Analytical model for predicting time-dependent lateral deformation of geosynthetics-reinforced soil walls with modular block facing

To date,few models are available in the literature to consider the creep behavior of geosynthetics when predicting the lateral deformation(d)of geosynthetics-reinforced soil(GRS)retaining walls.In this study,a general hyperbolic creep model was first introduced to describe the long-term deformation of geosynthetics,which is a function of elapsed time and two empirical parameters a and b.The conventional creep tests with three different tensile loads(Pr)were conducted on two uniaxial geogrids to determine their creep behavior,as well as the a-Pr and b-Pr relationships.The test results show that increasing Pr accelerates the development of creep deformation for both geogrids.Meanwhile,a and b respectively show exponential and negatively linear relationships with Pr,which were confirmed by abundant experimental data available in other studies.Based on the above creep model and relationships,an accurate and reliable analytical model was then proposed for predicting the time-dependent d of GRS walls with modular block facing,which was further validated using a relevant numerical investigation from the previous literature.Performance evaluation and comparison of the proposed model with six available prediction models were performed.Then a parametric study was carried out to evaluate the effects of wall height,vertical spacing of geogrids,unit weight and internal friction angle of backfills,and factor of safety against pullout on d at the end of construction and 5 years afterwards.The findings show that the creep effect not only promotes d but also raises the elevation of the maximum d along the wall height.Finally,the limitations and application prospects of the proposed model were discussed and analyzed.

Analytical Modeling and Mechanism Analysis of Time-Varying Excitation for Surface Defects in Rolling Element Bearings

Surface defects,including dents,spalls,and cracks,for rolling element bearings are the most common faults in rotating machinery.The accurate model for the time-varying excitation is the basis for the vibration mechanism analysis and fault feature extraction.However,in conventional investigations,this issue is not well and fully addressed from the perspective of theoretical analysis and physical derivation.In this study,an improved analytical model for time-varying displacement excitations(TVDEs)caused by surface defects is theoretically formulated.First and foremost,the physical mechanism for the effect of defect sizes on the physical process of rolling element-defect interaction is revealed.According to the physical interaction mechanism between the rolling element and different types of defects,the relationship between time-varying displacement pulse and defect sizes is further analytically derived.With the obtained time-varying displacement pulse,the dynamic model for the deep groove bearings considering the internal excitation caused by the surface defect is established.The nonlinear vibration responses and fault features induced by surface defects are analyzed using the proposed TVDE model.The results suggest that the presence of surface defects may result in the occurrence of the dual-impulse phenomenon,which can serve as indexes for surface-defect fault diagnosis.

Analytical model of 2D leakoff in waterflood-induced fractures

Waterflood-induced fractures,also known as self-induced fractures,spontaneously form at injection wells during waterflooding.These fractures propagate long distances through rock,allowing injected fluids to travel far away from a well,both within and outside the flooding layer.Essentially,the me-chanics of waterflood-induced fracture propagation is similar to that of hydraulic fractures,which are intentionally created for reservoir stimulation.Fracturing models developed for hydraulic fractures can also be applied to waterflood-induced fractures.However,waterflood-induced fractures are typically pumped with much larger volumes of water or brine and grow much longer in time.As a result,fluid leakoff from waterflood fractures into the formation is more extensive and two-dimensional(2D),a characteristic that is often ignored in a majority of modern fracturing simulators,making their appli-cation to waterflood fractures unreliable.In this work,we revisit the problem of leakoff for long-growing waterflood-induced fractures and develop a new analytical model for fluid leakoff that provides improved predictions of fracture geometry and can be easily implemented in fracturing simulators.We incorporate the developed solution into the classical Perkins-Kern-Nordgren(PKN)model of fracture growth,which shows that the choice of the Carter or a 2D leakoff model greatly impacts fracture ge-ometry at large time.The conducted parametric study shows while a toughness-dominated regime af-fects fracture evolution,most of fracture lifetime occurs in a viscosity-and-leakoff-dominated regime.We also develop an asymptotic solution for a leakoff profile in the limiting case of 2D leakoff domination(~~M and~~K).Finally,we study 3D fracture growth and out-of-zone injection with three layers and a complex structure of zones.The study shows that ignoring the 2D leakoff during simulation results in a significant overestimation of fracture geometry predictions.The present work,thus,plays an important role in improving waterflood fracture modelling,as it highlights the significance of 2D leakoff in waterflood-induced fractures and provides a reliable analytical model for fluid leakoff that can be incorporated into modern fracture simulators.

