The electromagnetic(EM)telemetry systems,employed for real-time data transmission from the borehole and the earth surface during drilling,are widely used in measurement-while-drilling(MWD)and logging-while-drilling(LW...The electromagnetic(EM)telemetry systems,employed for real-time data transmission from the borehole and the earth surface during drilling,are widely used in measurement-while-drilling(MWD)and logging-while-drilling(LWD).Several numerical methods,including the method of moments(MoM),the electric field integral equation(EFIE)method,and the finite-element(FE)method have been developed for the simulation of EM telemetry systems.The computational process of these methods is complicated and time-consuming.To solve this problem,we introduce an axisymmetric semi-analytical FE method(SAFEM)in the cylindrical coordinate system with the virtual layering technique for rapid simulation of EM telemetry in a layered earth.The proposed method divides the computational domain into a series of homogeneous layers.For each layer,only its cross-section is discretized,and a high-precision integration method based on Riccati equations is employed for the calculation of longitudinally homogeneous sections.The block-tridiagonal structure of the global coefficient matrix enables the use of the block Thomas algorithm,facilitating the efficient simulation of EM telemetry problems in layered media.After the theoretical development,we validate the accuracy and efficiency of our algorithm through a series of numerical experiments and comparisons with the Multiphysics modeling software COMSOL.We also discussed the impact of system parameters on EM telemetry signal and demonstrated the applicability of our method by testing it on a field dataset acquired from Dezhou,Shandong Province,China.展开更多
The increasing use of small material components in a wide range of industrial fields necessitates the development of an accurate and robust indentation testing method.To this end,this paper proposes an Energy-density-...The increasing use of small material components in a wide range of industrial fields necessitates the development of an accurate and robust indentation testing method.To this end,this paper proposes an Energy-density-equivalence for a Flat Indentation(E-FI)model based on the energy density equivalent principle.The proposed model describes the relationships among the material parameters of Hollomon's power law(H-law),flat indenter diameter,energy,and indentation displacement.An E-FI Method(E-FIM)that determines the H-law parameters of materials through the indentation test is also developed.The energy-displacement curves forward-predicted by the E-FI model(based on known H-law parameters of materials)and the H-law parameters of materials given by the E-FIM(based on known energy-displacement curves)are consistent with the results of Finite Element Analysis(FEA)and the H-law parameters of materials used as the input for FEA,respectively.Using E-FIM,the goodness of fit for both stress–strain curves with H-law,predicted based on the displacement with 2%signal interference,and that for stress–strain curves without interference is more than 0.98.The stress–strain relations predicted by E-FIM were consistent with the results obtained via uniaxial tensile tests of ten ductile materials.展开更多
The semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation for unsaturated soils with a semi-permeable drainage boundary are pre- seated. Two variables are introduced to transform the ...The semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation for unsaturated soils with a semi-permeable drainage boundary are pre- seated. Two variables are introduced to transform the two coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations （PDFs）, which are easily solved by the Laplace transform method. Then, the pore-water pressure, pore-air pressure, and soil settlement are obtained in the Laplace domain. The Crump method is adopted to perform the inverse Laplace transform in order to obtain the semi-analytical solutions in the time domain. It is shown that the proposed solutions are more applicable to various types of boundary conditions and agree well with the existing solutions from the literature. Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with single, double, mixed, and semi-permeable drainage boundaries. The changes in the pore-air and pore-water pres- sures and the soil settlement with the time factor at different values of the semi-permeable drainage boundary parameters are illustrated. In addition, parametric studies are con- ducted on the pore-air and pore-water pressures at different ratios （the air permeability coefficient to the water permeability coefficient） and depths.展开更多
Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harm...Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.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
This paper presents general semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and t...This paper presents general semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and poreair pressures into an equivalent set of partial differential equations （PDEs）, which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domMn. The Crump＇s method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature.展开更多
Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation...Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation efectiveness and precision, is presented for solving the acoustic radiation from a submerged infnite non-circular cylindrical shell stifened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work, besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The efects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efcient than the existing mixed FE-BE method.展开更多
