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.

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.

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.

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.

Dynamic Response of A Group of Cylindrical Storage Tanks with Baffles Considering the Effect of Soil Foundation

The sloshing in a group of rigid cylindrical tanks with baffles and on soil foundation under horizontal excitation is studied analytically.The solutions for the velocity potential are derived out by the liquid subdomain method.Equivalent models with mass-spring oscillators are established to replace continuous fluid.Combined with the least square technique,Chebyshev polynomials are employed to fit horizontal,rocking and horizontal-rocking coupling impedances of soil,respectively.A lumped parameter model for impedance is presented to describe the effects of soil on tank structures.A mechanical model for the soil-foundation-tank-liquid-baffle system with small amount of calculation and high accuracy is proposed using the substructure technique.The analytical solutions are in comparison with data from reported literature and numerical codes to validate the effectiveness and correctness of the model.Detailed dynamic properties and seismic responses of the soil-tank system are given for the baffle number,size and location as well as soil parameter.

Dynamic and electrical responses of a curved sandwich beam with glass reinforced laminate layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact

The dynamic responses and generated voltage in a curved sandwich beam with glass reinforced laminate(GRL)layers and a pliable core in the presence of a piezoelectric layer under low-velocity impact(LVI)are investigated.The current study aims to carry out a dynamic analysis on the sandwich beam when the impactor hits the top face sheet with an initial velocity.For the layer analysis,the high-order shear deformation theory(HSDT)and Frostig's second model for the displacement fields of the core layer are used.The classical non-adhesive elastic contact theory and Hunter's principle are used to calculate the dynamic responses in terms of time.In order to validate the analytical method,the outcomes of the current investigation are compared with those gained by the experimental tests carried out by other researchers for a rectangular composite plate subject to the LVI.Finite element(FE)simulations are conducted by means of the ABAQUS software.The effects of the parameters such as foam modulus,layer material,fiber angle,impactor mass,and its velocity on the generated voltage are reviewed.

Analytical study of subcritical crack growth under mode I loading to estimate the roof durability in underground excavation

The long-term stability of the roof is particularly important in designing underground rock structures.To estimate the durability of roof strata in underground excavation,a computation scheme of subcritical crack growth is proposed in this study.By adopting the proposed method,the potential collapse location of strata is derivable in accordance with a static model,the durability of roof strata can be estimated,a dynamic time step control strategy is achieved to balance the accuracy and speed of computing,and the initial crack size of rock can be estimated.In addition to the above,a mechanical model of underground excavation with non-uniformly distributed loads and partially yielded foundation is presented as the prototypical case.A set of case studies is carried out that showcase a power correlation between applied stress and roof durability.The allowable applied tensile stress for a 100-year life cycle is about 76%of the tensile strength.By using the proposed subcritical crack growth computation scheme,the roof stability in an underground excavation can be identified not only from the spatial view but also from the temporal perspective.

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.

Analytical large deformation shear strength for bolted rough discontinuous rock

Presented a new analytical model for studying the shear-tensile large deforma-tion behavior near the vicinity of joint interface for bolted rough discontinuous rock, and presented the formulation estimating global shear strength for bolted joints under shear-ing-tensile loads. The analytical strength curves of bolts contribution on reinforced discon-tinuous rocks as the function of joint displacements or deformation angle of a bolt at rock joints was obtained. Based on Barton’s equation on JRC roughness profiles, the theoreti-cal shearing strength of bolted rough joints was also established. Test results on bolted granite and marble specimen confirm the validity of the analytical approach.

Analytical solution for a strong free-surface water vortex describing flow in a full-scale gravitational vortex hydropower system

Strong free-surface water vortices are found throughout industrial hydraulic systems used for water treatment,flow regulation,and energy generation.Previous models using the volumetric flow rate as a model input have generally been semi-empirical,and have tended to have some limitations in terms of the design of practical hydropower systems.In this study,an analytical model of a strong free-surface water vortex was developed.This model only requires the water head and geometric parameters as its inputs and calculates the maximum volumetric flow rate,aircore diameter,and rotational constant.Detailed experimental depthedischarge data from a full-scale gravitational vortex hydropower system,unavailable in the relevant literature,were obtained,and the simulated results showed excellent agreement with the experimental observations.These data could be used to verify similar models using laboratory-scale physical models in order to investigate the scaling effects.In contrast to previous models,this model does not assume a constant average velocity across the vortex radius and allows precise calculation of the resultant velocity vectors.Therefore,this model presents advantages in turbine design for energy generation systems.

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 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.

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.

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.

Laboratory and numerical modelling of irrigation infiltration and nitrogen leaching in homogeneous soils

Nitrogen (N) plays a key role in crop growth and production;however,data are lacking especially regarding the interaction of biochar,grass cover,and irrigation on N leaching in saturated soil profiles.Eighteen soil columns with 20-cm diameter and 60-cm height were designed to characterize the effects of different grass cover and biochar combinations,i.e.,bare soil+0%biochar (control,CK),perennial ryegrass+0%biochar (C1),Festuca arundinacea+0%biochar (C2),perennial ryegrass+1%biochar (C3),perennial ryegrass+2%biochar (C4),perennial ryegrass+3%biochar (C5),F.arundinacea+1%biochar (C6),F.arundinacea+2% biochar (C7),and F.arundinacea+3%biochar (C8),on periodic irrigation infiltration and N leaching in homogeneous loess soils from July to December 2020.Leachates in CK were 10.2%–35.3%higher than those in C1 and C2.Both perennial ryegrass and F.arundinacea decreased the volumes of leachates and delayed the leaching process in the 1%,2%,and 3%biochar treatments,and the vertical leaching rate decreased with biochar addition.The N leaching losses were concentrated in the first few leaching tests,and both total N (TN) and nitrate (NO_(3)^(-))-N concentrations in CK and C1–C8 decreased with increasing leaching test times.Biochar addition (1%,2%,and 3%) could further reduce the leaching risk of NO_(3)^(-)-N and the NO_(3)^(-)-N loss decreased with biochar addition.However,compared to 1%biochar,2% biochar promoted the leaching of TN under both grass cover types.The N leaching losses in CK,C1,C2,C3,C4,C6,and C7 were primarily in the form of NO_(3)^(-)-N.Among these treatments,CK,C1,and C2had the highest cumulative leaching fractions NO_(3)^(-)-N (>90%),followed by those in C3,C4,C6,and C7 (>80%).The cumulative leaching fraction of NO_(3)^(-)-N decreased with increasing leaching test times and biochar addition,and 3%biochar addition (i.e.,C5 and C8) reduced it to approximately 50%.The one-dimensional advective-dispersive-reactive transport equation can be used as an effective numerical approach to simulate and predict NO_(3)^(-)-N leaching in saturated homogeneous soils.Understanding the effects of different biochar and grass combinations on N leaching can help us design environmentally friendly interventions to manage irrigated farming ecosystems and reduce N leaching into groundwater.