Three-Dimensional Analytical Modeling of Axial-Flux Permanent Magnet Drivers

In this paper, the axial-flux permanent magnet driver is modeledand analyzed in a simple and novel way under three-dimensional cylindricalcoordinates. The inherent three-dimensional characteristics of the deviceare comprehensively considered, and the governing equations are solved bysimplifying the boundary conditions. The axial magnetization of the sectorshapedpermanent magnets is accurately described in an algebraic form bythe parameters, which makes the physical meaning more explicit than thepurely mathematical expression in general series forms. The parameters of theBessel function are determined simply and the magnetic field distribution ofpermanent magnets and the air-gap is solved. Furthermore, the field solutionsare completely analytical, which provides convenience and satisfactoryaccuracy for modeling a series of electromagnetic performance parameters,such as the axial electromagnetic force density, axial electromagnetic force,and electromagnetic torque. The correctness and accuracy of the analyticalmodels are fully verified by three-dimensional finite element simulations and a15 kW prototype and the results of calculations, simulations, and experimentsunder three methods are highly consistent. The influence of several designparameters on magnetic field distribution and performance is studied and discussed.The results indicate that the modeling method proposed in this papercan calculate the magnetic field distribution and performance accurately andrapidly, which affords an important reference for the design and optimizationof axial-flux permanent magnet drivers.

Analytical modelling of the mechanical damage of soil induced by lightning strikes capturing electro-thermal,thermo-osmotic,and electro-osmotic effects

This article presents a mathematical model for simulating the mechanical behaviour of lightning strikes and analysing the resulting damage to the soil.This article focuses on the electro-thermal effect and seepage caused by lightning strikes in particular.Then,a numerical model based on the conservation laws of momentum,mass and energy is developed for soil subjected to lightning strikes.Comparisons to field observations and theoretical calculations are used to demonstrate the efficacy and accuracy of numerical simulations.The findings demonstrate that lightning strikes can cause soils to experience both seepage force and heat stress.Under the calculative condition of this article:by increasing the intrinsic permeability of the soil,k_(p)(≥10^(-10)m^(2)),the seepage force can be effectively reduced,hence reducing the risk of lightning strikes;improving the electrical conductivity of the soil β(≥10^(-1) S/m^(2))and lowering its thermal expansion coefficient(≤10^(-6)K^(-1))can greatly reduce the damage caused by lightning strikes to the soil.The preceding investigations demonstrate that the suggested model is capable of evaluating mechanical damage caused by lightning in the soil,and the findings contribute to a better understanding of soil mechanical response to lightning strikes.

Analytical Modelling and Experiment of Novel Rotary Electro-Mechanical Converter with Negative Feedback Mechanism for 2D Valve

