A generalization of the direct method of Clarkson and Kruskal for finding similarity reductions of partial differential equations with arbitrary functions is found and discussed for the generalized Burgers equation. T...A generalization of the direct method of Clarkson and Kruskal for finding similarity reductions of partial differential equations with arbitrary functions is found and discussed for the generalized Burgers equation. The corresponding reductions and the exact solutions due to the methods of the ordinary differential equations are then given by the methods. The results given here answer partially an open problem proposed by Clarkson, that is how to develop the direct method to seek symmetry reductions of nonlinear PDEs with arbitrary functions.展开更多
Two methods based on a slight modification of the regular traffic assignmentalgorithms are proposed to directly compute turn flows instead of estimating them from link flows orobtaining them by expanding the networks....Two methods based on a slight modification of the regular traffic assignmentalgorithms are proposed to directly compute turn flows instead of estimating them from link flows orobtaining them by expanding the networks. The first one is designed on the path-turn incidencerelationship, and it is similar to the computational procedure of link flows. It applies to thetraffic assignment algorithms that can provide detailed path structures. The second utilizes thelink-turn incidence relationship and the conservation of flow on links, a law deriving from thisrelationship. It is actually an improved version of Dial's logit assignment algorithm. The proposedapproaches can avoid the shortcomings both of the estimation methods, e. g. Furness's model andFrator's model, and of the network-expanding method in precision, stability and computation scale.Finally, they are validated by numerical examples.展开更多
Magnesium and its alloys are promising candidates for a new generation of biodegradable metals in orthopaedic applications due to their excellent biocompatibility,biodegradability,and mechanical properties that are si...Magnesium and its alloys are promising candidates for a new generation of biodegradable metals in orthopaedic applications due to their excellent biocompatibility,biodegradability,and mechanical properties that are similar to natural bone.However,direct in vitro assessment of these materials in the presence of cells is complicated by degradation products from the alloy that lead to a false positive for the most commonly used cell adhesion and cell proliferation assays.In this paper,a cyanine dye was used to quantitatively evaluate the in vitro biocompatibility of a Mg AZ31 alloy by both direct and indirect methods.The cytotoxicity of the corrosion products was evaluated via an indirect method;a 25%decrease in cell viability compared to control samples was observed.Moreover,direct assessment of cell adhesion and proliferation showed a statistically significant increase in cell number at the surface after 72 h.In addition,the degradation rate and surface characteristics of the Mg AZ31 alloy were evaluated for both direct and indirect tests.The degradation rate was unaffected by the presence of cells while evidence of an increase in calcium phosphate deposition on the magnesium alloy surface in the presence of cells was observed.This study demonstrates that a cyanine dye based assay provides a more accurate assessment of the overall in vitro biocompatibility of biodegradable metals than the more commonly used assays reported in the literature to date.展开更多
This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite differenc...This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.展开更多
In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear conve...In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear convection-diffusion problems.In the spatial discretization,both the original DDG methods and the refined DDG methods with interface corrections are considered.In the time discretization,the convection term is treated explicitly and the diffusion term implicitly.By the energy method,we show that the corresponding fully discrete schemes are unconditionally stable,in the sense that the time-stepis only required to be upper bounded by a constant which is independent of the mesh size h.Opti-mal error estimate is also obtained by the aid of a special global projection.Numerical experiments are given to verify the stability and accuracy of the proposed schemes.展开更多
A comparison of direct integration methods is madeand their efficiency is investigated for impact problems.New-mark,Wilson-θ,Central Difference and Houbolt Methodsare used as direct integration methods.Impact analysi...A comparison of direct integration methods is madeand their efficiency is investigated for impact problems.New-mark,Wilson-θ,Central Difference and Houbolt Methodsare used as direct integration methods.Impact analysisincludes that of elastic and large deformation based uponupdated Lagrangian including buckling check.The resultsshow that the direct integration methods give differentresults in different contact-impact cases.展开更多
<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the...<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>展开更多
This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis techniq...This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.展开更多
Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the random...Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the randomness of structural parameters,working condition and vibration environment are considered for fatigue life predication and reliability assessment.First,the lowcycle fatigue problem is modelled as stochastic static system with random parameters,while the high-cycle fatigue problem is considered as stochastic dynamic system under random excitations.Then,to deal with the two failure modes,the novel Direct Probability Integral Method(DPIM)is proposed,which is efficient and accurate for solving stochastic static and dynamic systems.The probability density functions of accumulated damage and fatigue life of turbine blade for low-cycle and high-cycle fatigue problems are achieved,respectively.Furthermore,the time–frequency hybrid method is advanced to enhance the computational efficiency for governing equation of system.Finally,the results of typical examples demonstrate high accuracy and efficiency of the proposed method by comparison with Monte Carlo simulation and other methods.It is indicated that the DPIM is a unified method for predication of random fatigue life for low-cycle and highcycle fatigue problems.The rotational speed,density,fatigue strength coefficient,and fatigue plasticity index have a high sensitivity to fatigue reliability of engine turbine blade.展开更多
To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direc...To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement.展开更多
The principle of direct method used in optimal control problem is introduced. Details of applying this method to flight trajectory generation are presented including calculation of velocity and controls histories. And...The principle of direct method used in optimal control problem is introduced. Details of applying this method to flight trajectory generation are presented including calculation of velocity and controls histories. And capabilities of flight and propulsion systems are considered also. Combined with digital terrain map technique, the direct method is applied to the three dimensional trajectory optimization for low altitude penetration, and simplex algorithm is used to solve the parameters in optimization. For the small number of parameters, the trajectory can be optimized in real time on board.展开更多
This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic So...This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.展开更多
A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is refo...A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.展开更多
Mechanical engineering structures and structural components are often subjected to cyclic thermomechanical loading which stresses their material beyond its elastic limits well inside the inelastic regime.Depending on ...Mechanical engineering structures and structural components are often subjected to cyclic thermomechanical loading which stresses their material beyond its elastic limits well inside the inelastic regime.Depending on the level of loading inelastic strains may lead either to failure,due to low cycle fatigue or ratcheting,or to safety,through elastic shakedown.Thus,it is important to estimate the asymptotic stress state of such structures.This state may be determined by cumbersome incremental time-stepping calculations.Direct methods,alternatively,have big computational advantages as they focus on the characteristics of these states and try to establish them,in a direct way,right from the beginning of the calculations.Among the very few such general-purpose direct methods,a powerful direct method which has been called RSDM has appeared in the literature.The method may directly predict any asymptotic state when the exact time history of the loading is known.The advantage of the method is due to the fact that it addresses the physics of the asymptotic cycle and exploits the cyclic nature of its expected residual stress distribution.Based on RSDM a method for the shakedown analysis of structures,called RSDM-S has also been developed.Despite most direct methods for shakedown,RSDM-S does not need an optimization algorithm for its implementation.Both RSDM and RSDM-S may be implemented in any Finite Element Code.A thorough review of both these methods,together with examples of implementation are presented herein.展开更多
One of the essential points of the direct-method single-wavelength anomalous diffraction （SAD） phasing for proteins is to express the bimodal SAD phase distribution by the sum of two Gaussian functions peaked respec...One of the essential points of the direct-method single-wavelength anomalous diffraction （SAD） phasing for proteins is to express the bimodal SAD phase distribution by the sum of two Gaussian functions peaked respectively at φh″＋｜△φh｜ and φh″-｜△φh｜. The probability for △φh being positive （P＋） can be derived based on the Cochran distribution in direct methods. Hence the SAD phase ambiguity can be resolved by multiplying the Gaussian function peaked at φh″＋｜△φh｜ with P＋ and multiplying the Gaussian function peaked at φh″-｜△φh｜ with P_ （=1- P＋）. The direct-method SAD h phasing has been proved powerful in breaking SAD phase ambiguities, in particular when anomalous-scattering signals are weak. However, the approximation of bimodal phase distributions by the sum of two Gaussian functions introduces considerable errors. In this paper we show that a much better approximation can be achieved by replacing the two Gaussian functions with two von Mises distributions. Test results showed that this leads to significant improvement on the efficiency of direct-method SAD-phasing.展开更多
