Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ ...Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.展开更多
Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs...Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.展开更多
A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illus...A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method.展开更多
A new modification of the Method of Lines is proposed for the solution of first order partial differential equations. The accuracy of the method is shown with the matrix analysis. The method is applied to a number of ...A new modification of the Method of Lines is proposed for the solution of first order partial differential equations. The accuracy of the method is shown with the matrix analysis. The method is applied to a number of test problems, on uniform grids, to compare the accuracy and computational efficiency with the standard method.展开更多
In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this...In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equa- tions. In this study, we compare two kinds of such wave equations： the first-order （velocity-stress） and the second- order （displacement-stress） separate elastic wave equa- tions, with the first-order （velocity-stress） and the second- order （displacement-stress） full （or mixed） elastic wave equations using a high-order staggered grid finite-differ- ence method. Comparisons are given of wavefield snap- shots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corre- sponding first-order or second-order full elastic wave equations. These mixed equations are computationallyslightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-com- ponent processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements.展开更多
To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’...To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.展开更多
In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering ...In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.展开更多
The interaction and its variation between magnetic grains in two kinds of magnetic recording tapes are investigated by first-order reversal curves （FORC） and the 5M method. The composition and microstructure of the ...The interaction and its variation between magnetic grains in two kinds of magnetic recording tapes are investigated by first-order reversal curves （FORC） and the 5M method. The composition and microstructure of the samples are characterised by x-ray diffraction and scanning electron microscope. The FORC diagram can provide more accurate information of the interaction and its variation, but the 5M curves cannot. The positive interaction field and the large variation of the interaction field have opposite effects on the δM curve.展开更多
The finite element method has established itself as an efficient numerical procedure for the solution of arbitrary-shaped field problems in space. Basically, the finite element method transforms the underlying differe...The finite element method has established itself as an efficient numerical procedure for the solution of arbitrary-shaped field problems in space. Basically, the finite element method transforms the underlying differential equation into a system of algebraic equations by application of the method of weighted residuals in conjunction with a finite element ansatz. However, this procedure is restricted to even-ordered differential equations and leads to symmetric system matrices as a key property of the finite element method. This paper aims in a generalization of the finite element method towards the solution of first-order differential equations. This is achieved by an approach which replaces the first-order derivative by fractional powers of operators making use of the square root of a Sturm-Liouville operator. The resulting procedure incorporates a finite element formulation and leads to a symmetric but dense system matrix. Finally, the scheme is applied to the barometric equation where the results are compared with the analytical solution and other numerical approaches. It turns out that the resulting numerical scheme shows excellent convergence properties.展开更多
In this article, we use the spin coherent state transformation and the ground state variational method to theoretically calculate the ground function. In order to consider the influence of the atom-atom interaction on...In this article, we use the spin coherent state transformation and the ground state variational method to theoretically calculate the ground function. In order to consider the influence of the atom-atom interaction on the extended Dicke model's ground state properties, the mean photon number, the scaled atomic population and the average ground energy are displayed. Using the self-consistent field theory to solve the atom-atom interaction, we discover the system undergoes a first-order quantum phase transition from the normal phase to the superradiant phase, but a famous Dicke-type second-order quantum phase transition without the atom-atom interaction. Meanwhile, the atom-atom interaction makes the phase transition point shift to the lower atom-photon collective coupling strength.展开更多
In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial deriv...In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.展开更多
Design for modem engineering system is becoming multidisciplinary and incorporates practical uncertainties; therefore, it is necessary to synthesize reliability analysis and the multidisciplinary design optimization ...Design for modem engineering system is becoming multidisciplinary and incorporates practical uncertainties; therefore, it is necessary to synthesize reliability analysis and the multidisciplinary design optimization （MDO） techniques for the design of complex engineering system. An advanced first order second moment method-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and the reliability analysis methods. It is seen through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.展开更多
The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear...The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.展开更多
The first order reliability method (FORM) is widely adopted for structural reliability evaluation due to its numerical efficiency. Concerning the issue of FORM often failing to converge when the limit state function (...The first order reliability method (FORM) is widely adopted for structural reliability evaluation due to its numerical efficiency. Concerning the issue of FORM often failing to converge when the limit state function (LSF) behaves high nonlinearity, a new iteration scheme called "rotated gradient algorithm (RGA)" is proposed and combined with Kriging model to evaluate the reliability of implicit performance function. In this paper, the Kriging model is applied to approximate the real LSF first. Then the scheme of RGA, constructed in terms of gradient information of two adjacent design points obtained during the process of calculation, is used to calculate the reliability index. Numerical examples show the validity in convergence and accuracy of the proposed methodfor arbitrary nonlinear performance function.展开更多