The manufacturing of spiral groove structure of two-dimensional valve(2D valve)feedback mechanism has shortcomings of both high cost and time-consuming.This paper presents a novel configuration of rotary electro-mechanical converter with negative feedback mechanism(REMC-NFM)in order to replace the feedback mechanism of spiral groove and thus reduce cost of valve manufacturing.In order to rapidly and quantitative evaluate the driving and feedback performance of the REMC-NFM,an analytical model taking leakage flux,edge effect and permeability nonlinearity into account is formulated based on the equivalent magnetic circuit approach.Then the model is properly simplified in order to obtain the optimal pitch angle.FEM simulation is used to study the influence of crucial parameters on the performance of REMC-NFM.A prototype of REMC-NFM is designed and machined,and an exclusive experimental platform is built.The torque-angle characteristics,torque-displacement characteristics,and magnetic flux density in the working air gap with different excitation currents are measured.The experimental results are in good agreement with the analytical and FEM simulated results,which verifies the correctness of the analytical model.For torque-angle characteristics,the overall torque increases with both current and rotation angle,which reaches about 0.48 N·m with 1.5 A and 1.5°.While for torque-displacement characteristics,the overall torque increases with current yet decrease with armature displacement due to the negative feedback mechanism,which is about 0.16 N·m with 1.5 A and 0.8 mm.Besides,experimental results of conventional torque motor are compared with counterparts of REMC-NFM in order to validate the simplified model.The research indicates that the REMC-NFM can be potentially used as the electro-mechanical converter for 2D valves in civil servo areas.

A simple analytical model of laser direct-drive thin shell target implosion

A high-neutron yield platform imploded by a thin shell target is generally built to probe nuclear science problems,and it has the advantages of high neutron yield,ultrashort fusion time,micro fusion zone,isotropic and monoenergetic neutron.Some analytical models have been proposed to interpret exploding-pusher target implosion driven by a long wavelength laser,whereas they are imperfect for a 0.35 μm laser implosion experiment.When using the 0.35 μm laser,the shell is ablated and accelerated to high implosion velocity governed by Newton’s law,ablation acceleration and quasi-adiabatic compression models are suitable to explain the implosion of a laser direct-drive thin shell target.The new analytical model scales bang time,ion temperature and neutron yield for large variations in laser power,target radius,shell thickness,and fuel pressure.The predicted results of the analytical model are in agreement with experimental data on the ShenguangIII prototype laser facility,100 kJ laser facility,Omega,and NIF,it demonstrates that the analytical model benefits the understanding of experiment performance and optimizing the target design of high neutron yield implosion.

Analytical Model for Underwater Wireless Sensor Network Energy Consumption Reduction

In an Underwater Wireless Sensor Network(UWSN),extreme energy loss is carried out by the early expiration of sensor nodes and causes a reduction in efficiency in the submerged acoustic sensor system.Systems based on clustering strategies,instead of each node sending information by itself,utilize cluster heads to collect information inside the clusters for forwarding collective information to sink.This can effectively minimize the total energy loss during transmission.The environment of UWSN is 3D architecture-based and follows a complex hierarchical clustering strategy involving its most effecting unique parameters such as propagation delay and limited transmission bandwidth.Round base clustering strategy works in rounds,where each round comprises three fundamental stages:cluster head selection,grouping or node association,and data aggregation followed by forwarding data to the sink.In UWSN,the energy consumed during the formation of clusters has been considered casually or completely evaded in the previous works.In this paper,the cluster head setup period has been considered the main contributor to extra energy utilizer.A numerical channel model is proposed to compute extra energy.It is performed by using a UWSN broad model.The results have shown that extra maximum energy consumption is approximately 12.9 percent of the system total energy consumed in information transmissions.

Analytical modeling and vibration analysis of fiber reinforced composite hexagon honeycomb sandwich cylindrical-spherical combined shells

This study analyzes and predicts the vibration characteristics of fiberreinforced composite sandwich(FRCS)cylindrical-spherical(CS)combined shells with hexagon honeycomb core(HHC)for the first time based on an analytical model developed,which makes good use of the advantage of the first-order shear deformation theory(FSDT),the multi-segment decomposition technique,the virtual spring technology,the Jacobi-Ritz approach,and the transfer function method.The equivalent material properties of HHC are firstly determined by the modified Gibson’s formula,and the related energy equations are derived for the HHC-FRCS-CS combined shells,from which the fundamental frequencies,the mode shapes,and the forced vibration responses are solved.The current model is verified through the discussion of convergence and comparative analysis with the associated published literature and finite element(FE)results.The effects of geometric parameters of HHC on the dynamic property of the structure are further investigated with the verified model.It reveals that the vibration suppression capability can be greatly enhanced by reducing the ratio of HHC thickness to total thickness and the ratio of wall thickness of honeycomb cell to overall radius,and by increasing the ratio of length of honeycomb cell to overall radius and honeycomb characteristic angle of HHC.