Low-thrust Earth-orbit transfers with 10^- 5-order thrust-to-weight ratios involve a large number of orbital revolutions which poses a real challenge to trajectory optimization. This article develops a direct method t...Low-thrust Earth-orbit transfers with 10^- 5-order thrust-to-weight ratios involve a large number of orbital revolutions which poses a real challenge to trajectory optimization. This article develops a direct method to optimize minimum-time low-thrust many-revolution Earth-orbit transfers. A parameterized control law in each orbit, in the form of the true optimal control, is proposed, and the time history of the parameters governing the control law is interpolated through a finite number of nodal values. The orbital averaging method is used to significantly reduce the computational workload and the trajectory optimization is conducted based on the orbital averaging dynamics expressed by nonsingular equinoctial elements. Furthermore, Earth＇s shadowing and perturbation effects are taken into account. The optimal transfer problem is thus converted to the parameter optimization problem that can be solved by nonlinear programming. Taking advantage of the mapping between the parameterized control law and the Lyapunov control law, a technique is proposed to acquire good initial guesses for optimization variables, which results in enlarged convergence domain of the direct optimization method. Numerical examples of optimal Earth-orbit transfers are presented.展开更多
Measurement of soil bulk density is important for understanding the physical, chemical, and biological properties of soil. Accurate and rapid soil bulk density measurement techniques play a significant role in agricul...Measurement of soil bulk density is important for understanding the physical, chemical, and biological properties of soil. Accurate and rapid soil bulk density measurement techniques play a significant role in agricultural experimental research. This review is a comprehensive summary of existing measurement methods and evaluates their advantages, disadvantages, potential sources of error,and directions for future development. These techniques can be broadly categorised as direct and indirect methods. Direct methods include core, clod, and excavation sampling, whereas indirect methods include the radiation and regression approaches. The core method is most widely used, but it is time consuming and difficult to use for sampling multiple soil depths. The size of the coring cylinder used, operator experience, sampling depth, and in-situ soil moisture content significantly affect its accuracy. The clod method is suitable for use with heavy clay soils, and its accuracy is dependent on equipment calibration, drying time, and operator experience, but the process is complicated and time consuming. Excavation techniques are most commonly used to evaluate the bulk density of forest soils, but have major limitations as they cannot be used in soils with large pores and their measurement accuracy is strongly influenced by soil texture and the type of analysis selected. The indirect methods appear to have greater accuracy than direct approaches, but have higher costs, are more complex, and require greater operator experience. One such approach uses gamma radiation, and its accuracy is strongly influenced by soil depth. Regression methods are economical as they can make indirect measurements, but these depend on good, quality data of soil texture and organic matter content and geographical and climatic properties. Also, like most of the other approaches, its accuracy decreases with sampling depth.展开更多
Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in prac...Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.展开更多
Al-Al3Ti composites were prepared by a direct reaction method, in which Al3Ti was formed by the reaction of Ti and Al in aluminum alloy melt. The morphology of Al3Ti changes apparently from the fine particle, needle-l...Al-Al3Ti composites were prepared by a direct reaction method, in which Al3Ti was formed by the reaction of Ti and Al in aluminum alloy melt. The morphology of Al3Ti changes apparently from the fine particle, needle-like to large block with the increase of Al3Ti content. The addition of magnesium can markedly change the morphology of Al3Ti and reduce their size. Short rod-like Al3Ti was formed and homogeneous distribution was obtained with the addition of 3 wt.% Mg. The effect of Al3Ti and Mg on the microstructure of Al-Al3Ti composites and the mechanism were also discussed.展开更多
Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed ...Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.展开更多
基金the National Natural Science Foundation of China(1 990 1 0 2 7)
文摘A generalization of the direct method of Clarkson and Kruskal for finding similarity reductions of partial differential equations with arbitrary functions is found and discussed for the generalized Burgers equation. The corresponding reductions and the exact solutions due to the methods of the ordinary differential equations are then given by the methods. The results given here answer partially an open problem proposed by Clarkson, that is how to develop the direct method to seek symmetry reductions of nonlinear PDEs with arbitrary functions.
文摘Two methods based on a slight modification of the regular traffic assignmentalgorithms are proposed to directly compute turn flows instead of estimating them from link flows orobtaining them by expanding the networks. The first one is designed on the path-turn incidencerelationship, and it is similar to the computational procedure of link flows. It applies to thetraffic assignment algorithms that can provide detailed path structures. The second utilizes thelink-turn incidence relationship and the conservation of flow on links, a law deriving from thisrelationship. It is actually an improved version of Dial's logit assignment algorithm. The proposedapproaches can avoid the shortcomings both of the estimation methods, e. g. Furness's model andFrator's model, and of the network-expanding method in precision, stability and computation scale.Finally, they are validated by numerical examples.
基金We gratefully acknowledge the Ministry of Education in the Kingdom of Saudi Arabia for financial support.