To avoid the high computational cost and much modification in the process of applying traditional reliability-based design optimization method, a new reliability-based concurrent subspace optimization approach is prop...To avoid the high computational cost and much modification in the process of applying traditional reliability-based design optimization method, a new reliability-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and reliability assessment methods. It is shown through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.展开更多
This study presents a new tool for solving stochastic boundary-value problems. This tool is created by modify the previous spectral stochastic meshless local Petrov-Galerkin method using the MLPG5 scheme. This modifie...This study presents a new tool for solving stochastic boundary-value problems. This tool is created by modify the previous spectral stochastic meshless local Petrov-Galerkin method using the MLPG5 scheme. This modified spectral stochastic meshless local Petrov-Galerkin method is selectively applied to predict the structural failure probability with the uncertainty in the spatial variability of mechanical properties. Except for the MLPG5 scheme, deriving the proposed spectral stochastic meshless local Petrov-Galerkin formulation adopts generalized polynomial chaos expansions of random mechanical properties. Predicting the structural failure probability is based on the first-order reliability method. Further comparing the spectral stochastic finite element-based and meshless local Petrov-Galerkin-based predicted structural failure probabilities indicates that the proposed spectral stochastic meshless local Petrov-Galerkin method predicts the more accurate structural failure probability than the spectral stochastic finite element method does. In addition, generating spectral stochastic meshless local Petrov-Galerkin results are considerably time-saving than generating Monte-Carlo simulation results does. In conclusion, the spectral stochastic meshless local Petrov-Galerkin method serves as a time-saving tool for solving stochastic boundary-value problems sufficiently accurately.展开更多
This paper formulates a two-dimensional strip packing problem as a non- linear programming （NLP） problem and establishes the first-order optimality conditions for the NLP problem. A numerical algorithm for solving t...This paper formulates a two-dimensional strip packing problem as a non- linear programming （NLP） problem and establishes the first-order optimality conditions for the NLP problem. A numerical algorithm for solving this NLP problem is given to find exact solutions to strip-packing problems involving up to 10 items. Approximate solutions can be found for big-sized problems by decomposing the set of items into small-sized blocks of which each block adopts the proposed numerical algorithm. Numerical results show that the approximate solutions to big-sized problems obtained by this method are superior to those by NFDH, FFDH and BFDH approaches.展开更多
The misch-metal （MM） partially substituted Nd-Fe-B sintered magnets were fabricated by the dual alloy method, and the crystal structure, microstructure, and magnetic properties were analyzed comprehensively. X-ray d...The misch-metal （MM） partially substituted Nd-Fe-B sintered magnets were fabricated by the dual alloy method, and the crystal structure, microstructure, and magnetic properties were analyzed comprehensively. X-ray diffraction （XRD） reveals that the increasing content of the MM has an inconsiderable effect on the crystallographic alignment of the magnets. Grains of the two main phases are uniformly distributed, and slightly deteriorate on the grain boundary. Due to the diffusion between the adjacent grains, the MM substituted Nd-Fe-B magnets contain three types of components with different Ce/La concentrations. Moreover, the first-order reversal curve （FORC） diagram is introduced to analyze the magnetization reversal process, coercivity mechanism, and distribution of reversal field in magnetic samples. The analysis indicates that there are two major reversal components, corresponding to the two different main phases. The domain nucleation and growth are determined to be the leading mechanism in controlling the magnetization reversal processes of the magnets sintered by the dual alloy method.展开更多
Theoretical investigation of the phase equilibria of the Fe-Ni alloy has been performed by combining the FLAPW total energy calculations and the Cluster Variation Method through the Cluster Expansion Method. The calcu...Theoretical investigation of the phase equilibria of the Fe-Ni alloy has been performed by combining the FLAPW total energy calculations and the Cluster Variation Method through the Cluster Expansion Method. The calculations have proved the stabilization of the LIE phase at 1：3 stoichiometry, which is in agreement with the experimental result, and predicted the existence of L1 0 as a stable phase below 550 K; this L1 0 phase has been missing in the conventional phase diagram. The calculations are extended to the Fe-rich region that is characterized by a wide range phase separation and has drawn considerable attention because of the intriguing Invar property associated with a Fe concentration of 65%. To reveal the origin of the phase separation, a P-V curve in an entire concentration range is derived by the second derivative of free energy functional of the disordered phase with respect to the volume. The calculation confirmed that the phase separation is caused by the breakdown of the mechanical-stability criterion. The newly calculated phase separation line combined with the L1 0 and L12Eorder-disordered phase boundaries provides phase equilibria in the wider concentration range of the system. Furthermore, a coefficient of thermal expansion （CTE） is attempted by incorporating the thermal vibration effect through harmonic approximation of the Debye-Gruneisen model. The Invar behavior has been reproduced, and the origin of this anomalous volume change has been discussed.展开更多
基金Sponsored by the National Natural Science Foundation of China(Grant No.11461021)the Natural Science Basic Research Plan in Shaanxi Province of China(Grant No.2017JM1014)
文摘Two new versions of accelerated first-order methods for minimizing convex composite functions are proposed. In this paper, we first present an accelerated first-order method which chooses the step size 1/ Lk to be 1/ L0 at the beginning of each iteration and preserves the computational simplicity of the fast iterative shrinkage-thresholding algorithm. The first proposed algorithm is a non-monotone algorithm. To avoid this behavior, we present another accelerated monotone first-order method. The proposed two accelerated first-order methods are proved to have a better convergence rate for minimizing convex composite functions. Numerical results demonstrate the efficiency of the proposed two accelerated first-order methods.