Semi-analytical model for quasi-double-layer surface electrode ion traps

To realize scale quantum processors,the surface-electrode ion trap is an effective scaling approach,including singlelayer,double-layer,and quasi-double-layer traps.To calculate critical trap parameters such as the trap center and trap depth,the finite element method(FEM) simulation was widely used,however,it is always time consuming.Moreover,the FEM simulation is also incapable of exhibiting the direct relationship between the geometry dimension and these parameters.To eliminate the problems above,House and Madsen et al.have respectively provided analytic models for single-layer traps and double-layer traps.In this paper,we propose a semi-analytical model for quasi-double-layer traps.This model can be applied to calculate the important parameters above of the ion trap in the trap design process.With this model,we can quickly and precisely find the optimum geometry design for trap electrodes in various cases.

Analytical Modeling for Translating Statistical Changes to Circuit Variability by Ultra⁃Deep Submicron Digital Circuit Design

This paper presents a physics⁃based compact gate delay model that includes all short⁃channel phenomena prevalent at the ultra⁃deep submicron technology node of 32 nm.To simplify calculations,the proposed model is connected to a compactα⁃power law⁃based(Sakurai⁃Newton)model.The model has been tested on a wide range of supply voltages.The model accurately predicts nominal delays and the delays under process variations.It has been shown that at lower technology nodes,the delay is more sensitive to threshold voltage variations,specifically at the sub⁃threshold operating region as compared with effective channel length variations above the threshold region.

Three-dimensional Analytical Modeling of Axial Flux Permanent Magnets Maglev Motor

The three-dimensional(3D)analytical model of the magnetic field in an Axial Flux Permanent Magnets Maglev Motor(AFPMMM)is proposed and investigated the influence of the structural parameters on electromagnetic characteristics.Firstly,the topology and working principle of the AFPMMM is introduced,and the model is transferred into a mathematical model in 3D cartesian coordinate.Then,the volume integral method and equivalent current sheets model is applied to find the 3D magnetic field distribution function of Halbach rotor.A unified form expression can be obtained by two dimensional discrete fourier transform(2-D DFT)is applied on the 3D magnetic field distribution function.Thirdly,the conductive and nonconductive regions of AFPMMM will be formulated by the second order vector potential(SOVP)to built the 3D analytic model.The expression of the lift force,torque and power losses was derived.Besides,the relationship between electromagnetic characteristics and structural parameters of the AFPMMM were analyzed based on 3D analytic model and validated using the 3D finite element analysis(FEA).Finally,the experiments based on a small scale prototype are carried out to verify the analytical results.

Analytical modeling of complex contact behavior between rock mass and lining structure

Based on the nondestructive test data of operating railway tunnels in China, this paper summarizes the basic characteristics of the complex contact behavior between the rock mass and lining structure. The contact modes are classified into dense contact, local non-contact, and loose contact. Subsequently, the corresponding mechanical model for each contact mode is developed according to its mechanical characteristics using the complex variable method. In the proposed mechanical model, a special algorithm is introduced to detect whether the local non-contact zone is re-contacted. Besides, a novel conformal mapping method is also proposed to accurately calculate the mechanical response of the concrete lining. Finally, the accuracy of the proposed method is verified by comparing it with the finite element method(FEM). Several parameter investigations are conducted to analyze the effects of different contact modes on the rock-lining interaction. The results show that:(i) the height of the local noncontact area does not have a significant effect on the contact stress distribution if no re-contact occurs;(ii) backfill grouting can reduce the local stress concentration caused by poor contact modes;and(iii) reducing the friction coefficient of the interface can lead to a more uniform distribution of internal forces in the concrete lining.

