This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not ...This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration （iterative） and the operator-splitting （non-iterative） is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom （SDOF） cantilever column with replaceable steel coupons that provides repeatable highly- nonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1：2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model ofa 1：2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.展开更多
Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that ...Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that the capability to capture dynamic loading was not explored. It was found that there were different quadrature equations to predict the next step displacement increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method, in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods.展开更多
This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method （IFM） and the homoge...This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method （IFM） and the homogenized initial system method （HISM）. In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods.展开更多
Deep learning(DL)has become a crucial technique for predicting the El Niño-Southern Oscillation(ENSO)and evaluating its predictability.While various DL-based models have been developed for ENSO predictions,many f...Deep learning(DL)has become a crucial technique for predicting the El Niño-Southern Oscillation(ENSO)and evaluating its predictability.While various DL-based models have been developed for ENSO predictions,many fail to capture the coherent multivariate evolution within the coupled ocean-atmosphere system of the tropical Pacific.To address this three-dimensional(3D)limitation and represent ENSO-related ocean-atmosphere interactions more accurately,a novel this 3D multivariate prediction model was proposed based on a Transformer architecture,which incorporates a spatiotemporal self-attention mechanism.This model,named 3D-Geoformer,offers several advantages,enabling accurate ENSO predictions up to one and a half years in advance.Furthermore,an integrated gradient method was introduced into the model to identify the sources of predictability for sea surface temperature(SST)variability in the eastern equatorial Pacific.Results reveal that the 3D-Geoformer effectively captures ENSO-related precursors during the evolution of ENSO events,particularly the thermocline feedback processes and ocean temperature anomaly pathways on and off the equator.By extending DL-based ENSO predictions from one-dimensional Niño time series to 3D multivariate fields,the 3D-Geoformer represents a significant advancement in ENSO prediction.This study provides details in the model formulation,analysis procedures,sensitivity experiments,and illustrative examples,offering practical guidance for the application of the model in ENSO research.展开更多
The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF me...The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.展开更多
The paper applied the isogeometric boundary element method(IGABEM)to thermoelastic problems.The Non-Uniform Rational B-splines(NURBS)used to construct geometric models are employed to discretize the boundary integral ...The paper applied the isogeometric boundary element method(IGABEM)to thermoelastic problems.The Non-Uniform Rational B-splines(NURBS)used to construct geometric models are employed to discretize the boundary integral formulation of the governing equation.Due to the existence of thermal stress,the domain integral term appears in the boundary integral equation.We resolve this problem by incorporating radial integration method into IGABEM which converts the domain integral to the boundary integral.In this way,IGABEM can maintain its advantages in dimensionality reduction and more importantly,seamless integration of CAD and numerical analysis based on boundary representation.The algorithm is verified by numerical examples.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
We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utiliz...We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.展开更多
The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes ...The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved.展开更多
In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thi...In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thing is to decompose a dynamic system into two sub-systems,a small-scale low-frequency system and a high-frequency system.The former can be analytically and efficiently solved with the mode superposition method,and the latter is dealt with through a time integration method such as the Newmark method.The summation of the responses of these two sub-systems is the responses of the original dynamic system.It is concluded that,with little sacrifice of efficiency,the combination method based on the strategy is more accurate than the combined time integration method,but it has the same accuracy order as that of the combined method.Numerical experiments validate the effectiveness of the proposed strategy.展开更多