文摘Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.
文摘A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method.
文摘A new modification of the Method of Lines is proposed for the solution of first order partial differential equations. The accuracy of the method is shown with the matrix analysis. The method is applied to a number of test problems, on uniform grids, to compare the accuracy and computational efficiency with the standard method.
基金partially supported by China National Major Science and Technology Project (Subproject No:2011ZX05024-001-03)
文摘In seismic exploration, it is common practice to separate the P-wavefield from the S-wavefield by the elastic wavefield decomposition technique, for imaging purposes. However, it is sometimes difficult to achieve this, especially when the velocity field is complex. A useful approach in multi-component analysis and modeling is to directly solve the elastic wave equations for the pure P- or S-wavefields, referred as the separate elastic wave equa- tions. In this study, we compare two kinds of such wave equations： the first-order （velocity-stress） and the second- order （displacement-stress） separate elastic wave equa- tions, with the first-order （velocity-stress） and the second- order （displacement-stress） full （or mixed） elastic wave equations using a high-order staggered grid finite-differ- ence method. Comparisons are given of wavefield snap- shots, common-source gather seismic sections, and individual synthetic seismogram. The simulation tests show that equivalent results can be obtained, regardless of whether the first-order or second-order separate elastic wave equations are used for obtaining the pure P- or S-wavefield. The stacked pure P- and S-wavefields are equal to the mixed wave fields calculated using the corre- sponding first-order or second-order full elastic wave equations. These mixed equations are computationallyslightly less expensive than solving the separate equations. The attraction of the separate equations is that they achieve separated P- and S-wavefields which can be used to test the efficacy of wave decomposition procedures in multi-com- ponent processing. The second-order separate elastic wave equations are a good choice because they offer information on the pure P-wave or S-wave displacements.
文摘To solve the first-order differential equation derived from the problem of a free-falling object and the problem arising from Newton’s law of cooling, the study compares the numerical solutions obtained from Picard’s and Taylor’s series methods. We have carried out a descriptive analysis using the MATLAB software. Picard’s and Taylor’s techniques for deriving numerical solutions are both strong mathematical instruments that behave similarly. All first-order differential equations in standard form that have a constant function on the right-hand side share this similarity. As a result, we can conclude that Taylor’s approach is simpler to use, more effective, and more accurate. We will contrast Rung Kutta and Taylor’s methods in more detail in the following section.
基金supported by the National Natural Science Foundation of China(Grant No.50379046)the Doctoral Fund of the Ministry of Education of China(Grant No.A50221)
文摘In order to address the complex uncertainties caused by interfacing between the fuzziness and randomness of the safety problem for embankment engineering projects, and to evaluate the safety of embankment engineering projects more scientifically and reasonably, this study presents the fuzzy logic modeling of the stochastic finite element method （SFEM） based on the harmonious finite element （HFE） technique using a first-order approximation theorem. Fuzzy mathematical models of safety repertories were introduced into the SFEM to analyze the stability of embankments and foundations in order to describe the fuzzy failure procedure for the random safety performance function. The fuzzy models were developed with membership functions with half depressed gamma distribution, half depressed normal distribution, and half depressed echelon distribution. The fuzzy stochastic mathematical algorithm was used to comprehensively study the local failure mechanism of the main embankment section near Jingnan in the Yangtze River in terms of numerical analysis for the probability integration of reliability on the random field affected by three fuzzy factors. The result shows that the middle region of the embankment is the principal zone of concentrated failure due to local fractures. There is also some local shear failure on the embankment crust. This study provides a referential method for solving complex multi-uncertainty problems in engineering safety analysis.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 50672008 and 50971023)Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20090006120019)
文摘The interaction and its variation between magnetic grains in two kinds of magnetic recording tapes are investigated by first-order reversal curves （FORC） and the 5M method. The composition and microstructure of the samples are characterised by x-ray diffraction and scanning electron microscope. The FORC diagram can provide more accurate information of the interaction and its variation, but the 5M curves cannot. The positive interaction field and the large variation of the interaction field have opposite effects on the δM curve.