Dynamic response of sandwich panel attached with a double mass-spring-damping system to shallow-buried explosion:Analytical modeling

How to ensure the safety of occupants has become a challenge for protective design of armored vehicles against intensive blast loadings.In this study,for armored vehicles subjected to shallow-buried explosions,an analytical model was established to characterize the dynamic performance of an all-metallic sandwich floorboard attached with a double mass-spring-damping system(mimicking seat and occupant),with the former consisting of a front face,a core and a rear face.For validation,numerical simulations with the method of finite elements(FE)were performed.Good agreement between analytical predictions and numerical results was achieved.The analytical model was then employed to quantify the effects of explosive mass,yield stress of material make,configurational parameters of sandwich panel,spring stiffness,and damping coefficient on dynamic response of the sandwich panel and double mass-spring-damping system.With increasing explosive mass and decreasing yield stress of material make,the peak displacements of rear face,seat and occupant were all found to increase.As core relative density was increased,these peak displacements also increased when the ratio of face thickness to core height was relatively small.Increasing the ratio of face thickness to core height led to increased peak accelerations of seat and occupant.The peak displacement of rear face was insensitive to the increase of either spring stiffness or damping coefficient,while the peak acceleration of occupant increased with increasing spring stiffness.Upon increasing the damping coefficient between the rear face and seat or that between the seat and occupant or both,the peak acceleration of occupant increased.With occupant safety duly considered,the proposed analytical model provides useful guidance for designing high-performance protective structures for armored vehicles subjected to intensive blast loadings.

Experimental investigation and analytically modeling of hysteretic behavior of rigid bus-flexible connectors of 220 kV electrical substations

This paper describes the quasi-static testing and analytical modelling of the hysteretic behavior of aluminum alloy rigid bus-flexible connectors of 220 kV electrical substations.The main objective of the study is to experimentally investigate the hysteretic behavior of six different types of rigid bus-flexible connectors 220 kV electrical substations when subjected to cyclic loading.Another objective is to theoretically study the flexibility and effectiveness of a previously proposed analytical model in fitting the experimental hysteresis loops of the tested rigid bus-flexible connectors.The experimental investigation indicates that the tested rigid bus-flexible connectors exhibit highly asymmetric hysteresis behavior along with tension stiffening effect.The theoretical study demonstrates that the generalized Bouc-Wen model has high flexibility and is effective in fitting the experimental hysteresis resisting force-displacement curves of the six tested rigid bus-flexible connectors.

Simplified Analytical Model for Estimation of Switching Loss of Cascode GaN HEMTs in Totem-pole PFC Converters

A practical analytical model to calculate the switching loss of cascode gallium nitride high electron mobility transistors(GaN HEMTs)is proposed.To facilitate analysis and application,the transmission delays introduced by Si MOSFET and interconnection inductances are ignored in modeling.Meanwhile,the nonlinear junction capacitances of the device and circuit stray inductances are also incorporated to increase the accuracy of the model.The turn-on and turn-off switching processes are described in detail and the simplified equations can be easily solved by using mathematical tools.Based on the analytical model,loss evaluation of totem-pole PFC converter is introduced briefly.Finally,the accuracy of the model is validated by comparing the calculated loss and converter’s efficiency with experiment results.Peak efficiency of 99.26%is achieved for a 3.6 kW single phase CCM Totem-Pole PFC AC/DC converter switching at 50 kHz based on 650 V cascode GaN HEMTs.