Based on the Hellinger-Reissner （H-R） mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analyt...Based on the Hellinger-Reissner （H-R） mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch is presented. The major steps of mathematical model are as follows： the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. Present method has wide application area.展开更多
This study focuses on the consolidation behavior and mathematical interpretation of partially-saturated ground improved by impervious column inclusion.The constitutive relations for soil skeleton,pore air and pore wat...This study focuses on the consolidation behavior and mathematical interpretation of partially-saturated ground improved by impervious column inclusion.The constitutive relations for soil skeleton,pore air and pore water for partially saturated soils are proposed in the context of partially-saturated ground improved by impervious column inclusion.Settlement equation and dissipation equations of excess pore air/water pressures for a partially saturated improved ground are then derived.The semi-analytical solutions for ground settlement and pore pressure dissipation are then obtained through the Laplace transform and validated by the existing solutions for two special cases in the literature and the numerical results obtained from the finite difference method.A series of parametric studies is finally conducted to investigate the influence of some key factors on consolidation of partially saturated ground improved by impervious column inclusion.Based on the parametric study,it can be found that a higher value of the area replacement ratio or modulus of the pile results in a longer dissipation time of excess pore air pressure(PAP),a shorter dissipation time of excess pore water pressure(PWP),and a lower normalized settlement.展开更多
Based on potential flow theory, a dissipative semi-analytical solution is developed for the wave resonance in the narrow gap between a fixed floating box and a vertical wall by using velocity potential decompositions ...Based on potential flow theory, a dissipative semi-analytical solution is developed for the wave resonance in the narrow gap between a fixed floating box and a vertical wall by using velocity potential decompositions and matched eigenfunction expansions. The energy dissipation near the box is modelled in the potential flow solution by introducing a quadratic pressure loss condition on the gap entrance. Such a treatment is inspired by the classical local head loss formula for the sudden change of cross section in channel flow, where the energy dissipation is assumed to be proportional to the square of local velocity for high Reynolds number flows. The dimensionless energy loss coefficient is calibrated based on experimental data. And it is found to be insensitive to the incident wave height and wave frequency. With the calibrated energy loss coefficient, the resonant wave height in gap and the reflection coefficient are calculated by the present dissipative semi-analytical solution. The predictions are in good agreement with experimental data. Case studies suggest that the maximum relative energy dissipation occurs near the resonant frequency, which leads to the minimum reflection coefficient. The horizontal wave forces on the box and the vertical wall attain also maximum values near the resonant frequency, while the vertical wave force on the box decreases abruptly there to a small value.展开更多
In this paper, a series of semi-analytical solutions to one-dimensional consolidation in unsaturated soils are obtained. The air governing equation by Fredlund for unsaturated soils consolidation is simplified. By app...In this paper, a series of semi-analytical solutions to one-dimensional consolidation in unsaturated soils are obtained. The air governing equation by Fredlund for unsaturated soils consolidation is simplified. By applying the Laplace transform and the Cayley-Hamilton theorem to the simplified governing equations of water and air, Darcy＇s law, and Fick＇s law, the transfer function between the state vectors at top and at any depth is then constructed. Finally, by the boundary conditions, the excess pore-water pressure, the excess pore-air pressure, and the soil settlement are obtained under several kinds of boundary conditions with the large-area uniform instantaneous loading. By the Crump method, the inverse Laplace transform is performed, and the semi-analytical solutions to the excess pore-water pressure, the excess pore-air pressure, and the soils settlement are obtained in the time domain. In the case of one surface which is permeable to air and water, comparisons between the semi-analytical solutions and the analytical solutions indicate that the semi-analytical solutions are correct. In the case of one surface which is permeable to air but impermeable to water, comparisons between the semi-analytical solutions and the results of the finite difference method are made, indicating that the semi-analytical solution is also correct.展开更多
A semi-analytical Monte Carlo (SMC) simulation was developed to simulate the propagation of laser-induced fluo- rescence (LIF) in an optically participating spray, which simultaneously exhibits spectrally dependent em...A semi-analytical Monte Carlo (SMC) simulation was developed to simulate the propagation of laser-induced fluo- rescence (LIF) in an optically participating spray, which simultaneously exhibits spectrally dependent emission, anisotropic scattering, absorption, and re-emission. The SMC simulation is described and then applied to an experimental configuration of a cloud of polydisperse droplets composed of water and sulforhodamine B dye. In the SMC simulation, the collected LIF flux on the remote receptor element is calculated as the global contribution from the emissive source, single, twice, … and nth collision events in any sequence. The effects on the fluorescence photons propagation of spray parameters like the dye concentration, droplets concentration, and droplets size are examined. Three spectral bands representing different optical properties are chosen to analyze the interference of absorption, scattering and re-emission on the detected LIF flux. The obtained spectral LIF flux distribution on the receptor demonstrates a “red shift” phenomenon.展开更多