With the rapid development of the social economy,the pace of urban-rural integration construction has been accelerating continuously.From the actual situation at this stage,it is necessary to maintain the sound relati...With the rapid development of the social economy,the pace of urban-rural integration construction has been accelerating continuously.From the actual situation at this stage,it is necessary to maintain the sound relationship of coordination,interaction and mutual advance between the city and the village.In the process of building urban-rural integration,we should focus on strengthening the development of land management,so as to improve the rationality of land development and utilization,and maximize the value of land while protecting rural farmland resources.The author explores and analyzes the problems existing in the land management work in the urban-rural integration construction.An effective way is put forward to carry out land management work in urban and rural integration construction,which contributes to the improvement of the quality of land management work.展开更多
This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First.vacco dynamies equations are written in the canonical form and the field form.second the gradient methods...This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First.vacco dynamies equations are written in the canonical form and the field form.second the gradient methods the single-componentmethods and the field method are used to integrate the dynamics equations of the corresponding holonomic system respectively.And considering the restriction of nonholonomic construint to the initial conditions the solutions of Vacco dynamics cquations of nonlinear nonholonomic system are obtained.展开更多
The idea of the gradient method for integrating the dynamical equations of a nonconservative system presented by Vujanovic is transplanted to a Birkhoffian system, which is a new method for the integration of Birkhoff...The idea of the gradient method for integrating the dynamical equations of a nonconservative system presented by Vujanovic is transplanted to a Birkhoffian system, which is a new method for the integration of Birkhoff＇s equations. First, the differential equations of motion of the Birkhoffian system are written out. Secondly, 2n Birkhoff＇s variables are divided into two parts, and assume that a part of the variables is the functions of the remaining part of the variables and time. Thereby, the basic quasi-linear partial differential equations are established. If a complete solution of the basic partial differential equations is sought out, the solution of the problem is given by a set of algebraic equations. Since one can choose n arbitrary Birkhoff＇s variables as the functions of n remains of variables and time in a specific problem, the method has flexibility. The major difficulty of this method lies in finding a complete solution of the basic partial differential equation. Once one finds the complete solution, the motion of the systems can be obtained without doing further integration. Finally, two examples are given to illustrate the application of the results.展开更多
Comprehensive English is a very basic and important course for English majors,according to the features of the text-book A New English Course,teachers should adopt the integration of grammar translation method and com...Comprehensive English is a very basic and important course for English majors,according to the features of the text-book A New English Course,teachers should adopt the integration of grammar translation method and communicative approach to improve students' linguistic competence and communicative competence.展开更多
The Finite Difference （FD） method is an important method for seismic numerical simulations. It helps us understand regular patterns in seismic wave propagation, analyze seismic attributes, and interpret seismic data...The Finite Difference （FD） method is an important method for seismic numerical simulations. It helps us understand regular patterns in seismic wave propagation, analyze seismic attributes, and interpret seismic data. However, because of its discretization, the FD method is only stable under certain conditions. The Arbitrary Difference Precise Integration （ADPI） method is based on the FD method and adopts an integration scheme in the time domain and an arbitrary difference scheme in the space domain. Therefore, the ADPI method is a semi-analytical method. In this paper, we deduce the formula for the ADPI method based on the 3D elastic equation and improve its stability. In forward modeling cases, the ADPI method was implemented in 2D and 3D elastic wave equation forward modeling. Results show that the travel time of the reflected seismic wave is accurate. Compared with the acoustic wave field, the elastic wave field contains more wave types, including PS- and PP- reflected waves, transmitted waves, and diffracted waves, which is important to interpretation of seismic data. The method can be easily applied to elastic wave equation numerical simulations for eoloical models.展开更多
The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field ...The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.展开更多
In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then th...In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then the field method for integrating these equations is given.Finally,an example illustrating the appli- cation of the integration method is given.展开更多
