal of the arterial graft design problem is to find an optimal graft built on an occluded artery, which can be mathematically modeled by a fluid based shape optimization problem. The smoothness of the graft is on...The goal of the arterial graft design problem is to find an optimal graft built on an occluded artery, which can be mathematically modeled by a fluid based shape optimization problem. The smoothness of the graft is one of the important aspects in the arterial graft design problem since it affects the flow of the blood significantly. As an attractive design tool for this problem, level set methods are quite efficient for obtaining better shape of the graft. In this paper, a cubic spline level set method and a radial basis function level set method are designed to solve the arterial graft design problem. In both approaches, the shape of the arterial graft is implicitly tracked by the zero-level contour of a level set function and a high level of smoothness of the graft is achieved. Numerical results show the efficiency of the algorithms in the arterial graft design.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
Grain scale plasticity of NiTi shape memory alloy(SMA)during uniaxial compression deformation at 400℃was investigated through two-dimensional crystal plasticity finite element simulation and corresponding analysis ba...Grain scale plasticity of NiTi shape memory alloy(SMA)during uniaxial compression deformation at 400℃was investigated through two-dimensional crystal plasticity finite element simulation and corresponding analysis based on the obtained orientation data.Stress and strain distributions of the deformed NiTi SMA samples confirm that there exhibits a heterogeneous plastic deformation at grain scale.Statistically stored dislocation(SSD)density and geometrically necessary dislocation(GND)density were further used in order to illuminate the microstructure evolution during uniaxial compression.SSD is responsible for sustaining plastic deformation and it increases along with the increase of plastic strain.GND plays an important role in accommodating compatible deformation between individual grains and thus it is correlated with the misorientation between neighboring grains,namely,a high GND density corresponds to large misorientation between grains and a low GND density corresponds to small misorientation between grains.展开更多
In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,wh...In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.展开更多
In this work, a design procedure extending the B-spline based finite cell method into shape optimization is developed for axisymmetric solids involving the centrifugal force effect. We first replace the traditional co...In this work, a design procedure extending the B-spline based finite cell method into shape optimization is developed for axisymmetric solids involving the centrifugal force effect. We first replace the traditional conforming mesh in the finite element method with structured cells that are fixed during the whole design process with a view to avoid the sophisticated re-meshing and eventual mesh distortion.Then, B-spline shape functions are further implemented to yield a high-order continuity field along the cell boundary in stress analysis. By means of the implicit description of the shape boundary, stress sensitivity is analytically derived with respect to shape design variables. Finally, we illustrate the efficiency and accuracy of the proposed protocol by several numerical test cases as well as a whole design procedure carried out on an aeronautic turbine disk.展开更多
This paper proposed a permanent magnet optimization method to suppress the air gap flux density harmonic of permanent magnet synchronous motor(PMSM).The method corrected the effective air gap length of the motor,calcu...This paper proposed a permanent magnet optimization method to suppress the air gap flux density harmonic of permanent magnet synchronous motor(PMSM).The method corrected the effective air gap length of the motor,calculated the magnetization length of the permanent in the case of parallel magnetization,and took the influence of the permanent magnet relative permeability into consideration.Based on these works,for a given sinusoidal air gap flux density waveform,the corresponding structural parameters can be calculated,so as to achieve the optimization of the permanent magnet.By using this method to optimize the shape of the magnet,the fundamental wave of the air gap flux density can be retained to the greatest extent,so as to eliminate harmonics and maintain the output capacity at the same time.The feasibility and accuracy of the method have been verified by finite element analysis(FEA)and prototype machine experiment.This method is simple and time-saving,and has a satisfactory accuracy,which provides a reference method for permanent magnet optimization of PMSM.展开更多
The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and nea...The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.展开更多
Trapezoidal pulse shaping algorithm is widely applied to improve signal-to-noise ratio(SNR), throughput and energy resolution with the properties of noise suppression, pile-up pulse separation and ballistic deficit co...Trapezoidal pulse shaping algorithm is widely applied to improve signal-to-noise ratio(SNR), throughput and energy resolution with the properties of noise suppression, pile-up pulse separation and ballistic deficit correction. The algorithm can be acquired by z transform method which is easier for derivation. However, the baseline drift of trapezoidal pulse appears because the noise superimposes on the input signal. In this paper,two new methods based on convergence analysis and noise suppression are proposed to remove the baseline drift resulting from trapezoidal pulse shaping. Simulations and experimental tests are carried out to verify the methods. The results demonstrate that the proposed methods can remove baseline drift in trapezoidal pulse shaping.展开更多