Secchi depth(SD,m)is a direct and intuitive measure of water's transparency,which is also an indicator of water quality.In 2015,a semi-analytical model was developed to derive SD from remote sensing reflectance,th...Secchi depth(SD,m)is a direct and intuitive measure of water's transparency,which is also an indicator of water quality.In 2015,a semi-analytical model was developed to derive SD from remote sensing reflectance,thus able to provide maps of water's transparency in satellite images.Here an in-situ dataset(338 stations)is used to evaluate its potential ability to monitor water quality in the coastal and estuarine waters,with measurements covering the Zhujiang(Pearl)River Estuary,the Yellow Sea and the East China Sea where measured SD values span a range of 0.2–21.0 m.As a preliminary validation result,according to the whole dataset,the unbiased percent difference(UPD)between estimated and measured SD is 23.3%(N=338,R^2=0.89),with about 60%of stations in the dataset having relative difference(RD)≤20%,over 80%of stations having RD≤40%.Furthermore,by excluding the field data which with relatively larger uncertainties,the semi-analytical model yielded the UPD of 17.7%(N=132,R^2=0.92)with SD range of 0.2–11.0 m.In addition,the semi-analytical model was applied to Landsat-8 images in the Zhujiang River Estuary,and retrieved high-quality mapping and reliable spatial-temporal patterns of water clarity.Taking into account the uncertainties associated with both field measurements and satellite data processing,and that there were no tuning of the semi-analytical model for these regions,these findings indicate highly robust retrieval of SD from spectral techniques for such turbid coastal and estuarine waters.The results suggest it is now possible to routinely monitor coastal water transparency or visibility at high-spatial resolutions from measurements,like Landsat-8 and Sentinel-2 and newly launched Gaofen-5.展开更多
Semi-analytical elasticity solutions for bending of angle-ply laminates in cylindrical bending are presented using the state-space-based differential quadrature method (SSDQM). Partial differential state equation is d...Semi-analytical elasticity solutions for bending of angle-ply laminates in cylindrical bending are presented using the state-space-based differential quadrature method (SSDQM). Partial differential state equation is derived from the basic equations of elasticity based on the state space concept. Then, the differential quadrature (DQ) technique is introduced to discretize the longitu- dinal domain of the plate so that a series of ordinary differential state equations are obtained at the discrete points. Meanwhile, the edge constrained conditions are handled directly using the stress and displacement components without the Saint-Venant principle. The thickness domain is solved analytically based on the state space formalism along with the continuity conditions at interfaces. The present method is validated by comparing the results to the exact solutions of Pagano’s problem. Numerical results for fully clamped thick laminates are presented, and the influences of ply angle on stress distributions are discussed.展开更多
In this paper,a semi-analytical method was proposed to evaluate the acoustic nonlinearity parameter for single crystals of Cu,Ag and Au.The acoustic nonlinearity parameter can be derived analytically by general expres...In this paper,a semi-analytical method was proposed to evaluate the acoustic nonlinearity parameter for single crystals of Cu,Ag and Au.The acoustic nonlinearity parameter can be derived analytically by general expressions in terms of the interatomic potentials with the distances between each pair of atoms in these transition metals.To evaluate the acoustic nonlinearity parameter,one needs to conduct one step molecular static simulation and obtain the equilibrium positions of all the atoms.Further,based on this method,numerical experiments with molecular dynamic code LAMMPS were given to compute the acoustic nonlinearity parameter of Cu,Ag and Au.To illustrate the validity of these expressions,comparison was made between calculation results and data in the literature.Reasonable agreement is observed.Because of the analytical nature of this method,it provides a fundamental understanding of the nonlinear elastic behavior of these transition metals.展开更多
The effect of axial shallow groove on the nonlinear dynamic response and buckling of laminated cylindrical shells subjected to radial compression loading was investigated. Based on the first-order shear deformation th...The effect of axial shallow groove on the nonlinear dynamic response and buckling of laminated cylindrical shells subjected to radial compression loading was investigated. Based on the first-order shear deformation theory （FSDT）, the nonlinear dynamic equations involving the transverse shear deformation and initial geometric imperfections were derived with the Hamilton philosophy. The axial shallow groove of the laminated composite cylindrical shell was treated as the initial geometric imperfections in the dynamic equations. A semi-analytical method of expanding displacements and loads along the circumferential direction and employing the finite difference method along the axial direction and in the time domain is used to solve the governing equations and obtain the dynamic response of the laminated shell. The B-R criterion was employed to determine the critical loads of dynamic buckling of the shell. The effects of the parameters of the shallow groove on the dynamic response and buckling were discussed in this paper and the results show that the axial shallow grooves greatly affect the dynamic response and buckling.展开更多