文摘Magnesium and its alloys are promising candidates for a new generation of biodegradable metals in orthopaedic applications due to their excellent biocompatibility,biodegradability,and mechanical properties that are similar to natural bone.However,direct in vitro assessment of these materials in the presence of cells is complicated by degradation products from the alloy that lead to a false positive for the most commonly used cell adhesion and cell proliferation assays.In this paper,a cyanine dye was used to quantitatively evaluate the in vitro biocompatibility of a Mg AZ31 alloy by both direct and indirect methods.The cytotoxicity of the corrosion products was evaluated via an indirect method;a 25%decrease in cell viability compared to control samples was observed.Moreover,direct assessment of cell adhesion and proliferation showed a statistically significant increase in cell number at the surface after 72 h.In addition,the degradation rate and surface characteristics of the Mg AZ31 alloy were evaluated for both direct and indirect tests.The degradation rate was unaffected by the presence of cells while evidence of an increase in calcium phosphate deposition on the magnesium alloy surface in the presence of cells was observed.This study demonstrates that a cyanine dye based assay provides a more accurate assessment of the overall in vitro biocompatibility of biodegradable metals than the more commonly used assays reported in the literature to date.
文摘This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.
基金the NSFC grant 11871428the Nature Science Research Program for Colleges and Universities of Jiangsu Province grant 20KJB110011Qiang Zhang:Research supported by the NSFC grant 11671199。
文摘In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear convection-diffusion problems.In the spatial discretization,both the original DDG methods and the refined DDG methods with interface corrections are considered.In the time discretization,the convection term is treated explicitly and the diffusion term implicitly.By the energy method,we show that the corresponding fully discrete schemes are unconditionally stable,in the sense that the time-stepis only required to be upper bounded by a constant which is independent of the mesh size h.Opti-mal error estimate is also obtained by the aid of a special global projection.Numerical experiments are given to verify the stability and accuracy of the proposed schemes.
文摘A comparison of direct integration methods is madeand their efficiency is investigated for impact problems.New-mark,Wilson-θ,Central Difference and Houbolt Methodsare used as direct integration methods.Impact analysisincludes that of elastic and large deformation based uponupdated Lagrangian including buckling check.The resultsshow that the direct integration methods give differentresults in different contact-impact cases.
文摘<div style="text-align:justify;"> In this paper, we study the error estimates for direct discontinuous Galerkin methods based on the upwind-biased fluxes. We use a newly global projection to obtain the optimal error estimates. The numerical experiments imply that <em>L</em><sup>2 </sup>norms error estimates can reach to order <em>k</em> + 1 by using time discretization methods. </div>
基金supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12071214)the Natural Science Foundation for Colleges and Universities of Jiangsu Province of China(Grant No.20KJB110011)+1 种基金supported by the National Science Foundation(Grant No.DMS-1620335)and the Simons Foundation(Grant No.637716)supported by the National Natural Science Foundation of China(Grant Nos.11871428 and 12272347).
文摘This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.
基金supports of the National Natural Science Foundation of China(Nos.12032008,12102080)the Fundamental Research Funds for the Central Universities,China(No.DUT23RC(3)038)are much appreciated。
文摘Fatigue analysis of engine turbine blade is an essential issue.Due to various uncertainties during the manufacture and operation,the fatigue damage and life of turbine blade present randomness.In this study,the randomness of structural parameters,working condition and vibration environment are considered for fatigue life predication and reliability assessment.First,the lowcycle fatigue problem is modelled as stochastic static system with random parameters,while the high-cycle fatigue problem is considered as stochastic dynamic system under random excitations.Then,to deal with the two failure modes,the novel Direct Probability Integral Method(DPIM)is proposed,which is efficient and accurate for solving stochastic static and dynamic systems.The probability density functions of accumulated damage and fatigue life of turbine blade for low-cycle and high-cycle fatigue problems are achieved,respectively.Furthermore,the time–frequency hybrid method is advanced to enhance the computational efficiency for governing equation of system.Finally,the results of typical examples demonstrate high accuracy and efficiency of the proposed method by comparison with Monte Carlo simulation and other methods.It is indicated that the DPIM is a unified method for predication of random fatigue life for low-cycle and highcycle fatigue problems.The rotational speed,density,fatigue strength coefficient,and fatigue plasticity index have a high sensitivity to fatigue reliability of engine turbine blade.
基金financially supported by the National Natural Science Foundation of China(No.41574127 and 41174104)the National Key Technology R&D Program for the 13th five-year plan(No.2016ZX05018006-006)
文摘To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement.
