This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are...This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.展开更多
Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an...Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an approach for the long-term extreme-response analysis of floating structures. A modified gradient-based retrieval algorithm in conjunction with the inverse first-order reliability method(IFORM) is proposed to enable the use of convolution models in long-term extreme analysis of structures with an analytical formula of response amplitude operator(RAO). The proposed algorithm ensures convergence stability and iteration accuracy and exhibits a higher computational efficiency than the traditional backtracking method. However, when the RAO of general offshore structures cannot be analytically expressed, the convolutional integration method fails to function properly. A numerical discretization approach is further proposed for offshore structures in the case when the analytical expression of the RAO is not feasible. Through iterative discretization of environmental contours(ECs) and RAOs, a detailed procedure is proposed to calculate the long-term response extremes of offshore structures. The validity and accuracy of the proposed approach are tested using a floating offshore wind turbine as a numerical example. The long-term extreme heave responses of various return periods are calculated via the IFORM in conjunction with a numerical discretization approach. The environmental data corresponding to N-year structural responses are located inside the ECs, which indicates that the selection of design points directly along the ECs yields conservative design results.展开更多
Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridyna...Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.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
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
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 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
In this paper,we formulate two new families of fourth-order explicit exponential Runge–Kutta(ERK)methods with four stages for solving first-order differential systems y'(t)+M y(t)=f(y(t)).The order conditions of ...In this paper,we formulate two new families of fourth-order explicit exponential Runge–Kutta(ERK)methods with four stages for solving first-order differential systems y'(t)+M y(t)=f(y(t)).The order conditions of these ERK methods are derived by comparing the Taylor series of the exact solution,which are exactly identical to the order conditions of explicit Runge–Kutta methods,and these ERK methods reduce to classical Runge–Kutta methods once M→0.Moreover,we analyze the stability properties and the convergence of these new methods.Several numerical examples are implemented to illustrate the accuracy and efficiency of these ERK methods by comparison with standard exponential integrators.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
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
We prove convergence for a meshfree first-order system least squares(FOSLS) partition of unity finite element method(PUFEM).Essentially,by virtue of the partition of unity,local approximation gives rise to global appr...We prove convergence for a meshfree first-order system least squares(FOSLS) partition of unity finite element method(PUFEM).Essentially,by virtue of the partition of unity,local approximation gives rise to global approximation in H(div)∩H(curl). The FOSLS formulation yields local a posteriori error estimates to guide the judicious allotment of new degrees of freedom to enrich the initial point set in a meshfree dis- cretization.Preliminary numerical results are provided and remaining challenges are discussed.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
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
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
Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact.In some practical problems,we can only obtain approximate values of the objective function and i...Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact.In some practical problems,we can only obtain approximate values of the objective function and its gradient.It is necessary to design optimization algorithms that can utilize inexact first-order information.In this paper,we propose an adaptive regularized quasi-Newton method to solve such problems.Under some mild conditions,we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method.Detailed implementations of our method,including the subspace technique to reduce the amount of computation,are presented.Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method,which can utilize the inexact first-order information effectively.展开更多
In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems f...In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems for four kinds of typical periodic composite materials,the main factors to determine the accuracy of first-order AHM and second-order AHM are found,and the physical interpretation of these factors is given.Furthermore,the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed,and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions.Finally,numerical experiments verify that MsFEM is essentially a first-order multiscale method for periodic composite materials.展开更多
The generalized differential quadrature method （GDQM） is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditi...The generalized differential quadrature method （GDQM） is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditions developed from the first-order shear deformation theory （FSDT）. The equations of motion are obtained applying Hamilton＇s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points ly- ing on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical tech- nique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.52109144,52025094 and 52222905).
文摘This paper introduces a novel approach for parameter sensitivity evaluation and efficient slope reliability analysis based on quantile-based first-order second-moment method(QFOSM).The core principles of the QFOSM are elucidated geometrically from the perspective of expanding ellipsoids.Based on this geometric interpretation,the QFOSM is further extended to estimate sensitivity indices and assess the significance of various uncertain parameters involved in the slope system.The proposed method has the advantage of computational simplicity,akin to the conventional first-order second-moment method(FOSM),while providing estimation accuracy close to that of the first-order reliability method(FORM).Its performance is demonstrated with a numerical example and three slope examples.The results show that the proposed method can efficiently estimate the slope reliability and simultaneously evaluate the sensitivity of the uncertain parameters.The proposed method does not involve complex optimization or iteration required by the FORM.It can provide a valuable complement to the existing approximate reliability analysis methods,offering rapid sensitivity evaluation and slope reliability analysis.