SP3 （simplified P3） theory is widely used in LWR （light water reactor） analyses to partly capture the transport effect, especially for pin-by-pin core analysis with pin size homogenization. In this paper, a SP3 co...SP3 （simplified P3） theory is widely used in LWR （light water reactor） analyses to partly capture the transport effect, especially for pin-by-pin core analysis with pin size homogenization. In this paper, a SP3 code named STELLA is developed and verified at SNERDI （Shanghai Nuclear Engineering Research and Design Institute）. For SP3 method, neutron transport equation can be transformed into two coupled equations in the same mathematical form as diffusion equation. In this work, SANM （semi-analytic nodal method） is used to solve diffusion-like equation, due to its easy to handle multi-group problem. Whole core nodal boundary net current coupling is used to improve convergence stability in SANM, instead of solving two-node problem. CMFD （coarse-mesh finite difference） acceleration method is employed for 0-th SP3 equation, which represents the neutron balance relationship. Three benchmarks are used to verify the SP3 code, STELLA. The first one is a self-defined one dimensional problem, which demonstrates SP3 method is extremely accurate, due to no academic approximation in one dimensional for SP3. The second one is a two dimensional one-group problem cited from Larsen＇s paper, which is usually used to verify and prove the SP3 code correct and accurate. And the third one is modified from 2D C5G7-MOX benchmark, whose numerical results indicate that STELLA is accurate and efficient in pin size level, compared to diffusion model.展开更多
Power system simulations that extend over a time period of minutes,hours,or even longer are called extendedterm simulations.As power systems evolve into complex systems with increasing interdependencies and richer dyn...Power system simulations that extend over a time period of minutes,hours,or even longer are called extendedterm simulations.As power systems evolve into complex systems with increasing interdependencies and richer dynamic behaviors across a wide range of timescales,extendedterm simulation is needed for many power system analysis tasks(e.g.,resilience analysis,renewable energy integration,cascading failures),and there is an urgent need for efficient and robust extendedterm simulation approaches.The conventional approaches are insufficient for dealing with the extendedterm simulation of multitimescale processes.This paper proposes an extendedterm simulation approach based on the semianalytical simulation(SAS)methodology.Its accuracy and computational efficiency are backed by SAS's high accuracy in eventdriven simulation,larger and adaptive time steps,and flexible switching between fulldynamic and quasisteadystate(QSS)models.We used this proposed extendedterm simulation approach to evaluate bulk power system restoration plans,and it demonstrates satisfactory accuracy and efficiency in this complex simulation task.展开更多
Usually, it is very difficult to find out an analytical solution to thermal conduction problems during high temperature welding. Therefore, as an important numerical approach, the method of lines （MOLs） is introduce...Usually, it is very difficult to find out an analytical solution to thermal conduction problems during high temperature welding. Therefore, as an important numerical approach, the method of lines （MOLs） is introduced to solve the temperature field characterized by high gradients. The basic idea of the method is to semi-discretize the governing equation of the problem into a system of ordinary differential equations （ODEs） defined on discrete lines by means of the finite difference method, by which the thermal boundary condition with high gradients are directly embodied in formulation. Thus the temperature field can be obtained by solving the ODEs. As a numerical example, the variation of an axisymmetrical temperature field along the plate thickness can be obtained.展开更多
Fatigue damage monitoring is critical metallic structure health monitoring of aircraft.The sensor should be high sensitive,easy to be integrated into structure and well adaptable for poor working conditions.Therefore,...Fatigue damage monitoring is critical metallic structure health monitoring of aircraft.The sensor should be high sensitive,easy to be integrated into structure and well adaptable for poor working conditions.Therefore,an attached eddy current sensor with flexible plane is put forward and its characteristics are analyzed.By extracting material′s conductivity as the crack features,forward semi-analytical model is established and parameter optimizations are carried out.Crack perturbation model of attached eddy current sensor is constructed,and perturbation voltages of sensing channels under three-dimension structural crack are obtained.To verify the sensor′s performance,monitoring experiment on crack extension is conducted under condition of 3 MHz frequency.The validation experimental results show that perturbation model of 2A12-T4 aluminum alloy agrees well with experiment results,and perturbation model errors of four sensing channels are within 25%.The attached eddy current sensor is capable of testing the crack nondestructively and measuring the crack extension quantitatively with the accuracy of 1mm.展开更多
基金supported by the Major Research Project on Scientific Instrument Development of the National Natural Science Foundation of China(42327901)National Natural Science Foundation of China(42030806,42074120,41904104,423B2405).