文摘The principle of direct method used in optimal control problem is introduced. Details of applying this method to flight trajectory generation are presented including calculation of velocity and controls histories. And capabilities of flight and propulsion systems are considered also. Combined with digital terrain map technique, the direct method is applied to the three dimensional trajectory optimization for low altitude penetration, and simplex algorithm is used to solve the parameters in optimization. For the small number of parameters, the trajectory can be optimized in real time on board.
基金Project supported by the Natural Science Foundation of China(10371009)Research Fund for the Doctoral Program Higher Education
文摘This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.
基金The Scientific Research Foundation of Nanjing University of Posts and Telecommunications(No.NY210049)
文摘A novel algorithm, i.e. the fast alternating direction method of multipliers （ADMM）, is applied to solve the classical total-variation （ TV ）-based model for image reconstruction. First, the TV-based model is reformulated as a linear equality constrained problem where the objective function is separable. Then, by introducing the augmented Lagrangian function, the two variables are alternatively minimized by the Gauss-Seidel idea. Finally, the dual variable is updated. Because the approach makes full use of the special structure of the problem and decomposes the original problem into several low-dimensional sub-problems, the per iteration computational complexity of the approach is dominated by two fast Fourier transforms. Elementary experimental results indicate that the proposed approach is more stable and efficient compared with some state-of-the-art algorithms.
文摘Mechanical engineering structures and structural components are often subjected to cyclic thermomechanical loading which stresses their material beyond its elastic limits well inside the inelastic regime.Depending on the level of loading inelastic strains may lead either to failure,due to low cycle fatigue or ratcheting,or to safety,through elastic shakedown.Thus,it is important to estimate the asymptotic stress state of such structures.This state may be determined by cumbersome incremental time-stepping calculations.Direct methods,alternatively,have big computational advantages as they focus on the characteristics of these states and try to establish them,in a direct way,right from the beginning of the calculations.Among the very few such general-purpose direct methods,a powerful direct method which has been called RSDM has appeared in the literature.The method may directly predict any asymptotic state when the exact time history of the loading is known.The advantage of the method is due to the fact that it addresses the physics of the asymptotic cycle and exploits the cyclic nature of its expected residual stress distribution.Based on RSDM a method for the shakedown analysis of structures,called RSDM-S has also been developed.Despite most direct methods for shakedown,RSDM-S does not need an optimization algorithm for its implementation.Both RSDM and RSDM-S may be implemented in any Finite Element Code.A thorough review of both these methods,together with examples of implementation are presented herein.
基金Project supported by the Innovation Foundation of the Chinese Academy of Sciences and by the National Basic Research Program of China(Grant No.2002CB713801)
文摘One of the essential points of the direct-method single-wavelength anomalous diffraction （SAD） phasing for proteins is to express the bimodal SAD phase distribution by the sum of two Gaussian functions peaked respectively at φh″＋｜△φh｜ and φh″-｜△φh｜. The probability for △φh being positive （P＋） can be derived based on the Cochran distribution in direct methods. Hence the SAD phase ambiguity can be resolved by multiplying the Gaussian function peaked at φh″＋｜△φh｜ with P＋ and multiplying the Gaussian function peaked at φh″-｜△φh｜ with P_ （=1- P＋）. The direct-method SAD h phasing has been proved powerful in breaking SAD phase ambiguities, in particular when anomalous-scattering signals are weak. However, the approximation of bimodal phase distributions by the sum of two Gaussian functions introduces considerable errors. In this paper we show that a much better approximation can be achieved by replacing the two Gaussian functions with two von Mises distributions. Test results showed that this leads to significant improvement on the efficiency of direct-method SAD-phasing.
基金National Natural Science Foundation of China (10603005)
文摘Low-thrust Earth-orbit transfers with 10^- 5-order thrust-to-weight ratios involve a large number of orbital revolutions which poses a real challenge to trajectory optimization. This article develops a direct method to optimize minimum-time low-thrust many-revolution Earth-orbit transfers. A parameterized control law in each orbit, in the form of the true optimal control, is proposed, and the time history of the parameters governing the control law is interpolated through a finite number of nodal values. The orbital averaging method is used to significantly reduce the computational workload and the trajectory optimization is conducted based on the orbital averaging dynamics expressed by nonsingular equinoctial elements. Furthermore, Earth＇s shadowing and perturbation effects are taken into account. The optimal transfer problem is thus converted to the parameter optimization problem that can be solved by nonlinear programming. Taking advantage of the mapping between the parameterized control law and the Lyapunov control law, a technique is proposed to acquire good initial guesses for optimization variables, which results in enlarged convergence domain of the direct optimization method. Numerical examples of optimal Earth-orbit transfers are presented.
