Firstly, the new combined error model of cumulative geoid height influenced by four error sources, including the inter-satellite range-rate of an interferometric laser （K-band） ranging system, the orbital position a...Firstly, the new combined error model of cumulative geoid height influenced by four error sources, including the inter-satellite range-rate of an interferometric laser （K-band） ranging system, the orbital position and velocity of a global positioning system （GPS） receiver and non-conservative force of an accelerometer, is established from the perspectives of the power spectrum principle in physics using the semi-analytical approach. Secondly, the accuracy of the global gravitational field is accurately and rapidly estimated based on the combined error model; the cumulative geoid height error is 1.985× 10^-1 m at degree 120 based on GRACE Level 1B measured observation errors of the year 2007 published by the US Jet Propulsion Laboratory （JPL）, and the cumulative geoid height error is 5.825 × 10^-2 m at degree 360 using GRACE Follow-On orbital altitude 250 km and inter-satellite range 50 km. The matching relationship of accuracy indexes from GRACE Follow-On key payloads is brought forward, and the dependability of the combined error model is validated. Finally, the feasibility of high-accuracy and high-resolution global gravitational field estimation from GRACE Follow-On is demonstrated based on different satellite orbital altitudes.展开更多
The calculation of frost heaving with ice lens formation is still not standard for construction projects using artificial ground freezing(AGF).In fine-grained material,ice lenses may initiate and lead to significant h...The calculation of frost heaving with ice lens formation is still not standard for construction projects using artificial ground freezing(AGF).In fine-grained material,ice lenses may initiate and lead to significant heaving at the ground surface,which should be considered in advance.However,the complex processes during ice lens formation are still not fully understood and difficult to capture in a simple approach.In the past,the semi-analytical approach of Konrad and Morgenstern used one soil constant,the“segregation potential(SP)”.It has been mainly and most successfully applied to the heave calculation of natural-induced soil freezing in cold regions.Its application to AGF has been so far unsuccessful.To solve this,a new semi-analytical approach is presented in this paper.It includes AGF conditions such as bottom-up freezing,temperature gradients to reach great freezing velocities,and a distinction between two freezing states.One is the freezing-up state until a certain frost body thickness is reached(thermal transient state),and the other is a holding phase where the frost body thickness is kept constant(thermal quasi-steady state).To test its ability,the results are applied to another freezing direction,the top-down freezing.The new approach is validated using two different frost-susceptible soils and,in total,50 frost heave tests.In the thermal transient region,where the SP is applicable,the two semi-analytical approaches are compared,showing improved performance of the current method by about 15%.展开更多
The two-dimensional transient response of an imperfect bonded circular lined pipeline lying in an elastic infinite medium is investigated.Imperfect boundary conditions between the surrounding elastic rock and the tunn...The two-dimensional transient response of an imperfect bonded circular lined pipeline lying in an elastic infinite medium is investigated.Imperfect boundary conditions between the surrounding elastic rock and the tunnel are modelled with a two-linear-spring design.The novelty of the manuscript consists in studying at the same time transient regimes and imperfect bonded interfaces for simulating the dynamic response of a tunnel embedded in an elastic infinite rock.Wave propagation fields in tunnel and rock are expressed in terms of infinite Bessel and Hankel series.To solve the transient problem,the Laplace transform and the associated Durbin’s algorithm are performed.To exhibit the dynamic responses,influences of various parameters such as the quality of the interface conditions and the thickness of the lining are presented.The dynamic hoop stresses and the solid displacements of both the tunnel and the rock are also proposed.展开更多
4 semi-analytical approach for the dynamic response of general thin plates whichemployes finite element discretization in space domain and a series of representation intime demain is developed on the basis of Curtin v...4 semi-analytical approach for the dynamic response of general thin plates whichemployes finite element discretization in space domain and a series of representation intime demain is developed on the basis of Curtin variational principles.The formulationof time series is also investigated so that the dynamic response of plates with arbitraryshape and boundary constraints can be achieved with adequate accuracy.展开更多
Tokamak plasma density evolution is generally modeled by a diffusion-convection equation in cylindrical geometry. By using a semi-analytical approach, we solve such an equation for a given diffusion coefficient and in...Tokamak plasma density evolution is generally modeled by a diffusion-convection equation in cylindrical geometry. By using a semi-analytical approach, we solve such an equation for a given diffusion coefficient and inward convection velocity as an arbitrary function of the radial position. Through variable separation, a Sturm-Liouville-type eigenvalue problem is solved, thereby constructing a complete set of orthogonal eigenfunctions. Based on the decomposition of the solution, the initial function, and the source function in these eigenfunctions, several problems of practical interest about the density evolution are analyzed. They include the density evolution, with boundary density not being zero; the density profile with internal transport barrier; the damping profile during particle source being shut-down. Results are found to be qualitatively consistent with the tokamak experiments.展开更多