文摘The finite element method has established itself as an efficient numerical procedure for the solution of arbitrary-shaped field problems in space. Basically, the finite element method transforms the underlying differential equation into a system of algebraic equations by application of the method of weighted residuals in conjunction with a finite element ansatz. However, this procedure is restricted to even-ordered differential equations and leads to symmetric system matrices as a key property of the finite element method. This paper aims in a generalization of the finite element method towards the solution of first-order differential equations. This is achieved by an approach which replaces the first-order derivative by fractional powers of operators making use of the square root of a Sturm-Liouville operator. The resulting procedure incorporates a finite element formulation and leads to a symmetric but dense system matrix. Finally, the scheme is applied to the barometric equation where the results are compared with the analytical solution and other numerical approaches. It turns out that the resulting numerical scheme shows excellent convergence properties.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11275118,11404198,91430109,61505100,51502189the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province(STIP)under Grant No.2014102+2 种基金the Launch of the Scientific Research of Shanxi University under Grant No.011151801004the National Fundamental Fund of Personnel Training under Grant No.J1103210The Natural Science Foundation of Shanxi Province under Grant No.2015011008
文摘In this article, we use the spin coherent state transformation and the ground state variational method to theoretically calculate the ground function. In order to consider the influence of the atom-atom interaction on the extended Dicke model's ground state properties, the mean photon number, the scaled atomic population and the average ground energy are displayed. Using the self-consistent field theory to solve the atom-atom interaction, we discover the system undergoes a first-order quantum phase transition from the normal phase to the superradiant phase, but a famous Dicke-type second-order quantum phase transition without the atom-atom interaction. Meanwhile, the atom-atom interaction makes the phase transition point shift to the lower atom-photon collective coupling strength.
文摘In this paper, we consider the initial-boundary value problem of two-dimensional first-order linear hyperbolic equation with variable coefficients. By using the upwind difference method to discretize the spatial derivative term and the forward and backward Euler method to discretize the time derivative term, the explicit and implicit upwind difference schemes are obtained respectively. It is proved that the explicit upwind scheme is conditionally stable and the implicit upwind scheme is unconditionally stable. Then the convergence of the schemes is derived. Numerical examples verify the results of theoretical analysis.
基金National Natural Science Foundation of China (10377015)
文摘Design for modem engineering system is becoming multidisciplinary and incorporates practical uncertainties; therefore, it is necessary to synthesize reliability analysis and the multidisciplinary design optimization （MDO） techniques for the design of complex engineering system. An advanced first order second moment method-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and the reliability analysis methods. It is seen through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.
基金supported by the National Natural Science Foundation of China (No.10662003)Educational Commission of Guangxi Province of China (No.200807MS109)
文摘The first order differential matrix equations of the host shell and constrained layer for a sandwich rotational shell are derived based on the thin shell theory.Employing the layer wise principle and first order shear deformation theory, only considering the shearing deformation of the viscoelastic layer, the integrated first order differential matrix equation of a passive constrained layer damping rotational shell is established by combining with the normal equilibrium equation of the viscoelastic layer.A highly precise transfer matrix method is developed by extended homogeneous capacity precision integration technology.The numerical results show that present method is accurate and effective.
文摘The first order reliability method (FORM) is widely adopted for structural reliability evaluation due to its numerical efficiency. Concerning the issue of FORM often failing to converge when the limit state function (LSF) behaves high nonlinearity, a new iteration scheme called "rotated gradient algorithm (RGA)" is proposed and combined with Kriging model to evaluate the reliability of implicit performance function. In this paper, the Kriging model is applied to approximate the real LSF first. Then the scheme of RGA, constructed in terms of gradient information of two adjacent design points obtained during the process of calculation, is used to calculate the reliability index. Numerical examples show the validity in convergence and accuracy of the proposed methodfor arbitrary nonlinear performance function.