文摘The electromagnetic(EM)telemetry systems,employed for real-time data transmission from the borehole and the earth surface during drilling,are widely used in measurement-while-drilling(MWD)and logging-while-drilling(LWD).Several numerical methods,including the method of moments(MoM),the electric field integral equation(EFIE)method,and the finite-element(FE)method have been developed for the simulation of EM telemetry systems.The computational process of these methods is complicated and time-consuming.To solve this problem,we introduce an axisymmetric semi-analytical FE method(SAFEM)in the cylindrical coordinate system with the virtual layering technique for rapid simulation of EM telemetry in a layered earth.The proposed method divides the computational domain into a series of homogeneous layers.For each layer,only its cross-section is discretized,and a high-precision integration method based on Riccati equations is employed for the calculation of longitudinally homogeneous sections.The block-tridiagonal structure of the global coefficient matrix enables the use of the block Thomas algorithm,facilitating the efficient simulation of EM telemetry problems in layered media.After the theoretical development,we validate the accuracy and efficiency of our algorithm through a series of numerical experiments and comparisons with the Multiphysics modeling software COMSOL.We also discussed the impact of system parameters on EM telemetry signal and demonstrated the applicability of our method by testing it on a field dataset acquired from Dezhou,Shandong Province,China.
基金co-supported by the National Natural Science Foundation of China(No.11872320)。
文摘The increasing use of small material components in a wide range of industrial fields necessitates the development of an accurate and robust indentation testing method.To this end,this paper proposes an Energy-density-equivalence for a Flat Indentation(E-FI)model based on the energy density equivalent principle.The proposed model describes the relationships among the material parameters of Hollomon's power law(H-law),flat indenter diameter,energy,and indentation displacement.An E-FI Method(E-FIM)that determines the H-law parameters of materials through the indentation test is also developed.The energy-displacement curves forward-predicted by the E-FI model(based on known H-law parameters of materials)and the H-law parameters of materials given by the E-FIM(based on known energy-displacement curves)are consistent with the results of Finite Element Analysis(FEA)and the H-law parameters of materials used as the input for FEA,respectively.Using E-FIM,the goodness of fit for both stress–strain curves with H-law,predicted based on the displacement with 2%signal interference,and that for stress–strain curves without interference is more than 0.98.The stress–strain relations predicted by E-FIM were consistent with the results obtained via uniaxial tensile tests of ten ductile materials.
基金Project supported by the National Natural Science Foundation of China(Nos.41630633 and11672172)
文摘The semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation for unsaturated soils with a semi-permeable drainage boundary are pre- seated. Two variables are introduced to transform the two coupled governing equations of pore-water and pore-air pressures into an equivalent set of partial differential equations （PDFs）, which are easily solved by the Laplace transform method. Then, the pore-water pressure, pore-air pressure, and soil settlement are obtained in the Laplace domain. The Crump method is adopted to perform the inverse Laplace transform in order to obtain the semi-analytical solutions in the time domain. It is shown that the proposed solutions are more applicable to various types of boundary conditions and agree well with the existing solutions from the literature. Several numerical examples are provided to investigate the consolidation behavior of an unsaturated single-layer soil with single, double, mixed, and semi-permeable drainage boundaries. The changes in the pore-air and pore-water pres- sures and the soil settlement with the time factor at different values of the semi-permeable drainage boundary parameters are illustrated. In addition, parametric studies are con- ducted on the pore-air and pore-water pressures at different ratios （the air permeability coefficient to the water permeability coefficient） and depths.
基金Project supported by the National Natural Science Foundation of China (No.10172038)
文摘Based on the transfer matrix method and the virtual source simulation technique, this paper proposes a novel semi-analytical and semi-numerical method for solving 2-D sound- structure interaction problems under a harmonic excitation.Within any integration segment, as long as its length is small enough,along the circumferential curvilinear coordinate,the non- homogeneous matrix differential equation of an elastic ring of complex geometrical shape can be rewritten in terms of the homogeneous one by the method of extended homogeneous capacity proposed in this paper.For the exterior fluid domain,the multi-circular virtual source simulation technique is adopted.The source density distributed on each virtual circular curve may be ex- panded as the Fourier's series.Combining with the inverse fast Fourier transformation,a higher accuracy and efficiency method for solving 2-D exterior Helmholtz's problems is presented in this paper.In the aspect of solution to the coupling equations,the state vectors of elastic ring induced by the given harmonic excitation and generalized forces of coefficients of the Fourier series can be obtained respectively by using a high precision integration scheme combined with the method of extended homogeneous capacity put forward in this paper.According to the superposition princi- ple and compatibility conditions at the interface between the elastic ring and fluid,the algebraic equation of system can be directly constructed by using the least square approximation.Examples of acoustic radiation from two typical fluid-loaded elastic rings under a harmonic concentrated force are presented.Numerical results show that the method proposed is more efficient than the mixed FE-BE method in common use.
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.
基金Project supported by the National Natural Science Foundation of China(Nos.41372279 and41630633)
文摘This paper presents general semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and poreair pressures into an equivalent set of partial differential equations （PDEs）, which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domMn. The Crump＇s method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature.
基金Project supported by the National Natural Science Foundation of China(No.10172038),the Doctoral Foundation ofthe National Education Ministry(No.20040487013)and the Natural Science Foundation of Guangxi(No.0339019).