Surface tension is one of important physical features of melt alloy. Many properties of melt alloy, such as graphite shape of cast iron and modified microstructure of aluminum alloy, can be evaluated by means of surfa...Surface tension is one of important physical features of melt alloy. Many properties of melt alloy, such as graphite shape of cast iron and modified microstructure of aluminum alloy, can be evaluated by means of surface tension. In order to evaluate and control the melt quality in-situ melting operation, the authors advanced a new method and developed an automatic device for fast measuring surface tension of melt alloy and applied it to the practice of rapid identifying graphite shape of cast iron. In this paper, the principle of fast measuring surface tension, the construction of the automatic measurement device and the examples of evaluating graphite shape of cast iron based on the new method and device are discussed.展开更多
It is necessary to reduce the currents of poloidal field(PF) coils as small as possible, during the static equilibrium design procedure of Experimental Advanced Superconductive Tokamak(EAST). The quasi-snowflake(QSF) ...It is necessary to reduce the currents of poloidal field(PF) coils as small as possible, during the static equilibrium design procedure of Experimental Advanced Superconductive Tokamak(EAST). The quasi-snowflake(QSF) divertor configuration is studied in this paper. Starting from a standard QSF plasma equilibrium, a new QSF equilibrium with 300 kA total plasma current is designed. In order to reduce the currents of PF6 and PF14, the influence of plasma shape on PF coil current distribution is analyzed. A fixed boundary equilibrium solver based on a non-rigid plasma model is used to calculate the flux distribution and PF coil current distribution. Then the plasma shape parameters are studied by the orthogonal method. According to the result, the plasma shape is redefined, and the calculated equilibrium shows that the currents of PF6 and PF14 are reduced by 3.592 kA and 2.773 kA, respectively.展开更多
Photoacoustic(PA) imaging has drawn tremendous research interest for various applications in biomedicine and experienced exponential growth over the past decade. Since the scattering effect of biological tissue on ult...Photoacoustic(PA) imaging has drawn tremendous research interest for various applications in biomedicine and experienced exponential growth over the past decade. Since the scattering effect of biological tissue on ultrasound is two-to three-orders magnitude weaker than that of light, photoacoustic imaging can effectively improve the imaging depth.However, as the depth of imaging further increases, the incident light is seriously affected by scattering that the generated photoacoustic signal is very weak and the signal-to-noise ratio(SNR) is quite low. Low SNR signals can reduce imaging quality and even cause imaging failure. In this paper, we proposed a new wavefront shaping and imaging method of low SNR photoacoustic signal using digital micromirror device(DMD) based superpixel method. We combined the superpixel method with DMD to modulate the phase and amplitude of the incident light, and the genetic algorithm(GA) was used as the wavefront shaping algorithm. The enhancement of the photoacoustic signal reached 10.46. Then we performed scanning imaging by moving the absorber with the translation stage. A clear image with contrast of 8.57 was obtained while imaging with original photoacoustic signals could not be achieved. The proposed method opens new perspectives for imaging with weak photoacoustic signals.展开更多
基金supported by a Major Research Project in Higher Education Institutions in Henan Province,with Project Number 23A560015.
文摘A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.
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supported by the National Natural Science Foundation of China (NSFC)under Grant Nos.12172350,11772322 and 11702238。
文摘We propose a combined shape and topology optimization approach in this research for 3D acoustics by using the isogeometric boundary element method with subdivision surfaces.The existing structural optimization methods mainly contain shape and topology schemes,with the former changing the surface geometric profile of the structure and the latter changing thematerial distribution topology or hole topology of the structure.In the present acoustic performance optimization,the coordinates of the control points in the subdivision surfaces fine mesh are selected as the shape design parameters of the structure,the artificial density of the sound absorbing material covered on the structure surface is set as the topology design parameter,and the combined topology and shape optimization approach is established through the sound field analysis of the subdivision surfaces boundary element method as a bridge.The topology and shape sensitivities of the approach are calculated using the adjoint variable method,which ensures the efficiency of the optimization.The geometric jaggedness and material distribution discontinuities that appear in the optimization process are overcome to a certain degree by the multiresolution method and solid isotropic material with penalization.Numerical examples are given to validate the effectiveness of the presented optimization approach.
基金This work was supported by the National Key R&D Program‘Transportation Infrastructure’project(No.2022YFB2603400).
