Semi analytical modeling of springback in arc bending and effect of forming load

The analytical model for springback in arc bending of sheet metal can serve as an excellent design support.The amount of springback is considerably influenced by the geometrical and the material parameters associated with the sheet metal.In addition,the applied load during the bending also has a significant influence.Although a number of numerical techniques have been used for this purpose,only few analytical models that can provide insight into the phenomenon are available.A phenomenological model for predicting the springback in arc bending was proposed based on strain as well as deformation energy based approaches.The results of the analytical model were compared with the published experimental as well as FE results of the authors,and the agreement was found to be satisfactory.

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.

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 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 Modeling for Corrosion-Induced Cover Cracking of Corrosive Reinforced Concrete Structures

An analytical model for predicting the corrosion-induced cracking of concrete cover of reinforced concrete(RC) structures was developed.The effects of influence factors such as practical initial defects,corrosion rate,strength and elastic modulus of concrete on the corrosion-induced cracking of concrete cover were investigated.It was found that the size of practical initial defects was the most effective factor.Therefore,improving the compactness of concrete is an effective way to improve the durability of RC structures.It was also demonstrated that the accelerated corrosion tests may be unfavorable in the study of the relationship between cracking time and crack width.

Analytical modeling of sandwich beam for piezoelectric bender elements

Piezoelectric bender elements are widely used as electromechanical sensors and actuators, An analytical sandwich beam model for piezoelectric bender elements was developed based on the first-order shear deformation theory （FSDT）, which assumes a single rotation angle for the whole cross-section and a quadratic distribution function for coupled electric potential in piezoelectric layers, and corrects the effect of transverse shear strain on the electric displacement integration. Free vibration analysis of simplysupported bender elements was carried out and the numerical results showed that, solutions of the present model for various thickness-to-length ratios are compared well with the exact two-dimensional solutions, which presents an efficient and accurate model for analyzing dynamic electromechanical responses of bender elements.

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 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 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.

Modeling and Comprehensive Review of Signaling Storms in 3GPP-Based Mobile Broadband Networks:Causes,Solutions,and Countermeasures

Control signaling is mandatory for the operation and management of all types of communication networks,including the Third Generation Partnership Project(3GPP)mobile broadband networks.However,they consume important and scarce network resources such as bandwidth and processing power.There have been several reports of these control signaling turning into signaling storms halting network operations and causing the respective Telecom companies big financial losses.This paper draws its motivation from such real network disaster incidents attributed to signaling storms.In this paper,we present a thorough survey of the causes,of the signaling storm problems in 3GPP-based mobile broadband networks and discuss in detail their possible solutions and countermeasures.We provide relevant analytical models to help quantify the effect of the potential causes and benefits of their corresponding solutions.Another important contribution of this paper is the comparison of the possible causes and solutions/countermeasures,concerning their effect on several important network aspects such as architecture,additional signaling,fidelity,etc.,in the form of a table.This paper presents an update and an extension of our earlier conference publication.To our knowledge,no similar survey study exists on the subject.

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.

Wavy properties and analytical modeling of free-surface flows in the development of the multi-domain method

The wavy （oscillatory both in space and in time） properties of free-surface flows due to presence of floating bodies are analyzed within the framework of the potential-flow theory by assuming that the fluid is perfect and flow irrotational. A so-called new multi-domain method has been developed based on the fluid domain division by an analytical control surface surrounding bodies and the application of different methods adapted in the external and internal domains. In the analytical domain external to the control surface, the fundamental solution satisfying the linear boundary condition on the free surface associated with a point singularity （often called Green fimction and referred here as point solution） is applied to capture all wavy features of free-surface flows extending horizontally to infinity. Unlike classical studies in which the control surface is discretized, the unknown velocity potential and its normal derivatives are expressed by expansions of orthogonal elementary functions. The velocity potential associa- ted with each elementary distribution （elementary solutions） on the control surface can be obtained by performing multi-fold inte- grals in an analytical way. In the domain internal to the control surface containing the bodies, we could apply different methods like the Rankine source method based on the boundary integral equations for which the elementary solutions obtained in the external domain playing the role of Dirichlet-to-Neumarm operator close the problem.

Analytical modeling and simulation of germanium single gate silicon on insulator TFET

This paper proposes a new two dimensional（2D） analytical model for a germanium（Ge） single gate silicon-on-insulator tunnel field effect transistor（SG SOI TFET）. The parabolic approximation technique is used to solve the 2D Poisson equation with suitable boundary conditions and analytical expressions are derived for the surfacepotential,theelectricfieldalongthechannelandtheverticalelectricfield.Thedeviceoutputtunnellingcurrent is derived further by using the electric fields. The results show that Ge based TFETs have significant improvements inon-currentcharacteristics.Theeffectivenessoftheproposedmodelhasbeenverifiedbycomparingtheanalytical model results with the technology computer aided design（TCAD） simulation results and also comparing them with results from a silicon based TFET.