文摘Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation efectiveness and precision, is presented for solving the acoustic radiation from a submerged infnite non-circular cylindrical shell stifened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work, besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The efects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efcient than the existing mixed FE-BE method.
基金Project supported by the National Natural Science Foundation of China (No. 10072038)
文摘Based on the Hellinger-Reissner （H-R） mixed variational principle for piezoelectric material, a unified 4-node Hamiltonian isoparametric element of anisotropy piezoelectric material is established. A new semi-analytical solution for the natural vibration of smart laminated plates and the transient response of the laminated cantilever with piezoelectric patch is presented. The major steps of mathematical model are as follows： the piezoelectric layer and host layer of laminated plate are considered as unattached three-dimensional bodies and discretized by the Hamiltonian isoparametric elements. The control equation of whole structure is derived by considering the compatibility of generalized displacements and generalized stresses on the interface between layers. There is no restriction for the side-face geometrical boundaries, the thickness and the number of layers of plate by the use of the present isoparametric element. Present method has wide application area.
基金The financial support from National Natural Science Foundation of China (Grant Nos. 12172211 and 52078021)Shanghai Key Laboratory of Rail Infrastructure Durability and System Safety, China (Grant No. R201904)
文摘This study focuses on the consolidation behavior and mathematical interpretation of partially-saturated ground improved by impervious column inclusion.The constitutive relations for soil skeleton,pore air and pore water for partially saturated soils are proposed in the context of partially-saturated ground improved by impervious column inclusion.Settlement equation and dissipation equations of excess pore air/water pressures for a partially saturated improved ground are then derived.The semi-analytical solutions for ground settlement and pore pressure dissipation are then obtained through the Laplace transform and validated by the existing solutions for two special cases in the literature and the numerical results obtained from the finite difference method.A series of parametric studies is finally conducted to investigate the influence of some key factors on consolidation of partially saturated ground improved by impervious column inclusion.Based on the parametric study,it can be found that a higher value of the area replacement ratio or modulus of the pile results in a longer dissipation time of excess pore air pressure(PAP),a shorter dissipation time of excess pore water pressure(PWP),and a lower normalized settlement.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51725903, 51490675 and 51490673)the Taishan Scholar Project of Shandong Province (Grant No. ts20190915)。
文摘Based on potential flow theory, a dissipative semi-analytical solution is developed for the wave resonance in the narrow gap between a fixed floating box and a vertical wall by using velocity potential decompositions and matched eigenfunction expansions. The energy dissipation near the box is modelled in the potential flow solution by introducing a quadratic pressure loss condition on the gap entrance. Such a treatment is inspired by the classical local head loss formula for the sudden change of cross section in channel flow, where the energy dissipation is assumed to be proportional to the square of local velocity for high Reynolds number flows. The dimensionless energy loss coefficient is calibrated based on experimental data. And it is found to be insensitive to the incident wave height and wave frequency. With the calibrated energy loss coefficient, the resonant wave height in gap and the reflection coefficient are calculated by the present dissipative semi-analytical solution. The predictions are in good agreement with experimental data. Case studies suggest that the maximum relative energy dissipation occurs near the resonant frequency, which leads to the minimum reflection coefficient. The horizontal wave forces on the box and the vertical wall attain also maximum values near the resonant frequency, while the vertical wave force on the box decreases abruptly there to a small value.
文摘In this paper, a series of semi-analytical solutions to one-dimensional consolidation in unsaturated soils are obtained. The air governing equation by Fredlund for unsaturated soils consolidation is simplified. By applying the Laplace transform and the Cayley-Hamilton theorem to the simplified governing equations of water and air, Darcy＇s law, and Fick＇s law, the transfer function between the state vectors at top and at any depth is then constructed. Finally, by the boundary conditions, the excess pore-water pressure, the excess pore-air pressure, and the soil settlement are obtained under several kinds of boundary conditions with the large-area uniform instantaneous loading. By the Crump method, the inverse Laplace transform is performed, and the semi-analytical solutions to the excess pore-water pressure, the excess pore-air pressure, and the soils settlement are obtained in the time domain. In the case of one surface which is permeable to air and water, comparisons between the semi-analytical solutions and the analytical solutions indicate that the semi-analytical solutions are correct. In the case of one surface which is permeable to air but impermeable to water, comparisons between the semi-analytical solutions and the results of the finite difference method are made, indicating that the semi-analytical solution is also correct.