文摘The compaction quality of subgrade filler strongly affects subgrade settlement.The main objective of this research is to analyze the macro-and micro-mechanical compaction characteristics of subgrade filler based on the real shape of coarse particles.First,an improved Viola-Jones algorithm is employed to establish a digitalized 2D particle database for coarse particle shape evaluation and discrete modeling purposes of subgrade filler.Shape indexes of 2D subgrade filler are then computed and statistically analyzed.Finally,numerical simulations are performed to quantitatively investigate the effects of the aspect ratio(AR)and interparticle friction coefficient(μ)on the macro-and micro-mechanical compaction characteristics of subgrade filler based on the discrete element method(DEM).The results show that with the increasing AR,the coarse particles are narrower,leading to the increasing movement of fine particles during compaction,which indicates that it is difficult for slender coarse particles to inhibit the migration of fine particles.Moreover,the average displacement of particles is strongly influenced by the AR,indicating that their occlusion under power relies on particle shapes.The dis-placement and velocity of fine particles are much greater than those of the coarse particles,which shows that compaction is primarily a migration of fine particles.Under the cyclic load,the interparticle friction coefficientμhas little effect on the internal structure of the sample;under the quasi-static loads,however,the increase inμwill lead to a significant increase in the porosity of the sample.This study could not only provide a novel approach to investigate the compaction mechanism but also establish a new theoretical basis for the evaluation of intelligent subgrade compaction.
基金supported by the the National Science and Technology Council(Grant Number:NSTC 112-2221-E239-022).
文摘To solve the Laplacian problems,we adopt a meshless method with the multiquadric radial basis function(MQRBF)as a basis whose center is distributed inside a circle with a fictitious radius.A maximal projection technique is developed to identify the optimal shape factor and fictitious radius by minimizing a merit function.A sample function is interpolated by theMQ-RBF to provide a trial coefficient vector to compute the merit function.We can quickly determine the optimal values of the parameters within a preferred rage using the golden section search algorithm.The novel method provides the optimal values of parameters and,hence,an optimal MQ-RBF;the performance of the method is validated in numerical examples.Moreover,nonharmonic problems are transformed to the Poisson equation endowed with a homogeneous boundary condition;this can overcome the problem of these problems being ill-posed.The optimal MQ-RBF is extremely accurate.We further propose a novel optimal polynomial method to solve the nonharmonic problems,which achieves high precision up to an order of 10^(−11).
文摘Accurately approximating higher order derivatives is an inherently difficult problem. It is shown that a random variable shape parameter strategy can improve the accuracy of approximating higher order derivatives with Radial Basis Function methods. The method is used to solve fourth order boundary value problems. The use and location of ghost points are examined in order to enforce the extra boundary conditions that are necessary to make a fourth-order problem well posed. The use of ghost points versus solving an overdetermined linear system via least squares is studied. For a general fourth-order boundary value problem, the recommended approach is to either use one of two novel sets of ghost centers introduced here or else to use a least squares approach. When using either ghost centers or least squares, the random variable shape parameter strategy results in significantly better accuracy than when a constant shape parameter is used.
文摘An effective optimization method for the shape/sizing design of composite wing structures is presented with satisfying weight-cutting results. After decoupling, a kind of two-layer cycled optimization strategy suitable for these integrated shape/sizing optimization is obtained. The uniform design method is used to provide sample points, and approximation models for shape design variables. And the results of sizing optimization are construct- ed with the quadratic response surface method (QRSM). The complex method based on QRSM is used to opti- mize the shape design variables and the criteria method is adopted to optimize the sizing design variables. Compared with the conventional method, the proposed algorithm is more effective and feasible for solving complex composite optimization problems and has good efficiency in weight cutting.
基金supported by the Office of Naval Research (Grant No.N000141010778) to the University of Oklahomathe National Natural Sciences Foundation of China (Grant Nos. 40930950,41075043,and 4092116037) to the Institute of Atmospheric Physicsprovided by NOAA/Office of Oceanic and Atmospheric Research under NOAA-University of Oklahoma Cooperative Agreement No. (NA17RJ1227),U.S. Department of Commerce
文摘Built on the integral formulas in Part I,numerical methods are developed for computing velocity potential and streamfunction in a limited domain.When there is no inner boundary(around a data hole) inside the domain,the total solution is the sum of the internally and externally induced parts.For the internally induced part,three numerical schemes(grid-staggering,local-nesting and piecewise continuous integration) are designed to deal with the singularity of the Green's function encountered in numerical calculations.For the externally induced part,by setting the velocity potential(or streamfunction) component to zero,the other component of the solution can be computed in two ways:(1) Solve for the density function from its boundary integral equation and then construct the solution from the boundary integral of the density function.(2) Use the Cauchy integral to construct the solution directly.The boundary integral can be discretized on a uniform grid along the boundary.By using local-nesting(or piecewise continuous integration),the scheme is refined to enhance the discretization accuracy of the boundary integral around each corner point(or along the entire boundary).When the domain is not free of data holes,the total solution contains a data-hole-induced part,and the Cauchy integral method is extended to construct the externally induced solution with irregular external and internal boundaries.An automated algorithm is designed to facilitate the integrations along the irregular external and internal boundaries.Numerical experiments are performed to evaluate the accuracy and efficiency of each scheme relative to others.