Shear behavior of single-joint bolted sandstone subjected to dryewet cycles:Experimental and analytical approaches

A series of direct shear tests under constant normal loading conditions were carried out on specimens of bolted sandstone single-joint treated with different numbers of dryewet cycles.The experimental results show that the peak shear strength and shear stiffness of bolted sandstone joints were significantly reduced after 12 dryewet cycles.The decrease in the shear strength of rough joints is more significant than that of flat joints.Due to the decrease in the strength of the surrounding rock,the deformation characteristics of the bolts are significantly affected by the number of dryewet cycles performed.With an increase in the number of dryewet cycles,the plastic hinge length of the bolt gradually increases,resulting in an increase in the corresponding shear displacement when the bolt breaks.Compared with the tensileeshear failure mode of the bolts in flat joints,the tensileebending failure mode arises for bolts in rough joints.A shear curve model describing the whole process of bolted rock joints is established based on the deterioration of rock mechanical parameters caused by dry‒wet cycles.The model proposed considers the change in the friction angle of the joint surface with the shear displacement,which is applied to the derivation of the model by introducing the dynamic evolutionary friction angle parameter.The reasonably good agreement between a predicted curve and the corresponding experimental curve indicates that this method can effectively predict the shear strength of a bolted rock joint involving rough joint under dryewet cycling conditions.

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.

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.

Consolidation of high replacement ratio stone column-reinforced ground:Analytical solutions incorporating clogging effect

The utilization of stone columns has emerged as a popular ground improvement strategy,whereas the drainage performance can be adversely hampered by clogging effect.Despite the ample progress of calculation methods for the consolidation of stone column-improved ground,theoretical investigations into the clogging effect have not been thoroughly explored.Furthermore,it is imperative to involve the column consolidation deformation to mitigate computational error on the consolidation of composite ground with high replacement ratios.In this context,an analytical model accounting for the initial clogging and coupled time and depth-dependent clogging of stone columns is established.Then,the resulting governing equations and analytical solutions are obtained under a new flow continuity relationship to incorporate column consolidation deformation.The accuracy and reliability of the proposed model are illustrated by degradation analysis and case studies with good agreements.Subsequently,the computed results of the current study are juxtaposed against the existing models,and an in-depth assessment of the impacts of several crucial parameters on the consolidation behavior is conducted.The results reveal that ignoring column consolidation deformation leads to an overestimate of the consolidation rate,with maximum error reaching up to 16%as the replacement ratio increases.Furthermore,the initial clogging also has a significant influence on the consolidation performance.Additionally,the increment of depth and time-clogging factors a and b will induce a noticeable retardation of the consolidation process,particularly in the later stage.

Extension of analytical model of solid-state phase transformation

Departing from an analytical phase transformation model, a new analytical approach to deduce transformed fraction for non-isothermal phase transformation was developed. In the new approach, the effect of the initial transformation temperature and the accurate ＂temperature integral＂ approximations are incorporated to obtain an extended analytical model. Numerical approach demonstrated that the extended analytical model prediction for transformed fraction and transformation rate is in good agreement with the exact numerical calculation. The new model can describe more precisely the kinetic behavior than the original analytical model, especially for transformation with relatively high initial transformation temperature. The kinetic parameters obtained from the new model are more accurate and reasonable than those from the original analytical model.

Development of fatigue analytical model of automotive dynamic parts made of semi-solid aluminum alloys

Automotive suspension control arm is used to join the steering knuckle to the vehicle frame. Its main function is to provide stability under fatigue stresses of loading and unloading in accelerating and braking. Conventionally, these parts were made of steel; however, fuel consumption and emission of polluting gases are strongly dependent on car weight. Recently, there is a try to develop and design much lighter and better fatigue resistant metal of semisolid A357 aluminum alloys. This work aims at a better understanding of identifying the fatigue strain-hardening parameters used for determining fatigue characteristics of aluminum suspension control arm using analytical and mathematical modeling. The most judicious method is to perform the fatigue tests on standardized test pieces and then plot two Wohler curves, mainly number of cycles as a function of the stress and as a function of the deformation. From these curves and following a certain mathematical and analytical methods, certain curves are plotted and then all of these coefficients are drawn. The new calculated parameters showed a clear improvement of the fatigue curve towards the experimental curve performed on the samples of aluminum alloy A357 compared with the same analytical curve for the same alloy.

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.