In order to obtain accurate probability integration method(PIM) parameters for surface movement of multi-panel mining, a genetic algorithm(GA) was used to optimize the parameters. As the measured surface movement is a...In order to obtain accurate probability integration method(PIM) parameters for surface movement of multi-panel mining, a genetic algorithm(GA) was used to optimize the parameters. As the measured surface movement is affected by more than one mining panel, traditional PIM parameter inversion model is difficult to ensure the reliability of the results due to the complexity of rock movement. With crossover,mutation and selection operators, GA can perform a global optimization search and has high computation efficiency. Compared with the pattern search algorithm, the fitness function can avoid falling into local minima traps. GA reduces the risk of local minima traps which improves the accuracy and reliability with the mutation mechanism. Application at Xuehu colliery shows that GA can be used to inverse the PIM parameters for multi-panel surface movement observation, and reliable results can be obtained. The research provides a new way for back-analysis of PIM parameters for mining subsidence under complex conditions.展开更多
A model based on the curvature integration method has been applied in an online plate leveling system. However, there are some shortcomings in the current leveling models. On the one hand, the models cannot deal with ...A model based on the curvature integration method has been applied in an online plate leveling system. However, there are some shortcomings in the current leveling models. On the one hand, the models cannot deal with the leveling process of plates with a random curvature distribution. On the other hand, the current models are suitable only for stable leveling processes and ignore the biting in and tailing out stages. This study presents a new plate-leveling model based on the curvature integration method, which can describe the leveling process of plates with random curvature distribution. Further, the model is solved in two cases in order to take the biting in and tailing out stages into consideration. The proposed model is evaluated by comparing with a plate leveling experiment. Finally, the leveling process of a plate with a wave bent is studied using the proposed model. It is found that the contact angles vary greatly during the biting in and tailing out stages. However, they are relatively steady during the 5 roller leveling stage. In addition, the contact angle of roller No. 2 is the smallest, which is close to 0. Roller leveling can effectively eliminate bending in the plate, but there are regions in the head and tail of the plate, where roller leveling is not effective. The non-leveling region length is about 2 times that of the roller space. This study proposes a quasi-static plate-leveling model, which makes it possible to analyze the dynamic straightening process using a curvature integration method. It also makes it possible to analyze the straightening process of a plate with random curvature distribution.展开更多
The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficu...The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.展开更多
基金National Science Foundation(NSF)under grant No.CMMI-0748111
文摘This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration （iterative） and the operator-splitting （non-iterative） is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom （SDOF） cantilever column with replaceable steel coupons that provides repeatable highly- nonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1：2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model ofa 1：2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.
基金Science Council (NSC),Chinese Taipei Under Grant No.NSC-96-2221-E-027-030
文摘Numerical properties of the time integration method proposed by the first author of this paper in 2007 are the same as those of the constant average acceleration method （AAM） for linear elastic systems, except that the capability to capture dynamic loading was not explored. It was found that there were different quadrature equations to predict the next step displacement increment. A modified quadrature equation of this method was derived so that the equation to determine the next step displacement was numerically equivalent to the equation used in the constant AAM. It was verified that the original form of this method, in general, had a better capability to capture dynamic loadings than the constant AAM. This excellent property, in addition to computational efficiency, will help to make this method competitive with general secondorder accurate integration methods.
基金Hunan Provincial Natural Science Foundation Under Grant No.02JJY2085
文摘This paper introduces two new types of precise integration methods based on Chebyshev polynomial of the first kind for dynamic response analysis of structures, namely the integral formula method （IFM） and the homogenized initial system method （HISM）. In both methods, nonlinear variable loadings within time intervals are simulated using Chebyshev polynomials of the first kind before a direct integration is performed. Developed on the basis of the integral formula, the recurrence relationship of the integral computation suggested in this paper is combined with the Crout decomposed method to solve linear algebraic equations. In this way, the IFM based on Chebyshev polynomial of the first kind is constructed. Transforming the non-homogenous initial system to the homogeneous dynamic system, and developing a special scheme without dimensional expansion, the HISM based on Chebyshev polynomial of the first kind is able to avoid the matrix inversion operation. The accuracy of the time integration schemes is examined and compared with other commonly used schemes, and it is shown that a greater accuracy as well as less time consuming can be achieved. Two numerical examples are presented to demonstrate the applicability of these new methods.