基金Projects(51305091,51475101)supported by the National Natural Science Foundation of ChinaProject(20132304120025)supported by Specialized Research Fund for the Doctoral Program of Higher Education,China
文摘In order to present the microstructures of dynamic recrystallization(DRX) in different deformation zones of hot extruded NiTi shape memory alloy(SMA) pipe coupling,a simulation approach combining finite element method(FEM) with cellular automaton(CA) was developed and the relationship between the macroscopic field variables and the microscopic internal variables was established.The results show that there exists a great distinction among the microstructures in different zones of pipe coupling because deformation histories of these regions are diverse.Large plastic deformation may result in fine recrystallized grains,whereas the recrystallized grains may grow very substantially if there is a rigid translation during the deformation,even if the final plastic strain is very large.As a consequence,the deformation history has a significant influence on the evolution path of the DRX as well as the final microstructures of the DRX,including the morphology,the mean grain size and the recrystallization fraction.
基金Supported by National Foundation of Natural Science(11471092)Natural Science Foundation of Zhejiang Province(LZ13A010003)Foundation of Zhejiang Educational Committee(Y201121891)
文摘The goal of the arterial graft design problem is to find an optimal graft built on an occluded artery, which can be mathematically modeled by a fluid based shape optimization problem. The smoothness of the graft is one of the important aspects in the arterial graft design problem since it affects the flow of the blood significantly. As an attractive design tool for this problem, level set methods are quite efficient for obtaining better shape of the graft. In this paper, a cubic spline level set method and a radial basis function level set method are designed to solve the arterial graft design problem. In both approaches, the shape of the arterial graft is implicitly tracked by the zero-level contour of a level set function and a high level of smoothness of the graft is achieved. Numerical results show the efficiency of the algorithms in the arterial graft design.
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Projects(51475101,51305091,51305092)supported by the National Natural Science Foundation of China
文摘Grain scale plasticity of NiTi shape memory alloy(SMA)during uniaxial compression deformation at 400℃was investigated through two-dimensional crystal plasticity finite element simulation and corresponding analysis based on the obtained orientation data.Stress and strain distributions of the deformed NiTi SMA samples confirm that there exhibits a heterogeneous plastic deformation at grain scale.Statistically stored dislocation(SSD)density and geometrically necessary dislocation(GND)density were further used in order to illuminate the microstructure evolution during uniaxial compression.SSD is responsible for sustaining plastic deformation and it increases along with the increase of plastic strain.GND plays an important role in accommodating compatible deformation between individual grains and thus it is correlated with the misorientation between neighboring grains,namely,a high GND density corresponds to large misorientation between grains and a low GND density corresponds to small misorientation between grains.
文摘In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.
基金supported by the National Natura Science Foundation of China (Grant 51275424)973 Program (Gran2011CB610304)+1 种基金Research Fund for the Doctoral Program of Higher Education of China (Grant 20126102130003)the opening project (Grant KFJJ13-6M) of the State Key Laboratory of Explosion Science and Technology (Beijing Institute of Technology)
文摘In this work, a design procedure extending the B-spline based finite cell method into shape optimization is developed for axisymmetric solids involving the centrifugal force effect. We first replace the traditional conforming mesh in the finite element method with structured cells that are fixed during the whole design process with a view to avoid the sophisticated re-meshing and eventual mesh distortion.Then, B-spline shape functions are further implemented to yield a high-order continuity field along the cell boundary in stress analysis. By means of the implicit description of the shape boundary, stress sensitivity is analytically derived with respect to shape design variables. Finally, we illustrate the efficiency and accuracy of the proposed protocol by several numerical test cases as well as a whole design procedure carried out on an aeronautic turbine disk.
文摘This paper proposed a permanent magnet optimization method to suppress the air gap flux density harmonic of permanent magnet synchronous motor(PMSM).The method corrected the effective air gap length of the motor,calculated the magnetization length of the permanent in the case of parallel magnetization,and took the influence of the permanent magnet relative permeability into consideration.Based on these works,for a given sinusoidal air gap flux density waveform,the corresponding structural parameters can be calculated,so as to achieve the optimization of the permanent magnet.By using this method to optimize the shape of the magnet,the fundamental wave of the air gap flux density can be retained to the greatest extent,so as to eliminate harmonics and maintain the output capacity at the same time.The feasibility and accuracy of the method have been verified by finite element analysis(FEA)and prototype machine experiment.This method is simple and time-saving,and has a satisfactory accuracy,which provides a reference method for permanent magnet optimization of PMSM.