基金the Nationa Natural Science Foundation of China (Grant No. 10377015)
文摘To avoid the high computational cost and much modification in the process of applying traditional reliability-based design optimization method, a new reliability-based concurrent subspace optimization approach is proposed based on the comparison and analysis of the existing multidisciplinary optimization techniques and reliability assessment methods. It is shown through a canard configuration optimization for a three-surface transport that the proposed method is computationally efficient and practical with the least modification to the current deterministic optimization process.
文摘This study presents a new tool for solving stochastic boundary-value problems. This tool is created by modify the previous spectral stochastic meshless local Petrov-Galerkin method using the MLPG5 scheme. This modified spectral stochastic meshless local Petrov-Galerkin method is selectively applied to predict the structural failure probability with the uncertainty in the spatial variability of mechanical properties. Except for the MLPG5 scheme, deriving the proposed spectral stochastic meshless local Petrov-Galerkin formulation adopts generalized polynomial chaos expansions of random mechanical properties. Predicting the structural failure probability is based on the first-order reliability method. Further comparing the spectral stochastic finite element-based and meshless local Petrov-Galerkin-based predicted structural failure probabilities indicates that the proposed spectral stochastic meshless local Petrov-Galerkin method predicts the more accurate structural failure probability than the spectral stochastic finite element method does. In addition, generating spectral stochastic meshless local Petrov-Galerkin results are considerably time-saving than generating Monte-Carlo simulation results does. In conclusion, the spectral stochastic meshless local Petrov-Galerkin method serves as a time-saving tool for solving stochastic boundary-value problems sufficiently accurately.
基金State Foundstion of Ph.D Units of China(2003-05)under Grant 20020141013the NNSF(10471015)of Liaoning Province,China.
文摘This paper formulates a two-dimensional strip packing problem as a non- linear programming （NLP） problem and establishes the first-order optimality conditions for the NLP problem. A numerical algorithm for solving this NLP problem is given to find exact solutions to strip-packing problems involving up to 10 items. Approximate solutions can be found for big-sized problems by decomposing the set of items into small-sized blocks of which each block adopts the proposed numerical algorithm. Numerical results show that the approximate solutions to big-sized problems obtained by this method are superior to those by NFDH, FFDH and BFDH approaches.
基金Project supported by the National Natural Science Foundation of China(Grant No.51590880)the National Key Research and Development Program of China(Grant Nos.2014CB643702 and 2016YFB0700903)+1 种基金Key Research Program of the Chinese Academy of Sciences of Chinathe Inner Mongolia Science and Technology Major Project of China 2016
文摘The misch-metal （MM） partially substituted Nd-Fe-B sintered magnets were fabricated by the dual alloy method, and the crystal structure, microstructure, and magnetic properties were analyzed comprehensively. X-ray diffraction （XRD） reveals that the increasing content of the MM has an inconsiderable effect on the crystallographic alignment of the magnets. Grains of the two main phases are uniformly distributed, and slightly deteriorate on the grain boundary. Due to the diffusion between the adjacent grains, the MM substituted Nd-Fe-B magnets contain three types of components with different Ce/La concentrations. Moreover, the first-order reversal curve （FORC） diagram is introduced to analyze the magnetization reversal process, coercivity mechanism, and distribution of reversal field in magnetic samples. The analysis indicates that there are two major reversal components, corresponding to the two different main phases. The domain nucleation and growth are determined to be the leading mechanism in controlling the magnetization reversal processes of the magnets sintered by the dual alloy method.
文摘Theoretical investigation of the phase equilibria of the Fe-Ni alloy has been performed by combining the FLAPW total energy calculations and the Cluster Variation Method through the Cluster Expansion Method. The calculations have proved the stabilization of the LIE phase at 1：3 stoichiometry, which is in agreement with the experimental result, and predicted the existence of L1 0 as a stable phase below 550 K; this L1 0 phase has been missing in the conventional phase diagram. The calculations are extended to the Fe-rich region that is characterized by a wide range phase separation and has drawn considerable attention because of the intriguing Invar property associated with a Fe concentration of 65%. To reveal the origin of the phase separation, a P-V curve in an entire concentration range is derived by the second derivative of free energy functional of the disordered phase with respect to the volume. The calculation confirmed that the phase separation is caused by the breakdown of the mechanical-stability criterion. The newly calculated phase separation line combined with the L1 0 and L12Eorder-disordered phase boundaries provides phase equilibria in the wider concentration range of the system. Furthermore, a coefficient of thermal expansion （CTE） is attempted by incorporating the thermal vibration effect through harmonic approximation of the Debye-Gruneisen model. The Invar behavior has been reproduced, and the origin of this anomalous volume change has been discussed.
