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
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
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
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
A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinfo...A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous matrix.This framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact conditions.The mathematical formulation of the local problems and the effective coefficients are presented by the AHM.The local problems obtained from the AHM are solved by the FEM,which is denoted as the SAFEM.The numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.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
This is a very attractive article. It combines fascinating new methodology with a most interesting dataset, and a highly motivating presentation. However, despite the many
The authors are to be congratulated for an innovative paper in terms of both modelling methodology and subject matter significance. The analysis of short time series is known to be
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.
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.
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.
基金Project supported by the National Council of Humanities,Sciences,and Technologies of Mexico(Nos.CF-2023-G-792 and CF-2023-G-1458)the National Council for Scientific and Technological Development of Brazil(No.09/2023)the Research on Productivity of Brazil(No.307188/2023-0)。
文摘A semi-analytical finite element method(SAFEM),based on the two-scale asymptotic homogenization method(AHM)and the finite element method(FEM),is implemented to obtain the effective properties of two-phase fiber-reinforced composites(FRCs).The fibers are periodically distributed and unidirectionally aligned in a homogeneous matrix.This framework addresses the static linear elastic micropolar problem through partial differential equations,subject to boundary conditions and perfect interface contact conditions.The mathematical formulation of the local problems and the effective coefficients are presented by the AHM.The local problems obtained from the AHM are solved by the FEM,which is denoted as the SAFEM.The numerical results are provided,and the accuracy of the solutions is analyzed,indicating that the formulas and results obtained with the SAFEM may serve as the reference points for validating the outcomes of experimental and numerical computations.
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.
文摘This is a very attractive article. It combines fascinating new methodology with a most interesting dataset, and a highly motivating presentation. However, despite the many
文摘The authors are to be congratulated for an innovative paper in terms of both modelling methodology and subject matter significance. The analysis of short time series is known to be