基金Supported by the National Natural Science Foundation of China (Grant Nos.52088102 and 51879287)National Key Research and Development Program of China (Grant No.2022YFB2602301)。
文摘Long-term responses of floating structures pose a great concern in their design phase. Existing approaches for addressing long-term extreme responses are extremely cumbersome for adoption. This work aims to develop an approach for the long-term extreme-response analysis of floating structures. A modified gradient-based retrieval algorithm in conjunction with the inverse first-order reliability method(IFORM) is proposed to enable the use of convolution models in long-term extreme analysis of structures with an analytical formula of response amplitude operator(RAO). The proposed algorithm ensures convergence stability and iteration accuracy and exhibits a higher computational efficiency than the traditional backtracking method. However, when the RAO of general offshore structures cannot be analytically expressed, the convolutional integration method fails to function properly. A numerical discretization approach is further proposed for offshore structures in the case when the analytical expression of the RAO is not feasible. Through iterative discretization of environmental contours(ECs) and RAOs, a detailed procedure is proposed to calculate the long-term response extremes of offshore structures. The validity and accuracy of the proposed approach are tested using a floating offshore wind turbine as a numerical example. The long-term extreme heave responses of various return periods are calculated via the IFORM in conjunction with a numerical discretization approach. The environmental data corresponding to N-year structural responses are located inside the ECs, which indicates that the selection of design points directly along the ECs yields conservative design results.
文摘Using Euler’s first-order explicit(EE)method and the peridynamic differential operator(PDDO)to discretize the time and internal crystal-size derivatives,respectively,the Euler’s first-order explicit method–peridynamic differential operator(EE–PDDO)was obtained for solving the one-dimensional population balance equation in crystallization.Four different conditions during crystallization were studied:size-independent growth,sizedependent growth in a batch process,nucleation and size-independent growth,and nucleation and size-dependent growth in a continuous process.The high accuracy of the EE–PDDO method was confirmed by comparing it with the numerical results obtained using the second-order upwind and HR-van methods.The method is characterized by non-oscillation and high accuracy,especially in the discontinuous and sharp crystal size distribution.The stability of the EE–PDDO method,choice of weight function in the PDDO method,and optimal time step are also discussed.
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.
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.
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.
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Supported by NSFC(Grant No.12071419)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2024MA056)。
文摘In this paper,we formulate two new families of fourth-order explicit exponential Runge–Kutta(ERK)methods with four stages for solving first-order differential systems y'(t)+M y(t)=f(y(t)).The order conditions of these ERK methods are derived by comparing the Taylor series of the exact solution,which are exactly identical to the order conditions of explicit Runge–Kutta methods,and these ERK methods reduce to classical Runge–Kutta methods once M→0.Moreover,we analyze the stability properties and the convergence of these new methods.Several numerical examples are implemented to illustrate the accuracy and efficiency of these ERK methods by comparison with standard exponential integrators.
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We prove convergence for a meshfree first-order system least squares(FOSLS) partition of unity finite element method(PUFEM).Essentially,by virtue of the partition of unity,local approximation gives rise to global approximation in H(div)∩H(curl). The FOSLS formulation yields local a posteriori error estimates to guide the judicious allotment of new degrees of freedom to enrich the initial point set in a meshfree dis- cretization.Preliminary numerical results are provided and remaining challenges are discussed.
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.
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(Grant No.NSFC-11971118).
文摘Classical quasi-Newton methods are widely used to solve nonlinear problems in which the first-order information is exact.In some practical problems,we can only obtain approximate values of the objective function and its gradient.It is necessary to design optimization algorithms that can utilize inexact first-order information.In this paper,we propose an adaptive regularized quasi-Newton method to solve such problems.Under some mild conditions,we prove the global convergence and establish the convergence rate of the adaptive regularized quasi-Newton method.Detailed implementations of our method,including the subspace technique to reduce the amount of computation,are presented.Encouraging numerical results demonstrate that the adaptive regularized quasi-Newton method is a promising method,which can utilize the inexact first-order information effectively.
基金the National Natural Science Foundation of China(No.11501449 and 11471262)the Center for high performance computing of Northwestern Polytechnical University.
文摘In this paper,we discuss the numerical accuracy of asymptotic homogenization method(AHM)and multiscale finite element method(MsFEM)for periodic composite materials.Through numerical calculation of the model problems for four kinds of typical periodic composite materials,the main factors to determine the accuracy of first-order AHM and second-order AHM are found,and the physical interpretation of these factors is given.Furthermore,the way to recover multiscale solutions of first-order AHM and MsFEM is theoretically analyzed,and it is found that first-order AHM and MsFEM provide similar multiscale solutions under some assumptions.Finally,numerical experiments verify that MsFEM is essentially a first-order multiscale method for periodic composite materials.
文摘The generalized differential quadrature method （GDQM） is employed to con- sider the free vibration and critical speed of moderately thick rotating laminated compos- ite conical shells with different boundary conditions developed from the first-order shear deformation theory （FSDT）. The equations of motion are obtained applying Hamilton＇s concept, which contain the influence of the centrifugal force, the Coriolis acceleration, and the preliminary hoop stress. In addition, the axial load is applied to the conical shell as a ratio of the global critical buckling load. The governing partial differential equations are given in the expressions of five components of displacement related to the points ly- ing on the reference surface of the shell. Afterward, the governing differential equations are converted into a group of algebraic equations by using the GDQM. The outcomes are achieved considering the effects of stacking sequences, thickness of the shell, rotating velocities, half-vertex cone angle, and boundary conditions. Furthermore, the outcomes indicate that the rate of the convergence of frequencies is swift, and the numerical tech- nique is superior stable. Three comparisons between the selected outcomes and those of other research are accomplished, and excellent agreement is achieved.