基金the Government and Ministry of Higher Education and Scientific Research, Iraq, for providing funding for this study as a scholarship for Ph.D. student for the first author Ahmed Abed Gatea Al-Shammary
文摘Measurement of soil bulk density is important for understanding the physical, chemical, and biological properties of soil. Accurate and rapid soil bulk density measurement techniques play a significant role in agricultural experimental research. This review is a comprehensive summary of existing measurement methods and evaluates their advantages, disadvantages, potential sources of error,and directions for future development. These techniques can be broadly categorised as direct and indirect methods. Direct methods include core, clod, and excavation sampling, whereas indirect methods include the radiation and regression approaches. The core method is most widely used, but it is time consuming and difficult to use for sampling multiple soil depths. The size of the coring cylinder used, operator experience, sampling depth, and in-situ soil moisture content significantly affect its accuracy. The clod method is suitable for use with heavy clay soils, and its accuracy is dependent on equipment calibration, drying time, and operator experience, but the process is complicated and time consuming. Excavation techniques are most commonly used to evaluate the bulk density of forest soils, but have major limitations as they cannot be used in soils with large pores and their measurement accuracy is strongly influenced by soil texture and the type of analysis selected. The indirect methods appear to have greater accuracy than direct approaches, but have higher costs, are more complex, and require greater operator experience. One such approach uses gamma radiation, and its accuracy is strongly influenced by soil depth. Regression methods are economical as they can make indirect measurements, but these depend on good, quality data of soil texture and organic matter content and geographical and climatic properties. Also, like most of the other approaches, its accuracy decreases with sampling depth.
基金the National High Technology Research and Development Program of China(Grant No.2012AA011603)
文摘Linear scan computed tomography （LCT） is of great benefit to online industrial scanning and security inspection due to its characteristics of straight-line source trajectory and high scanning speed. However, in practical applications of LCT, there are challenges to image reconstruction due to limited-angle and insufficient data. In this paper, a new reconstruction algorithm based on total-variation （TV） minimization is developed to reconstruct images from limited-angle and insufficient data in LCT. The main idea of our approach is to reformulate a TV problem as a linear equality constrained problem where the objective function is separable, and then minimize its augmented Lagrangian function by using alternating direction method （ADM） to solve subproblems. The proposed method is robust and efficient in the task of reconstruction by showing the convergence of ADM. The numerical simulations and real data reconstructions show that the proposed reconstruction method brings reasonable performance and outperforms some previous ones when applied to an LCT imaging problem.
文摘Al-Al3Ti composites were prepared by a direct reaction method, in which Al3Ti was formed by the reaction of Ti and Al in aluminum alloy melt. The morphology of Al3Ti changes apparently from the fine particle, needle-like to large block with the increase of Al3Ti content. The addition of magnesium can markedly change the morphology of Al3Ti and reduce their size. Short rod-like Al3Ti was formed and homogeneous distribution was obtained with the addition of 3 wt.% Mg. The effect of Al3Ti and Mg on the microstructure of Al-Al3Ti composites and the mechanism were also discussed.
基金Supported by the National Natural Science Foundation of China(61203021)the Key Science and Technology Program of Liaoning Province(2011216011)+1 种基金the Natural Science Foundation of Liaoning Province(2013020024)the Program for Liaoning Excellent Talents in Universities(LJQ2015061)
文摘Electrical capacitance tomography(ECT)has been applied to two-phase flow measurement in recent years.Image reconstruction algorithms play an important role in the successful applications of ECT.To solve the ill-posed and nonlinear inverse problem of ECT image reconstruction,a new ECT image reconstruction method based on fast linearized alternating direction method of multipliers(FLADMM)is proposed in this paper.On the basis of theoretical analysis of compressed sensing(CS),the data acquisition of ECT is regarded as a linear measurement process of permittivity distribution signal of pipe section.A new measurement matrix is designed and L1 regularization method is used to convert ECT inverse problem to a convex relaxation problem which contains prior knowledge.A new fast alternating direction method of multipliers which contained linearized idea is employed to minimize the objective function.Simulation data and experimental results indicate that compared with other methods,the quality and speed of reconstructed images are markedly improved.Also,the dynamic experimental results indicate that the proposed algorithm can ful fill the real-time requirement of ECT systems in the application.