基金Supported by the Laoshan Laboratory(No.LSKJ202202402)the National Natural Science Foundation of China(No.42030410)+2 种基金the Startup Foundation for Introducing Talent of Nanjing University of Information Science&Technology,and Jiangsu Innovation Research Group(No.JSSCTD 202346)supported by the China National Postdoctoral Program for Innovative Talents(No.BX20240169)the China Postdoctoral Science Foundation(No.2141062400101)。
文摘Deep learning(DL)has become a crucial technique for predicting the El Niño-Southern Oscillation(ENSO)and evaluating its predictability.While various DL-based models have been developed for ENSO predictions,many fail to capture the coherent multivariate evolution within the coupled ocean-atmosphere system of the tropical Pacific.To address this three-dimensional(3D)limitation and represent ENSO-related ocean-atmosphere interactions more accurately,a novel this 3D multivariate prediction model was proposed based on a Transformer architecture,which incorporates a spatiotemporal self-attention mechanism.This model,named 3D-Geoformer,offers several advantages,enabling accurate ENSO predictions up to one and a half years in advance.Furthermore,an integrated gradient method was introduced into the model to identify the sources of predictability for sea surface temperature(SST)variability in the eastern equatorial Pacific.Results reveal that the 3D-Geoformer effectively captures ENSO-related precursors during the evolution of ENSO events,particularly the thermocline feedback processes and ocean temperature anomaly pathways on and off the equator.By extending DL-based ENSO predictions from one-dimensional Niño time series to 3D multivariate fields,the 3D-Geoformer represents a significant advancement in ENSO prediction.This study provides details in the model formulation,analysis procedures,sensitivity experiments,and illustrative examples,offering practical guidance for the application of the model in ENSO research.
文摘The compact implicit integration factor （cIIF） method is an efficient time discretization scheme for stiff nonlinear diffusion equations in two and three spatial dimensions. In the current work, we apply the cIIF method to some complex-valued nonlinear evolutionary equations such as the nonlinear SchrSdinger （NLS） equation and the complex Ginzburg-Landau （GL） equation. Detailed algorithm formulation and practical implementation of cIIF method are performed. The numerical results indicate that this method is very accurate and efficient.
基金This study was funded by the National Natural Science Foundation of China(NSFC)(Grant Nos.11702238,51904202 and 11902212)and Nanhu Scholars Program for Young Scholars of XYNU.
文摘The paper applied the isogeometric boundary element method(IGABEM)to thermoelastic problems.The Non-Uniform Rational B-splines(NURBS)used to construct geometric models are employed to discretize the boundary integral formulation of the governing equation.Due to the existence of thermal stress,the domain integral term appears in the boundary integral equation.We resolve this problem by incorporating radial integration method into IGABEM which converts the domain integral to the boundary integral.In this way,IGABEM can maintain its advantages in dimensionality reduction and more importantly,seamless integration of CAD and numerical analysis based on boundary representation.The algorithm is verified by numerical examples.
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.
基金The NNSF (10371137 and 10201034) of Chinathe Foundation (20030558008) of Doctoral Program of National Higher Education, Guangdong Provincial Natural Science Foundation (1011170) of China and the Advanced Research Foundation of Zhongshan UniversityThe US National Science Foundation (9973427 and 0312113)NSF (10371122) of China and the Chinese Academy of Sciences under the program of "Hundred Distinguished Young Chinese Scientists."
文摘We propose two error control techniques for numerical integrations in fast multiscale collocation methods for solving Fredholm integral equations of the second kind with weakly singular kernels. Both techniques utilize quadratures for singular integrals using graded points. One has a polynomial order of accuracy if the integrand has a polynomial order of smoothness except at the singular point and the other has exponential order of accuracy if the integrand has an infinite order of smoothness except at the singular point. We estimate the order of convergence and computational complexity of the corresponding approximate solutions of the equation. We prove that the second technique preserves the order of convergence and computational complexity of the original collocation method. Numerical experiments are presented to illustrate the theoretical estimates.
基金Work sponsored by"Ministero dell' University"CNR of Italy
文摘The purpose of this paper is to propose and study local spline approximation methods for singular product integration,for which;i)the precision degree is the highest possible using splint approximation; ii) the nodes fan be assumed equal to arbitrary points,where the integrand function f is known; iii) the number of the requested evaluations of f at the nodes is low,iv) a satisfactory convergence theory can be proved.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.11872090 and 12172023).