Analytical model for straight hemming based on minimum energy method

An analytical model for straight hemming was developed based on minimum energy method to study the effect of flanging die corner radius on hemming qualities.In order to calculate plastic strain and strain energy more exactly,the neutral layer of specimen corner after hemming is assumed to be a half ellipse with its major semi-axis unknown.Isotropic hardening rule is adopted to describe bending and reverse bending processes neglecting Bauschinger effect.The model takes into account the material property parameters in order to satisfy a wide application range of different materials.Specimen profile,creepage/growing(roll-in/roll-out) and maximum equivalent strain are predicted,which are greatly influenced by the flanging die corner radius.Experimental facilities were designed and hemming experiments were undertaken.The predicted results of the present analytical model were compared to experimental data as well as finite element(FE) simulation results.It was confirmed that they are in good agreement,and the model can be used to evaluate whether the material used as an outer panel for hemming is appropriate and to optimize process parameters when the material used for hemming is changed.

A 2×2 MIMO Throughput Analytical Model for RF Front End Optimization

With a given communication protocol,performance optimization of a multiple-input multipleoutput(MIMO)wireless system mainly lies on the design of the radio frequency(RF)front end.Currently,the optimization is mainly achieved based on experiences,such as promoting the multiple antenna gains and reducing their correlations.This experience-based method works to a certain extent,but is inefficient since the final performance impact by each sub-system is not quantified.The challenge lies on how to find the most limiting factor that restricts the overall communication throughput.This paper presents an analytical model for throughput calculations of 2×2 MIMO wireless system,which is built on a first step of maximum rate calculated under the chosen protocol and channel,followed by a second step of throughput baseline measurement,and continued with the third step of throughput calculations of the overall system according to the actual settings of subsystems.The model can provide a detailed diagnostic report of each RF factor,which will directly point out the imperfections and make the troubleshooting and debugging much more effective.Besides,throughput is analyzed in a mathematical approach that allows the performance more predictable during the design phase.

Analytical model of cutting force in axial ultrasonic vibration-assisted milling in-situ TiB_(2)/7050Al PRMMCs

Ultrasonic vibration-assisted milling has been widely applied in machining the difficultto-cut materials owing to the remarkable improvements in reducing the cutting force.However,analytical models to reveal the mechanism and predict the cutting force of ultrasonic vibrationassisted milling metal matrix composites are still needed to be developed.In this paper,an analytical model of cutting force was established for ultrasonic vibration-assisted milling in-situ TiB_(2)/7050 Al metal matrix composites.During modeling,change of motion of the cutting tool,contact of toolchip-workpiece and acceleration of the chip caused by ultrasonic vibration was considered based on equivalent oblique cutting model.Meanwhile,material properties,tool geometry,cutting parameters and vibration parameters were taken into consideration.Furthermore,the developed analytical force model was validated with and without ultrasonic vibration milling experiments on in-situ TiB_(2)/7050 Al metal matrix composites.The predicted cutting forces show to be consistent well with the measured cutting forces.Besides,the relative error of instantaneous maximum forces between the predicted and measured data is from 0.4%to 15.1%.The analytical model is significant for cutting force prediction not only in ultrasonic-vibration assisted milling but also in conventional milling in-situ TiB_(2)/7050 Al metal matrix composites,which was proved with general applicability.

Modeling discrete-time analytical models based on random early detection: Exponential and linear

Congestion control is among primary topics in computer network in which random early detection(RED)method is one of its common techniques.Nevertheless,RED suffers from drawbacks in particular when its“average queue length”is set below the buffer’s“minimum threshold”position which makes the router buffer quickly overflow.To deal with this issue,this paper proposes two discrete-time queue analytical models that aim to utilize an instant queue length parameter as a congestion measure.This assigns mean queue length(mql)and average queueing delay smaller values than those for RED and eventually reduces buffers overflow.A comparison between RED and the proposed analytical models was conducted to identify the model that offers better performance.The proposed models outperform the classic RED in regards to mql and average queueing delay measures when congestion exists.This work also compares one of the proposed models(RED-Linear)with another analytical model named threshold-based linear reduction of arrival rate(TLRAR).The results of the mql,average queueing delay and the probability of packet loss for TLRAR are deteriorated when heavy congestion occurs,whereas,the results of our RED-Linear were not impacted and this shows superiority of our model.