文摘The wave propagation behavior in an elastic wedge-shaped medium with an arbitrary shaped cylindrical canyon at its vertex has been studied.Numerical computation of the wave displacement field is carried out on and near the canyon surfaces using weighted-residuals(moment method).The wave displacement fields are computed by the residual method for the cases of elliptic,circular,rounded-rectangular and flat-elliptic canyons,The analysis demonstrates that the resulting surface displacement depends,as in similar previous analyses,on several factors including,but not limited,to the angle of the wedge,the geometry of the vertex,the frequencies of the incident waves,the angles of incidence,and the material properties of the media.The analysis provides intriguing results that help to explain geophysical observations regarding the amplification of seismic energy as a function of site conditions.
基金Supported by National High Technology Research and Development Program of China(863 Program)(No.2012AA061804-03)
文摘Trapezoidal pulse shaping algorithm is widely applied to improve signal-to-noise ratio(SNR), throughput and energy resolution with the properties of noise suppression, pile-up pulse separation and ballistic deficit correction. The algorithm can be acquired by z transform method which is easier for derivation. However, the baseline drift of trapezoidal pulse appears because the noise superimposes on the input signal. In this paper,two new methods based on convergence analysis and noise suppression are proposed to remove the baseline drift resulting from trapezoidal pulse shaping. Simulations and experimental tests are carried out to verify the methods. The results demonstrate that the proposed methods can remove baseline drift in trapezoidal pulse shaping.
文摘Surface tension is one of important physical features of melt alloy. Many properties of melt alloy, such as graphite shape of cast iron and modified microstructure of aluminum alloy, can be evaluated by means of surface tension. In order to evaluate and control the melt quality in-situ melting operation, the authors advanced a new method and developed an automatic device for fast measuring surface tension of melt alloy and applied it to the practice of rapid identifying graphite shape of cast iron. In this paper, the principle of fast measuring surface tension, the construction of the automatic measurement device and the examples of evaluating graphite shape of cast iron based on the new method and device are discussed.
基金Project supported by the National Natural Science Foundation of China(Grant No.51677051)the Institute of Plasma Physics,Chinese Academy of Sciences
文摘It is necessary to reduce the currents of poloidal field(PF) coils as small as possible, during the static equilibrium design procedure of Experimental Advanced Superconductive Tokamak(EAST). The quasi-snowflake(QSF) divertor configuration is studied in this paper. Starting from a standard QSF plasma equilibrium, a new QSF equilibrium with 300 kA total plasma current is designed. In order to reduce the currents of PF6 and PF14, the influence of plasma shape on PF coil current distribution is analyzed. A fixed boundary equilibrium solver based on a non-rigid plasma model is used to calculate the flux distribution and PF coil current distribution. Then the plasma shape parameters are studied by the orthogonal method. According to the result, the plasma shape is redefined, and the calculated equilibrium shows that the currents of PF6 and PF14 are reduced by 3.592 kA and 2.773 kA, respectively.
基金Project supported by the National Key Research and Development Program of China(Grant No.2017YFB1104500)the Beijing Natural Science Foundation,China(Grant No.7182091)+1 种基金the National Natural Science Foundation of China(Grant No.21627813)the Research Projects on Biomedical Transformation of China–Japan Friendship Hospital(Grant No.PYBZ1801)。
文摘Photoacoustic(PA) imaging has drawn tremendous research interest for various applications in biomedicine and experienced exponential growth over the past decade. Since the scattering effect of biological tissue on ultrasound is two-to three-orders magnitude weaker than that of light, photoacoustic imaging can effectively improve the imaging depth.However, as the depth of imaging further increases, the incident light is seriously affected by scattering that the generated photoacoustic signal is very weak and the signal-to-noise ratio(SNR) is quite low. Low SNR signals can reduce imaging quality and even cause imaging failure. In this paper, we proposed a new wavefront shaping and imaging method of low SNR photoacoustic signal using digital micromirror device(DMD) based superpixel method. We combined the superpixel method with DMD to modulate the phase and amplitude of the incident light, and the genetic algorithm(GA) was used as the wavefront shaping algorithm. The enhancement of the photoacoustic signal reached 10.46. Then we performed scanning imaging by moving the absorber with the translation stage. A clear image with contrast of 8.57 was obtained while imaging with original photoacoustic signals could not be achieved. The proposed method opens new perspectives for imaging with weak photoacoustic signals.