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 Modelling of Shot-peening Residual Stress on Welding Carbon Steel Surface Layer

The residual stress distribution was studied by an analytical model, due to shot peening on the welding carbon steel surface layer. The initial welding residual stresses before shot peening were taken into consideration in this analytical model. The Hertzian elastic contact theory was used to get the elastic compression stress state after impact on the surface layer. The initial welding stress field and the shot peening stress field would superpose and the welding surface layer would yield based on the elastic-plastic evaluation, then the residual stress after shot peening can be achieved. The influence of initial welding residual stress on the stress distribution after shot peening was analyzed and discussed. A series of experiments were carried out and the residual stress on the welding surface was determined by X-ray diffractometer before and after shot peening. The calculation results of the analytical model are consistent with the experimental results. The critical shot velocities when welding surface layer yielded and reverse yielded were calculated. While the welded joint surface material reversely yielded, the maximum compressive residual stress would not obviously increase with the increase of shot velocity, the thickness of the compressive stress layer would be increased. Welding residual tensile stress can enlarge the thickness of the compressive stress layer at the same shot velocity when reverse yield appeared.

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 and Numerical Modelling of FRP Debonding from Concrete Substrate under Pure Shearing

External bonding of fiber reinforced polymer （FRP） composites on the concrete structures has been proved to be an effective and efficient way to strengthen concrete structures. For a FRP strengthened concrete beam, it is usually observed that the failure occurs in the concrete and a thin layer of concrete is attached on the surface of the debonded FRP plate. To study the debond behavior between concrete and FRP composites, an analytical model based on the three-parameter model is developed to study the debonding behavior for the FRP-to-concrete joint under pure shearing. Then, nonlinear FEM analysis is conducted to verify the PrOposed analytical model. The FEM results shows good agreement with the results from the model. Finally, with the analytical model, sensitivity analyses are performed to study the effect of the interracial parameters or the ~eometric parameters on the debondin~ behavior.

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.

A new analytical model for thermal stresses in multi-phase materials and lifetime prediction methods

Based on the fundamental equations of the mechanics of solid continuum, the paper employs an analytical model for determination of elastic thermal stresses in isotropic continuum represented by periodically distributed spherical particles with different distributions in an infinite matrix, imaginarily divided into identical cells with dimensions equal to inter-particle distances, containing a central spherical particle with or without a spherical envelope on the particle surface. Consequently, the multi-particle-（envelope）- matrix system, as a model system regarding the analytical modelling, is applicable to four types of multi-phase materials. As functions of the particle volume fraction v, the inter-particle distances dl, d2, d3 along three mutually per- pendicular axes, and the particle and envelope radii, R1 and R2, respectively, the thermal stresses within the cell, are originated during a cooling process as a consequence of the difference in thermal expansion coefficients of phases rep- resented by the matrix, envelope and particle. Analytical-（experimental）-computational lifetime prediction methods for multi-phase materials are proposed, which can be used in engineering with appropriate values of parameters of real multi-phase materials.

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.

Impact of water table on hierarchically nested groundwater flow system

Water table configuration gives rise to hierarchically nested groundwater flow systems.However,there remains a lack of comprehensive understanding regarding the controlling factors of water table and its impact on flow systems.Moreover,it remains challenging to identify characteristics of water table space variation through limited groundwater observations at the regional scale.Based on two ideal two-dimensional cross-section analytical models,this study presents a simplified approach to preliminarily assess the nonlinear interactions between water table variation and three driving factors:Topography,geol-ogy and climate.Two criteria,C1 and C2,are utilized to address issues at different scales ranging from basin to local:(i)the influence of various factors on water table configuration;and(ii)the influence of water table on groundwater flow pattern.Then,the Ordos Plateau is taken as an example to explore the role of the water table in nested groundwater systems using the provided approach and criterion.The applica-tion of this approach in the Ordos Plateau demonstrates its appropriateness as a practical method for prelim-inarily determining the characteristics of water table configuration and its impact on flow systems.The study explores the mechanism influencing spatial variation in the water table and improves understanding of the interaction between topography,geology,and climate on groundwater flow patterns.

