Multi-domain equivalent method for prediction of elastic modulus of complex fractured rock mass

Reliable estimation of deformation and failure behaviors of fractured rock mass is important for practical engineering design.This study proposes a multi-domain equivalent method for fracture network to estimate the deformation properties of complex fractured rock mass.It comprehends both the advantages of the discrete fracture network model and the equivalent continuum model to capture the features of discontinuities explicitly while reducing computational intensity.The complex fracture network is stochastically split into a number of subfracture networks according to the domain,length or angle.An analytical solution is derived to infer theoretically the relationship between the elastic moduli of the original complex fractured rock mass and the split subfractured rock masses by introducing a correction term based on the deformation superposition principle.Numerical simulations are conducted to determine the elastic moduli of split subfractured rock masses using universal distinct element code(UDEC),while the elastic modulus of the original model is estimated based on the currently proposed analytical relationship.The results show that the estimation accuracy with the current domainbased splitting model is far superior compared to those with the other two splitting models.Thus,the estimation method of elastic modulus of complex fractured rock mass based on domain splitting mode of fracture network is identified as the multi-domain equivalent method proposed in this paper.The reliability of this method is evaluated,and its high computational efficiency is demonstrated through exemplification with regard to different geometric configurations for stochastically artificial discrete fracture network.The proposed multi-domain equivalent method constructs the theoretical framework except for the regression analysis hypothesis compared to the density-reduced model equivalent method.

Calculating the Number of Pregnant Women Receiving Standardized Services for PMTCT of HIV in Liangshan Prefecture,Based on the Equivalent Method

Objective To calculate the number of pregnant women who receive standardized prevention of mother-to-child transmission(PMTCT)services for HIV annually.Methods HIV-positive pregnant women in six counties of Liangshan Prefecture in 2017 were selected as study subjects.The entire process,from when the subjects first received the PMTCT of HIV services to the end,was divided into four stages,which were further divided into 25 phases.The equivalent coefficient was used to indicate the weight of workload in each phase.Seven experts were invited to score the equivalent coefficient;the number of pregnant women who received standardized services to prevent the transmission of HIV was calculated.Results A total of 663 HIV-positive pregnant women were registered in six Liangshan Prefecture counties in 2017.This figure was converted into 7,780 person-months devoted to HIV-positive pregnant women,with 260 person-months(3.34%)spent on the first antenatal care,1,510 person-months(19.41%)during pregnancy,378 person-months(4.86%)on delivery,and 5,632 person-months(72.39%)on post-partum period.The equivalent coefficient calculation showed that 314 HIV-positive pregnant women received standardized PMTCT services.Conclusion The number of pregnant women receiving standardized services for the PMTCT of HIV can be calculated accurately using the equivalent method to identify the gap between the level of PMTCT of HIV intervention services needed and the actual workload.

A new equivalent method to obtain the stoichiometric fuel-air cloud from the inhomogeneous cloud based on FLACS-dispersion

The fuel-air cloud resulting from an accidental discharge event is normally irregular in shape and varying in concentration. Performance of dispersion simulations using the computational fluid dynamics （CFD）-based tool FLACS can get an uneven and irregular cloud. For the performance of gas explosion study with FLACS, the equivalent stoichiometric fuel-air cloud concept is widely applied to get a representative distribution of explosion loads. The Q9 cloud model that is employed in FLACS is an equivalent fuel-air cloud representation, in which the laminar burning velocity with first order SL and volume expansion ratio are taken into consideration. However, during an explosion in congested areas, the main part of the combustion involves turbulent flame propagation. Hence, to give a more reasonable equivalent fuel-air size, the turbulent burning velocity must be taken into consideration. The paper presents a new equivalent cloud method using the turbulent burning velocity, which is described as a function of SL, deduced from the TNO multi- energy method.

AN EQUIVALENT CONTINUUM METHOD OF LATTICE STRUCTURES

An equivalent continuum method is developed to analyze the effective stiffness of three-dimensional stretching dominated lattice materials. The strength and three-dimensional plastic yield surfaces are calculated for the equivalent continuum. A yielding model is formulated and compared with the results of other models. The bedding-in effect is considered to include the compliance of the lattice joints. The predicted stiffness and strength are in good agreement with the experimental data, validating the present model in the prediction of the mechanical properties of stretching dominated lattice structures.