文摘In this article,the mode superposition method is combined with a time integration method like the trapezoidal rule to improve solution accuracy for linear dynamic systems.In this combination strategy,the essential thing is to decompose a dynamic system into two sub-systems,a small-scale low-frequency system and a high-frequency system.The former can be analytically and efficiently solved with the mode superposition method,and the latter is dealt with through a time integration method such as the Newmark method.The summation of the responses of these two sub-systems is the responses of the original dynamic system.It is concluded that,with little sacrifice of efficiency,the combination method based on the strategy is more accurate than the combined time integration method,but it has the same accuracy order as that of the combined method.Numerical experiments validate the effectiveness of the proposed strategy.
文摘With the rapid development of the social economy,the pace of urban-rural integration construction has been accelerating continuously.From the actual situation at this stage,it is necessary to maintain the sound relationship of coordination,interaction and mutual advance between the city and the village.In the process of building urban-rural integration,we should focus on strengthening the development of land management,so as to improve the rationality of land development and utilization,and maximize the value of land while protecting rural farmland resources.The author explores and analyzes the problems existing in the land management work in the urban-rural integration construction.An effective way is put forward to carry out land management work in urban and rural integration construction,which contributes to the improvement of the quality of land management work.
文摘This paper presents the integration methods for vacco dynmmies equations of nonlinear nonholononic system,First.vacco dynamies equations are written in the canonical form and the field form.second the gradient methods the single-componentmethods and the field method are used to integrate the dynamics equations of the corresponding holonomic system respectively.And considering the restriction of nonholonomic construint to the initial conditions the solutions of Vacco dynamics cquations of nonlinear nonholonomic system are obtained.
基金The National Natural Science Foundation of China(No.10972151)
文摘The idea of the gradient method for integrating the dynamical equations of a nonconservative system presented by Vujanovic is transplanted to a Birkhoffian system, which is a new method for the integration of Birkhoff＇s equations. First, the differential equations of motion of the Birkhoffian system are written out. Secondly, 2n Birkhoff＇s variables are divided into two parts, and assume that a part of the variables is the functions of the remaining part of the variables and time. Thereby, the basic quasi-linear partial differential equations are established. If a complete solution of the basic partial differential equations is sought out, the solution of the problem is given by a set of algebraic equations. Since one can choose n arbitrary Birkhoff＇s variables as the functions of n remains of variables and time in a specific problem, the method has flexibility. The major difficulty of this method lies in finding a complete solution of the basic partial differential equation. Once one finds the complete solution, the motion of the systems can be obtained without doing further integration. Finally, two examples are given to illustrate the application of the results.
文摘Comprehensive English is a very basic and important course for English majors,according to the features of the text-book A New English Course,teachers should adopt the integration of grammar translation method and communicative approach to improve students' linguistic competence and communicative competence.
基金supported by the National Science and Technology Major Project of China(Grant No. 2011ZX05004-003,2011ZX05014-006-006)the National Key Basic Research Program of China(Grant No. 2013CB228602)the Natural Science Foundation of China(Grant No. 40974066)
文摘The Finite Difference （FD） method is an important method for seismic numerical simulations. It helps us understand regular patterns in seismic wave propagation, analyze seismic attributes, and interpret seismic data. However, because of its discretization, the FD method is only stable under certain conditions. The Arbitrary Difference Precise Integration （ADPI） method is based on the FD method and adopts an integration scheme in the time domain and an arbitrary difference scheme in the space domain. Therefore, the ADPI method is a semi-analytical method. In this paper, we deduce the formula for the ADPI method based on the 3D elastic equation and improve its stability. In forward modeling cases, the ADPI method was implemented in 2D and 3D elastic wave equation forward modeling. Results show that the travel time of the reflected seismic wave is accurate. Compared with the acoustic wave field, the elastic wave field contains more wave types, including PS- and PP- reflected waves, transmitted waves, and diffracted waves, which is important to interpretation of seismic data. The method can be easily applied to elastic wave equation numerical simulations for eoloical models.