In this study,the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-ba...In this study,the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method.The material properties including tensile modulus,shear modulus,and density of the plate were assumed to be spatially varying and uncertain.Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties.The stochastic fields were decomposed via application of the K arhunen-Loeve theorem.A first-order shear deformation theory was assumed,following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies.The stochastic equations of motion of the plate were obtained using the variational principle.The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies,and the corresponding mode shapes of the plate were determined using a polynomial chaos approach.The proposed method significantly reduced the size of the mathematical models of the structure,which is very useful for enhancing the computational efficiency of stochastic simulations.The methodology was verifed using a stochastic finite element method and the available results in literature.The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated,and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.展开更多
Firstly, the Earth＇s gravitational field from the past Challenging Minisatellite Payload （CHAMP） mission is determined using the energy conservation principle, the combined error model of the cumulative geoid heigh...Firstly, the Earth＇s gravitational field from the past Challenging Minisatellite Payload （CHAMP） mission is determined using the energy conservation principle, the combined error model of the cumulative geoid height influenced by three instrument errors from the current Gravity Recovery and Climate Experiment （GRACE） and future GRACE Follow-On missions is established based on the semi-analytical method, and the Earth＇s gravitational field from the executed Gravity Field and Steady-State Ocean Circulation Explorer （GOCE） mission is recovered by the space-time-wise approach. Secondly, the cumulative geoid height errors are 1.727 × 10^-1 m, 1.839 × 10^-1 m and 9.025 × 10^ -2 m at degrees 70,120 and 250 from the implemented three-stage satellite gravity missions consisting of CHAMP, GRACE and GOCE, which preferably accord with those from the existing earth gravity field models involving EIGEN-CHAMP03S, EICEN-GRACE02S and GO_CONS GCF 2 DIR R1. The cumulative geoid height error is 6.847 × 10 ^-2 m at degree 250 from the future GRACE Follow-On mission. Finally, the complementarity among the four-stage satellite gravity missions including CHAMP, GRACE, GOCE and GRACE Follow-On is demonstrated contrastively.展开更多
A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, u...A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures.展开更多
基金supported by the National Natural Science Foundation of China (Grant No 40674038)the Funds of the Chinese Academy of Sciences for Key Topics in Innovation Engineering (Grant Nos KZCX2-YW-143 and KZCX2-YW-202)+1 种基金the National High Technology Research and Development Program of China (863) (Grant Nos 2009AA12Z138 and 2006AA09Z153)the Grant-in-Aid for Scientific Research of Japan (Grant No B19340129)
文摘Firstly, the new combined error model of cumulative geoid height influenced by four error sources, including the inter-satellite range-rate of an interferometric laser （K-band） ranging system, the orbital position and velocity of a global positioning system （GPS） receiver and non-conservative force of an accelerometer, is established from the perspectives of the power spectrum principle in physics using the semi-analytical approach. Secondly, the accuracy of the global gravitational field is accurately and rapidly estimated based on the combined error model; the cumulative geoid height error is 1.985× 10^-1 m at degree 120 based on GRACE Level 1B measured observation errors of the year 2007 published by the US Jet Propulsion Laboratory （JPL）, and the cumulative geoid height error is 5.825 × 10^-2 m at degree 360 using GRACE Follow-On orbital altitude 250 km and inter-satellite range 50 km. The matching relationship of accuracy indexes from GRACE Follow-On key payloads is brought forward, and the dependability of the combined error model is validated. Finally, the feasibility of high-accuracy and high-resolution global gravitational field estimation from GRACE Follow-On is demonstrated based on different satellite orbital altitudes.
基金supported by the German Research Foundation(DFG)under the project“Investigation and calculation of frost heave considering specific boundary conditions of ground freezing”(Grant No.409760547).
文摘The calculation of frost heaving with ice lens formation is still not standard for construction projects using artificial ground freezing(AGF).In fine-grained material,ice lenses may initiate and lead to significant heaving at the ground surface,which should be considered in advance.However,the complex processes during ice lens formation are still not fully understood and difficult to capture in a simple approach.In the past,the semi-analytical approach of Konrad and Morgenstern used one soil constant,the“segregation potential(SP)”.It has been mainly and most successfully applied to the heave calculation of natural-induced soil freezing in cold regions.Its application to AGF has been so far unsuccessful.To solve this,a new semi-analytical approach is presented in this paper.It includes AGF conditions such as bottom-up freezing,temperature gradients to reach great freezing velocities,and a distinction between two freezing states.One is the freezing-up state until a certain frost body thickness is reached(thermal transient state),and the other is a holding phase where the frost body thickness is kept constant(thermal quasi-steady state).To test its ability,the results are applied to another freezing direction,the top-down freezing.The new approach is validated using two different frost-susceptible soils and,in total,50 frost heave tests.In the thermal transient region,where the SP is applicable,the two semi-analytical approaches are compared,showing improved performance of the current method by about 15%.