Flow Dynamics during the Hydrocarbon Exploitation for Prevention and Management of Water Venues in Oil Field: A Study Case of Crystal Field in Badila/Chad

The southern part of the Lake Chad basin is under the gas and oil petroleum industry due to its hydrocarbon potential for about twenty years. This project stands out as the main challenges of the hydrocarbon production and the management of fluxes particularly the groundwater venues. A comprehensive study is thus conducted to develop a dynamic and analytic model for diagnosing the production performances with a particular view on the management of groundwater venues. The three main concerned reservoirs subdivided on subunits evidence their proper characteristics. The porous media, their densities, the internal flows and the water injection techniques such as water flooding were thus adopted. The oil viscosity variability within the reservoirs creates different levels of mobility between water and oil, highlighting the challenges of water management. The material balance model and the behavior of the well analysis were taken in consideration within the identified aquifer, emphasizing the importance of keeping the pressure through injection. The control of water productions, the management of the reservoir, the well strategical position and the specific completions lead to the model functioning. In addition, the CO log and the Pulsed Neutron indicate their limitations as a result of the water salinity and the porosity of the aquifer. The management of groundwater venues at Badila requires various approaches throughout the lifetime of the Crystal field such as the data acquisition and remediation actions and prevention, under a permanent monitoring of the dynamic fluxes in the reservoirs.

Simple analytical model for depth-averaged velocity in meandering compound channels

A simple but applicable analytical model is presented to predict the lat- eral distribution of the depth-averaged velocity in meandering compound channels. The governing equation with curvilinear coordinates is derived from the momentum equation and the flow continuity equation under the condition of quasi-uniform flow. A series of experiments are conducted in a large-scale meandering compound channel. Based on the experimental data, a magnitude analysis is carried out for the governing equation, and two lower-order shear stress terms are ignored. Four groups of experimental data from different sources are used to verify the predictive capability of this model, and good predictions are obtained. Finally, the determination of the velocity parameter and the limitation of this model are discussed.

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.

AN ANALYTICAL SOLUTION FOR THE MODEL OF DRUG DISTRIBUTION AND ABSORPTION IN SMALL INTESTINE

According to the physiological and anatomical characteristics of small intestine,neglecting the effect of its motility on the distribution and absorption of drug and nutrient,Y.Miyamoto et al.proposed a model of two-dimensional laminar flow in a circular porous tube with permeable wall and calculated the concentration profile of drugby numerical analysis.In this paper,we give a steady-state analytical solution of the above model including deactivationterm.The obtained results are in agreement with the results of their numerical analysis. Moreover the analytical solution presented in this paper reveals the relation among the physiological parameters of the model and describes the basic absorption rule of drug and nutrient through the intestinal wall and hence pro- vides a theoretical basis for determining the permeability and reflection coefficient through in situ experiments.

ANALYTICAL MODEL ALGORITHM FOR DYNAMICS OF ROBOTIC MANIPULATORS

A simple analytical model method for dynamics of robotic manipulators is proposed.Problem of deriving model matrix elements is transformed into problem of solving for driving forceand driving torque under specified condition by recursive dynamic equations. Expressions of reaction force in arbitrary joint in numeric-symbolic form are also derived. The properties of modelmatrices are given. Corresponding software which can recognize and manipulate symbols is developed and can be used to generate model and real-time code of robotic dynamics.

A two-dimensional analytical subthreshold behavior model for junctionless dual-material cylindrical surrounding-gate MOSFETs

A two-dimensional analytical subthreshold behavior model for junctionless dual-material cylindrical surrounding- gate （JLDMCSG） metal-oxide-semiconductor field-effect transistors （MOSFETs） is proposed. It is derived by solving the two-dimensional Poisson＇s equation in two continuous cylindrical regions with any simplifying assumption. Using this analytical model, the subthreshold characteristics of JLDMCSG MOSFETs are investigated in terms of channel electro- static potential, horizontal electric field, and subthreshold current. Compared to junctionless single-material cylindrical surrounding-gate MOSFETs, JLDMCSG MOSFETs can effectively suppress short-channel effects and simultaneously im- prove carrier transport efficiency. It is found that the subthreshold current of JLDMCSG MOSFETs can be significantly reduced by adopting both a thin oxide and thin silicon channel. The accuracy of the analytical model is verified by its good agreement with the three-dimensional numerical simulator ISE TCAD.

Analytical Model of Elastic Modulus and Coefficient of Thermal Expansion for 2.5D C/SiC Composite

To make better use of 2.5D C/SiC composites in industry, it is necessary to understand the mechanical properties. A finite element model＇of 2.5D composites is established, by considering the fiber undulation and the porosity in 2.5D C/SiC composites. The fiber direction of warp is defined by cosine function to simulate the undulation of warp, and based on uniform strain assumption, analytical model of the elastic modulus and coefficient of thermal expansion （CTE） for 2.5D C/SiC composites were established by using dual- scale model. The result is found to correlate reasonably well with the predicted results and experimental results. The parametric study also demonstrates the effects of the fiber volume fraction, distance of warp yarn, and porosity in micro-scale on the mechanical properties and the coefficients of thermal expansion.