Application of the method of equivalent edge currents to composite scattering from the cone-cylinder above a dielectric rough sea surface

Compared with scattering from a rough surface only, composite scattering from a target above a rough surface has become so practical that it is a subject of great interest. At present, this problem has been solved by some numerical methods which will produce an enormous calculation amount. In order to overcome this shortcoming, the reciprocity theorem （RT） and the method of equivalent edge currents （MEC） are used in this paper. Due to the advantage of RT, the difficulty in computing the secondary scattered fields is reduced. Simultaneously, MEC, a high-frequency method with edge diffraction considered, is used to calculate the scattered field from the cone-cylinder target with a high accuracy and efficiency. The backscattered field and the polarization currents of the rough sea surface are evaluated by the Kirchhoff approximation （KA） method and physical optics （PO） method, respectively. The effects of the backscattering radar cross section （RCS） and the Doppler spectrum on the size of the target and the windspeed of the sea surface for different incident angles are analysed in detail.

AN EQUIVALENT NONLINEARIZATION METHOD FOR ANALYSINGRESPONSE OF NONLINEAR SYSTEMS TO RANDOM EXCITATIONS

In this paper, a new equivalent nonlinearization method is developed and used in analysing the response of nonlinear systems to Gaussian while noise excitation. Its basic idea and calculation method are expounded. With the help of the presented method, several kinds of usual nonlinear random vibration systems are analyzed. The numerical results show that the mean square responses of the proposed approach are much closer to the exact solutions or Monte Carlo solutions, than that obtained from equivalent linearization method.

Shim coil design for Halbach magnet by equivalent magnetic dipole method

Low-field nuclear magnetic resonance magnet（2 MHz） is required for rock core analysis. However, due to its low field strength, it is hard to achieve a high uniform B0 field only by using the passive shimming. Therefore, active shimming is necessarily used to further improve uniformity for Halbach magnet. In this work, an equivalent magnetic dipole method is presented for designing shim coils. The minimization of the coil power dissipation is considered as an optimal object to minimize coil heating effect, and the deviation from the target field is selected as a penalty function term. The lsqnonlin optimization toolbox of MATLAB is used to solve the optimization problem. Eight shim coils are obtained in accordance with the contour of the stream function. We simulate each shim coil by ANSYS Maxwell software to verify the validity of the designed coils. Measurement results of the field distribution of these coils are consistent with those of the target fields.The uniformity of the B0 field is improved from 114.2 ppm to 26.9 ppm after using these shim coils.

Equivalent magnetic dipole method used to design gradient coil for unilateral magnetic resonance imaging

The conventional magnetic resonance imaging（MRI） equipment cannot measure large volume samples nondestructively in the engineering site for its heavy weight and closed structure. In order to realize the mobile MRI, this study focuses on the design of gradient coil of unilateral magnet. The unilateral MRI system is used to image the local area above the magnet. The current density distribution of the gradient coil cannot be used as a series of superconducting nuclear magnetic resonance gradient coils, because the region of interest（ROI） and the wiring area of the unilateral magnet are both cylindrical side arc surfaces. Therefore, the equivalent magnetic dipole method is used to design the gradient coil, and the algorithm is improved for the special case of the wiring area and the ROI, so the X and Y gradient coils are designed.Finally, a flexible printed circuit board（PCB） is used to fabricate the gradient coil, and the magnetic field distribution of the ROI is measured by a Gauss meter, and the measured results match with the simulation results. The gradient linearities of x and y coils are 2.82% and 3.56%, respectively, less than 5% of the commercial gradient coil requirement.

A METHOD FOR CALCULATING TRANSIENT FUNCTIONS OF EQUIVALENT DETERMINISTIC INPUT

In the present paper the analytical formulas for calculating the equivalent deterministictransients for multivariable cross correlated random processes are developed.The formulaspermit the determination of the Root-mean-square of the responses of a lineartime-invariant system to stationary multiple random inputs in the time domain.The methodis applicable in the study of flight of airplanes in atmospheric turbulence and is also usefulfor general engineering applications of stochastc processes control.

Ice-Induced Vibrational Response of Single-Pile Offshore Wind-Turbine Foundations

Important challenges must be addressed to make wind turbines sustainable renewable energy sources.A typical problem concerns the design of the foundation.If the pile diameter is larger than that of the jacket platform,traditional mechanical models cannot be used.In this study,relying on the seabed soil data of an offshore wind farm,the m-method and the equivalent embedded method are used to address the single-pile wind turbine foundation problem for different pile diameters.An approach to determine the equivalent pile length is also proposed accordingly.The results provide evidence for the effectiveness and reliability of the model based on the equivalent embedded method.