基金Project supported by the National Natural Science Foundation of China (No. 60534030)the Scholarship of French Embassy in China and the Doctoral Grant from French Embassy in China
文摘A semi-analytical Monte Carlo (SMC) simulation was developed to simulate the propagation of laser-induced fluo- rescence (LIF) in an optically participating spray, which simultaneously exhibits spectrally dependent emission, anisotropic scattering, absorption, and re-emission. The SMC simulation is described and then applied to an experimental configuration of a cloud of polydisperse droplets composed of water and sulforhodamine B dye. In the SMC simulation, the collected LIF flux on the remote receptor element is calculated as the global contribution from the emissive source, single, twice, … and nth collision events in any sequence. The effects on the fluorescence photons propagation of spray parameters like the dye concentration, droplets concentration, and droplets size are examined. Three spectral bands representing different optical properties are chosen to analyze the interference of absorption, scattering and re-emission on the detected LIF flux. The obtained spectral LIF flux distribution on the receptor demonstrates a “red shift” phenomenon.
基金The National Natural Science Foundation of China under contract No.61527810the Marine Science and Technology Fund from Director of South China Sea Branch+1 种基金State Oceanic Administration of China under contract No.180101the Key Laboratory Open Project Fund of Technology and Application for Safeguarding of Marine Rights and Interests,State Oceanic Administration of China under contract No.1720。
文摘Secchi depth(SD,m)is a direct and intuitive measure of water's transparency,which is also an indicator of water quality.In 2015,a semi-analytical model was developed to derive SD from remote sensing reflectance,thus able to provide maps of water's transparency in satellite images.Here an in-situ dataset(338 stations)is used to evaluate its potential ability to monitor water quality in the coastal and estuarine waters,with measurements covering the Zhujiang(Pearl)River Estuary,the Yellow Sea and the East China Sea where measured SD values span a range of 0.2–21.0 m.As a preliminary validation result,according to the whole dataset,the unbiased percent difference(UPD)between estimated and measured SD is 23.3%(N=338,R^2=0.89),with about 60%of stations in the dataset having relative difference(RD)≤20%,over 80%of stations having RD≤40%.Furthermore,by excluding the field data which with relatively larger uncertainties,the semi-analytical model yielded the UPD of 17.7%(N=132,R^2=0.92)with SD range of 0.2–11.0 m.In addition,the semi-analytical model was applied to Landsat-8 images in the Zhujiang River Estuary,and retrieved high-quality mapping and reliable spatial-temporal patterns of water clarity.Taking into account the uncertainties associated with both field measurements and satellite data processing,and that there were no tuning of the semi-analytical model for these regions,these findings indicate highly robust retrieval of SD from spectral techniques for such turbid coastal and estuarine waters.The results suggest it is now possible to routinely monitor coastal water transparency or visibility at high-spatial resolutions from measurements,like Landsat-8 and Sentinel-2 and newly launched Gaofen-5.
基金Project supported by the National Natural Science Foundation of China (No. 10432030)the China Postdoctoral Science Foundation (No. 20060401071)the Program for New Century Excellent Talent in University of China (No. NCET-05-0510)
文摘Semi-analytical elasticity solutions for bending of angle-ply laminates in cylindrical bending are presented using the state-space-based differential quadrature method (SSDQM). Partial differential state equation is derived from the basic equations of elasticity based on the state space concept. Then, the differential quadrature (DQ) technique is introduced to discretize the longitu- dinal domain of the plate so that a series of ordinary differential state equations are obtained at the discrete points. Meanwhile, the edge constrained conditions are handled directly using the stress and displacement components without the Saint-Venant principle. The thickness domain is solved analytically based on the state space formalism along with the continuity conditions at interfaces. The present method is validated by comparing the results to the exact solutions of Pagano’s problem. Numerical results for fully clamped thick laminates are presented, and the influences of ply angle on stress distributions are discussed.
基金financially supported by the National Sci-Tech Support Plan(No.2015BAF06B01)。
文摘In this paper,a semi-analytical method was proposed to evaluate the acoustic nonlinearity parameter for single crystals of Cu,Ag and Au.The acoustic nonlinearity parameter can be derived analytically by general expressions in terms of the interatomic potentials with the distances between each pair of atoms in these transition metals.To evaluate the acoustic nonlinearity parameter,one needs to conduct one step molecular static simulation and obtain the equilibrium positions of all the atoms.Further,based on this method,numerical experiments with molecular dynamic code LAMMPS were given to compute the acoustic nonlinearity parameter of Cu,Ag and Au.To illustrate the validity of these expressions,comparison was made between calculation results and data in the literature.Reasonable agreement is observed.Because of the analytical nature of this method,it provides a fundamental understanding of the nonlinear elastic behavior of these transition metals.