文摘The two-dimensional transient response of an imperfect bonded circular lined pipeline lying in an elastic infinite medium is investigated.Imperfect boundary conditions between the surrounding elastic rock and the tunnel are modelled with a two-linear-spring design.The novelty of the manuscript consists in studying at the same time transient regimes and imperfect bonded interfaces for simulating the dynamic response of a tunnel embedded in an elastic infinite rock.Wave propagation fields in tunnel and rock are expressed in terms of infinite Bessel and Hankel series.To solve the transient problem,the Laplace transform and the associated Durbin’s algorithm are performed.To exhibit the dynamic responses,influences of various parameters such as the quality of the interface conditions and the thickness of the lining are presented.The dynamic hoop stresses and the solid displacements of both the tunnel and the rock are also proposed.
文摘4 semi-analytical approach for the dynamic response of general thin plates whichemployes finite element discretization in space domain and a series of representation intime demain is developed on the basis of Curtin variational principles.The formulationof time series is also investigated so that the dynamic response of plates with arbitraryshape and boundary constraints can be achieved with adequate accuracy.
文摘Tokamak plasma density evolution is generally modeled by a diffusion-convection equation in cylindrical geometry. By using a semi-analytical approach, we solve such an equation for a given diffusion coefficient and inward convection velocity as an arbitrary function of the radial position. Through variable separation, a Sturm-Liouville-type eigenvalue problem is solved, thereby constructing a complete set of orthogonal eigenfunctions. Based on the decomposition of the solution, the initial function, and the source function in these eigenfunctions, several problems of practical interest about the density evolution are analyzed. They include the density evolution, with boundary density not being zero; the density profile with internal transport barrier; the damping profile during particle source being shut-down. Results are found to be qualitatively consistent with the tokamak experiments.
文摘In this study,the influences of spatially varying stochastic properties on free vibration analysis of composite plates were investigated via development of a new approach named the deterministic-stochastic Galerkin-based semi-analytical method.The material properties including tensile modulus,shear modulus,and density of the plate were assumed to be spatially varying and uncertain.Gaussian fields with first-order Markov kernels were utilized to define the aforementioned material properties.The stochastic fields were decomposed via application of the K arhunen-Loeve theorem.A first-order shear deformation theory was assumed,following which the displacement field was defined using admissible trigonometric modes to derive the potential and kinetic energies.The stochastic equations of motion of the plate were obtained using the variational principle.The deterministic-stochastic Galerkin-based method was utilized to find the probability space of natural frequencies,and the corresponding mode shapes of the plate were determined using a polynomial chaos approach.The proposed method significantly reduced the size of the mathematical models of the structure,which is very useful for enhancing the computational efficiency of stochastic simulations.The methodology was verifed using a stochastic finite element method and the available results in literature.The sensitivity of natural frequencies and corresponding mode shapes due to the uncertainty of material properties was investigated,and the results indicated that the higher-order modes are more sensitive to uncertainty propagation in spatially varying properties.
基金supported by the Main Direction Program of Knowledge Innovation of Chinese Academy of Sciences for Distinguished Young Scholar(KZCX2-EW-QN114)the National Natural Science Foundation of China(41004006,41131067,11173049 and 41274041)+7 种基金the Merit-based Scientific Research Foundation of the State Ministry of Human Resources and Social Security of China for Returned Overseas Chinese Scholars(Z01101)the Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy,Ministry of Education,China(11-01-02)the Open Research Fund Program of the Key Laboratory of Geo-Informatics of National Administration of Surveying,Mapping and Geoinformation of China(201322)the Open Research Fund Program of the State Key Laboratory of Geoinformation Engineering,China(SKLGIE2013-M-1-5)the Main Direction Program of Institute of Geodesy and Geophysics,Chinese Academy of Sciences(Y309451045)the Research Fund Program of State Key Laboratory of Geodesy and Earth's Dynamics,China(Y309491050)the Research Fund of the National Civilian Space Infrastructure Project(Y419341034)the Research Fund of the Lu Jiaxi Young Talent and the Youth Innovation Promotion Association of Chinese Academy of Science(Y305171017)
文摘Firstly, the Earth＇s gravitational field from the past Challenging Minisatellite Payload （CHAMP） mission is determined using the energy conservation principle, the combined error model of the cumulative geoid height influenced by three instrument errors from the current Gravity Recovery and Climate Experiment （GRACE） and future GRACE Follow-On missions is established based on the semi-analytical method, and the Earth＇s gravitational field from the executed Gravity Field and Steady-State Ocean Circulation Explorer （GOCE） mission is recovered by the space-time-wise approach. Secondly, the cumulative geoid height errors are 1.727 × 10^-1 m, 1.839 × 10^-1 m and 9.025 × 10^ -2 m at degrees 70,120 and 250 from the implemented three-stage satellite gravity missions consisting of CHAMP, GRACE and GOCE, which preferably accord with those from the existing earth gravity field models involving EIGEN-CHAMP03S, EICEN-GRACE02S and GO_CONS GCF 2 DIR R1. The cumulative geoid height error is 6.847 × 10 ^-2 m at degree 250 from the future GRACE Follow-On mission. Finally, the complementarity among the four-stage satellite gravity missions including CHAMP, GRACE, GOCE and GRACE Follow-On is demonstrated contrastively.
基金supported by the National Natural Science Foundation of China (No.10972084)
文摘A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures.