Load Reduction Test Method of Similarity Theory and BP Neural Networks of Large Cranes

Static load tests are an important means of supervising and detecting a crane＇s lift capacity. Due to space restrictions, however, there are difficulties and potential danger when testing large bridge cranes. To solve the loading problems of large-tonnage cranes during testing, an equivalency test is proposed based on the similarity theory and BP neural networks. The maximum stress and displacement of a large bridge crane is tested in small loads, combined with the training neural network of a similar structure crane through stress and displacement data which is collected by a physics simulation progressively loaded to a static load test load within the material scope of work. The maximum stress and displacement of a crane under a static load test load can be predicted through the relationship of stress, displacement, and load. By measuring the stress and displacement of small tonnage weights, the stress and displacement of large loads can be predicted, such as the maximum load capacity, which is 1.25 times the rated capacity. Experimental study shows that the load reduction test method can reflect the lift capacity of large bridge cranes. The load shedding predictive analysis for Sanxia 1200 t bridge crane test data indicates that when the load is 1.25 times the rated lifting capacity, the predicted displacement and actual displacement error is zero. The method solves the problem that lifting capacities are difficult to obtain and testing accidents are easily possible when 1.25 times related weight loads are tested for large tonnage cranes.

EQUIVALENT NORMAL CURVATURE APPROACH MILLING MODEL OF MACHINING FREEFORM SURFACES

A new milling methodology with the equivalent normal curvature milling model machining freeform surfaces is proposed based on the normal curvature theorems on differential geometry. Moreover, a specialized whirlwind milling tool and a 5-axis CNC horizontal milling machine are introduced. This new milling model can efficiently enlarge the material removal volume at the tip of the whirlwind milling tool and improve the producing capacity. The machining strategy of this model is to regulate the orientation of the whirlwind milling tool relatively to the principal directions of the workpiece surface at the point of contact, so as to create a full match with collision avoidance between the workpiece surface and the symmetric rotational surface of the milling tool. The practical results show that this new milling model is an effective method in machining complex three- dimensional surfaces. This model has a good improvement on finishing machining time and scallop height in machining the freeform surfaces over other milling processes. Some actual examples for manufacturing the freeform surfaces with this new model are given.

Analysis of temperature field for a surface-mounted and interior permanent magnet synchronous motor adopting magnetic-thermal coupling method

Aiming at obtaining high power density of surface-mounted and interior permanent magnet synchronous motor(SIPMSM),it is important to accurately calculate the temperature field distribution of SIPMSM,and a magnetic-thermal coupling method is proposed.The magnetic-thermal coupling mechanism is analyzed.The thermal network model and finite element model are built by this method,respectively.The effects of power frequency on iron losses and temperature fields are analyzed by the magnetic-thermal coupling finite element model under the condition of rated load,and the relationship between the load and temperature field is researched under the condition of the synchronous speed.In addition,the equivalent thermal network model is used to verify the magnetic-thermal coupling method.Then the temperatures of various nodes are obtained.The results show that there are advantages in both computational efficiency and accuracy for the proposed coupling method,which can be applied to other permanent magnet motors with complex structures.

Analysis for Transmission of Composite Structure with Graphene Using Equivalent Circuit Model

A simple analytical method is presented to analyze the transmission of electromagnetic plane waves through multilayer stacked composite two-dimensional( 2D) structures at microwave frequencies. Unlike the traditional structure,high impedance surface with graphene sheet is proposed. The structure includes graphene and thin metal patches and meshes. Simple analytical formulas are introduced for the surface impedance of graphene and for the grid impedance of electrically dense arrays of metal square patches or strips. The result of transmission properties is based on the dynamic tunable model of the high impedance surface,which considers the surface conductivity of graphene layer. The transmission coefficient obtained by using the equivalent circuit method is validated against full-wave numerical simulations. The considered equivalent circuit method can be useful in the design of graphene tunable planar devices.

Scattering Analysis of Bi-anisotropic Materials Using Fast Dipole Method

Electromagnetic scattering from inhomogeneous three-dimensional( 3D) bi-anisotropic scatterers is formulated in terms of the volume integral equation( VIE) method. Based on the volume equivalence principle,the VIE is represented in terms of a pair of coupled bi-anisotropic polarized volume electric and magnetic flux densities. The VIE is solved using the method of moments( MoM) combined with tetrahedral mesh. Then the fast dipole method( FDM) based on the equivalent dipole method( EDM) is extended to analyze the scattering of bi-anisotropic media by solving the VIE. Finally,some numerical results are given to demonstrate the accuracy of the developed method for the scattering analysis of the bi-anisotropic media.

Modification of SDOF model for reinforced concrete beams under close-in explosion

In this paper,a modified single-degree-of-freedom(SDOF)model of reinforced concrete(RC)beams under close-in explosion is proposed by developing the specific impulse equivalent method and flexural resistance calculation method.The equivalent uniform specific impulse was obtained based on the local conservation of momentum and global conservation of kinetic energy.Additionally,the influence of load uniformity,boundary condition and complex material behaviors(e.g.strain rate effect,hardening/softening and hoop-confined effect)was considered in the resistance calculation process by establishing a novel relationship between external force,bending moment,curvature and deflection successively.The accuracy of the proposed model was verified by carrying out field explosion tests on four RC beams with the scaled distances of 0.5 m/kg~(1/3)and 0.75 m/kg~(1/3).The test data in other literatures were also used for validation.As a result,the equivalent load implies that the blast load near the mid-span of beams would contribute more to the maximum displacement,which was also observed in the tests.Moreover,both the resistance model and test results declare that when the blast load becomes more concentrated,the ultimate resistance would become lower,and the compressive concrete would be more prone to softening and crushing.Finally,based on the modified SDOF model,the calculated maximum displacements agreed well with the test data in this paper and other literatures.This work fully proves the rationality of the modified SDOF method,which will contribute to a more accurate damage assessment of RC structures under close-in explosion.