基金Project supported by the National Natural Science Foundation of China （Grant No. 10202013）
文摘The effect of axial shallow groove on the nonlinear dynamic response and buckling of laminated cylindrical shells subjected to radial compression loading was investigated. Based on the first-order shear deformation theory （FSDT）, the nonlinear dynamic equations involving the transverse shear deformation and initial geometric imperfections were derived with the Hamilton philosophy. The axial shallow groove of the laminated composite cylindrical shell was treated as the initial geometric imperfections in the dynamic equations. A semi-analytical method of expanding displacements and loads along the circumferential direction and employing the finite difference method along the axial direction and in the time domain is used to solve the governing equations and obtain the dynamic response of the laminated shell. The B-R criterion was employed to determine the critical loads of dynamic buckling of the shell. The effects of the parameters of the shallow groove on the dynamic response and buckling were discussed in this paper and the results show that the axial shallow grooves greatly affect the dynamic response and buckling.
文摘SP3 （simplified P3） theory is widely used in LWR （light water reactor） analyses to partly capture the transport effect, especially for pin-by-pin core analysis with pin size homogenization. In this paper, a SP3 code named STELLA is developed and verified at SNERDI （Shanghai Nuclear Engineering Research and Design Institute）. For SP3 method, neutron transport equation can be transformed into two coupled equations in the same mathematical form as diffusion equation. In this work, SANM （semi-analytic nodal method） is used to solve diffusion-like equation, due to its easy to handle multi-group problem. Whole core nodal boundary net current coupling is used to improve convergence stability in SANM, instead of solving two-node problem. CMFD （coarse-mesh finite difference） acceleration method is employed for 0-th SP3 equation, which represents the neutron balance relationship. Three benchmarks are used to verify the SP3 code, STELLA. The first one is a self-defined one dimensional problem, which demonstrates SP3 method is extremely accurate, due to no academic approximation in one dimensional for SP3. The second one is a two dimensional one-group problem cited from Larsen＇s paper, which is usually used to verify and prove the SP3 code correct and accurate. And the third one is modified from 2D C5G7-MOX benchmark, whose numerical results indicate that STELLA is accurate and efficient in pin size level, compared to diffusion model.
基金supported by the lab-directed research&develop-ment(LDRD)program of Argonne National Laboratory and U.S.DOE Advanced Grid Modeling Program grant DE-OE0000875.
文摘Power system simulations that extend over a time period of minutes,hours,or even longer are called extendedterm simulations.As power systems evolve into complex systems with increasing interdependencies and richer dynamic behaviors across a wide range of timescales,extendedterm simulation is needed for many power system analysis tasks(e.g.,resilience analysis,renewable energy integration,cascading failures),and there is an urgent need for efficient and robust extendedterm simulation approaches.The conventional approaches are insufficient for dealing with the extendedterm simulation of multitimescale processes.This paper proposes an extendedterm simulation approach based on the semianalytical simulation(SAS)methodology.Its accuracy and computational efficiency are backed by SAS's high accuracy in eventdriven simulation,larger and adaptive time steps,and flexible switching between fulldynamic and quasisteadystate(QSS)models.We used this proposed extendedterm simulation approach to evaluate bulk power system restoration plans,and it demonstrates satisfactory accuracy and efficiency in this complex simulation task.
基金National Natural Science Foundation of China (50574097 90305023)
文摘Usually, it is very difficult to find out an analytical solution to thermal conduction problems during high temperature welding. Therefore, as an important numerical approach, the method of lines （MOLs） is introduced to solve the temperature field characterized by high gradients. The basic idea of the method is to semi-discretize the governing equation of the problem into a system of ordinary differential equations （ODEs） defined on discrete lines by means of the finite difference method, by which the thermal boundary condition with high gradients are directly embodied in formulation. Thus the temperature field can be obtained by solving the ODEs. As a numerical example, the variation of an axisymmetrical temperature field along the plate thickness can be obtained.
基金supported by the National Natural Science Foundation of China(No.51175509)
文摘Fatigue damage monitoring is critical metallic structure health monitoring of aircraft.The sensor should be high sensitive,easy to be integrated into structure and well adaptable for poor working conditions.Therefore,an attached eddy current sensor with flexible plane is put forward and its characteristics are analyzed.By extracting material′s conductivity as the crack features,forward semi-analytical model is established and parameter optimizations are carried out.Crack perturbation model of attached eddy current sensor is constructed,and perturbation voltages of sensing channels under three-dimension structural crack are obtained.To verify the sensor′s performance,monitoring experiment on crack extension is conducted under condition of 3 MHz frequency.The validation experimental results show that perturbation model of 2A12-T4 aluminum alloy agrees well with experiment results,and perturbation model errors of four sensing channels are within 25%.The attached eddy current sensor is capable of testing the crack nondestructively and measuring the crack extension quantitatively with the accuracy of 1mm.