基金supported by the National Natural Science Foundation of China (Grant No. 50879090)
文摘The singularities, oscillatory performances and the contributing factors to the 3-＇D translating-pulsating source Green function of deep-water Havelock form which consists of a local disturbance part and a far-field wave-like part, are analyzed systematically. Relative numerical integral methods about the two parts are presented in this paper. An improved method based on LOBATTO rule is used to eliminate singularities caused respectively by infinite discontinuity and jump discontinuous node from the local disturbance part function, which makes the improvement of calculation efficiency and accuracy possible. And variable substitution is applied to remove the singularity existing at the end of the integral interval of the far-field wave-like part function. Two auxiliary techniques such as valid interval calculation and local refinement of integral steps technique in narrow zones near false singularities are applied so as to avoid unnecessary integration of invalid interval and improve integral accordance. Numerical test results have proved the efficiency and accuracy in these integral methods that thus can be applied to calculate hydrodynamic performance of floating structures moving in waves.
基金The Project is supported by the National Natural Science Foundation of China
文摘In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then the field method for integrating these equations is given.Finally,an example illustrating the appli- cation of the integration method is given.
基金provided by the National Natural Science Foundation of China(No.51404272)the Hunan Province Key Laboratory of Coal Resources Clean-Utilization and Mine Environment Protection(No.E21224)
文摘In order to obtain accurate probability integration method(PIM) parameters for surface movement of multi-panel mining, a genetic algorithm(GA) was used to optimize the parameters. As the measured surface movement is affected by more than one mining panel, traditional PIM parameter inversion model is difficult to ensure the reliability of the results due to the complexity of rock movement. With crossover,mutation and selection operators, GA can perform a global optimization search and has high computation efficiency. Compared with the pattern search algorithm, the fitness function can avoid falling into local minima traps. GA reduces the risk of local minima traps which improves the accuracy and reliability with the mutation mechanism. Application at Xuehu colliery shows that GA can be used to inverse the PIM parameters for multi-panel surface movement observation, and reliable results can be obtained. The research provides a new way for back-analysis of PIM parameters for mining subsidence under complex conditions.
基金Supported by National Hi-tech Research and Development Program of China(863 Program,Grant No.2013AA031302)National Natural Science Foundation of China(Grant No.51805024)
文摘A model based on the curvature integration method has been applied in an online plate leveling system. However, there are some shortcomings in the current leveling models. On the one hand, the models cannot deal with the leveling process of plates with a random curvature distribution. On the other hand, the current models are suitable only for stable leveling processes and ignore the biting in and tailing out stages. This study presents a new plate-leveling model based on the curvature integration method, which can describe the leveling process of plates with random curvature distribution. Further, the model is solved in two cases in order to take the biting in and tailing out stages into consideration. The proposed model is evaluated by comparing with a plate leveling experiment. Finally, the leveling process of a plate with a wave bent is studied using the proposed model. It is found that the contact angles vary greatly during the biting in and tailing out stages. However, they are relatively steady during the 5 roller leveling stage. In addition, the contact angle of roller No. 2 is the smallest, which is close to 0. Roller leveling can effectively eliminate bending in the plate, but there are regions in the head and tail of the plate, where roller leveling is not effective. The non-leveling region length is about 2 times that of the roller space. This study proposes a quasi-static plate-leveling model, which makes it possible to analyze the dynamic straightening process using a curvature integration method. It also makes it possible to analyze the straightening process of a plate with random curvature distribution.
基金financial support from Hunan Provincial Natura1 Science Foundation of China,Grant Number:02JJY2085,for this study
文摘The precise time step integration method proposed for linear time-invariant homogeneous dynamic systems can provide precise numerical results that approach an exact solution at the integration points. However, difficulty arises when the algorithm is used for non-homogeneous dynamic systems, due to the inverse matrix calculation and the simulation accuracy of the applied loading. By combining the Gaussian quadrature method and state space theory with the calculation technique of matrix exponential function in the precise time step integration method, a new modified precise time step integration method （e.g., an algorithm with an arbitrary order of accuracy） is proposed. In the new method, no inverse matrix calculation or simulation of the applied loading is needed, and the computing efficiency is improved. In particular, the proposed method is independent of the quality of the matrix H. If the matrix H is singular or nearly singular, the advantage of the method is remarkable. The numerical stability of the proposed algorithm is discussed and a numerical example is given to demonstrate the validity and efficiency of the algorithm.