An Improved Time-Domain Inverse Technique for Localization and Quantifcation of Rotating Sound Sources

The time-domain inverse technique based on the time-domain rotating equivalent source method has been proposed to localize and quantify rotating sound sources. However, this technique encounters two problems to be addressed: one is the time-consuming process of solving the transcendental equation at each time step, and the other is the difculty of controlling the instability problem due to the time-varying transfer matrix. In view of that, an improved technique is proposed in this paper to resolve these two problems. In the improved technique, a de-Dopplerization method in the time-domain rotating reference frame is frst applied to eliminate the Doppler efect caused by the source rotation in the measured pressure signals, and then the restored pressure signals without the Doppler efect are used as the inputs of the time-domain stationary equivalent source method to locate and quantify sound sources. Compared with the original technique, the improved technique can avoid solving the transcendental equation at each time step, and facilitate the treatment of the instability problem because the transfer matrix does not change with time. Numerical simulation and experimental results show that the improved technique can eliminate the Doppler efect efectively, and then localize and quantify the rotating nonstationary or broadband sources accurately. The results also demonstrate that the improved technique can guarantee a more stable reconstruction and compute more efciently than the original one.

Average temperature calculation for straight single-row-piped frozen soil wall

The average temperature of frozen soil wall is an essential parameter in the process of design, construction, and safety manage- ment of artificial ground freezing engineering. It is the basis of calculating frozen soil＇s mechanical parameters, fiarther prediction of bearing capacity and, ultimately, safety evaluation of the frozen soil wall. Regarding the average temperature of sin- gle-row-piped frozen soil wall, this paper summarizes several current calculation methods and their shortcomings. Furthermore, on the basis of Bakholdin＇s analytical solution for the temperature field under straight single-row-piped freezing, two new calcula- tion models, namely, the equivalent trapezoid model and the equivalent triangle model, are proposed. These two approaches are used to calculate the average temperature of a certain cross section which indicates the condition of the whole frozen soil wall. Considering the possible parameter range according to the freezing pipe layout that might be applied in actual construction, this paper compares the average temperatures of frozen soil walls obtained by the equivalent trapezoid method and the equivalent tri- angle method with that obtained by numerical integration of Bakholdin＇s analytical solution. The results show that the discrepancies are extremely small and these two new approaches are better than currently prevailing methods. However, the equivalent triangle method boasts higher accuracy and a simpler formula compared with the equivalent trapezoid method.

Driving Force and Ecosystem Service Values Estimation in the Extreme Arid Region from 1975 to 2015:A Case Study of Alxa League,China

The research on ecosystem service values(ESVs)estimation in arid region is weak.We took the Alxa League of China’s Inner Mongolia Autonomous Region,an extreme arid region,as an example and constructed an equivalent coefficient method to assess its ESVs from 1975 to 2015,by determining the standard unit of ESVs and the basic equivalent of the value of different ecosystem services per unit area based on the regional characteristics,literature research,expert knowledge and land use data.The results show that the ESVs first decreased from 83170.4 million yuan(RMB)in 1975 to 82337.8 million yuan(RMB)in 2000 and then increased to84033.6 million yuan(RMB)in 2015,and the ESV of sparse grassland and desert account for about 33%and 29%of the total ESVs,respectively.Among the four service types,the regulating services,support services,supply services and cultural services account for66.5%,22.8%,6.0%and 4.7%,respectively.The changes of ESVs in Alxa League are determined by the socio-economic development and ecological changes.This study provides a new method to estimate the ESVs in arid region by integrating existing methods and regional characteristics,such as the cost of water for arid ecosystems.

Stochastic response of fractional-order van der Pol oscillator

We studied the response of fractional-order van de Pol oscillator to Gaussian white noise excitation in this letter. An equivalent integral-order nonlinear stochastic system is obtained to replace the given system based on the principle of minimum mean-square error. Through stochastic averaging, an averaged Ito equation is deduced. We obtained the Fokker–Planck–Kolmogorov equation connected to the averaged Ito equation and solved it to yield the approximate stationary response of the system. The analytical solution is confirmed by using Monte Carlo simulation.