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 Solutions for Testing of Baroclinic and Wind-Driven Three-Dimensional Hydrodynamic Models

It is always a challenge for a model developer to verify a three-dimensional hydrodynamic model, especially for the baroclinic term over variable topography, due to a lack of observational data sets or suitable analytical solutions. In this paper, exact solutions for the periodic forcing by surface heat flux and wind stress are given by solving the linearized equations of motion neglecting the rotation, advection and horizontal diffusion terms. The temperature at the bottom is set to a prescribed periodic value and a slip condition on flow is enforced at the bottom. The geometry of the quarter annulus, which has been extensively studied for two- and three-dimensional analytical solutions of unstratified water bodies, is used with a general power law variation of the bottom slope in the radial direction and is constant in the azimuthal direction. The analytical solutions are derived in a cylindrical coordinate system, which describes the three-dimensional fluid field in a Cartesian coordinate system. The results presented in this paper should provide a foundation for studying and verifying the baroclinic term over a varied topography in a three-dimensional numerical model.

DECISION-MAKING OF SLICING SCHEME IN FUSED DEPOSITION MODELING PROCESS BASED ON ANALYTICAL HIERARCHICAL PROCESS

Based on analyzing the influences of a slicing scheme on stair-stepping effect, supporting structure, efficiency and deformation, etc. , analytical hierarchical process （AHP） combining with fuzzy synthetic evaluation is introduced to make decision in slicing schemes for a processing part. The application in determining the slicing scheme for a computer mouse during prototyping shows that the method increases the rationality during decision- making and improves quality and efficiency for the prototyping part.

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.

Analytical model for power dissipation in cell membranes in suspensions exposed to electric fields

Due to interaction among cells, it is too complex to build an exactanalytical model for the power dissipation within the cell membrane in suspensions exposed toexternal fields. An approximate equivalence method is proposed to resolve this problem. Based on theeffective medium theory, the transmembrane voltage on cells in suspensions was investigated by theequivalence principle. Then the electric field in the cell membrane was determined. Finally,analytical solutions for the power dissipation within the cell membrane in suspensions exposed toexternal fields were derived according to the Joule principle. The equations show that theconductive power dissipation is predominant within the cell membrane in suspensions exposed todirect current or lower frequencies, and dielectric power dissipation prevails at high frequenciesexceeding the relaxation frequency of the exposed membrane.

An Analytical Model of Electron Mobility for Strained-Si Channel nMOSFETs

An analytical model of electron mobility for strained-silicon channel nMOSFETs is proposed in this paper. The model deals directly with the strain tensor,and thus is independent of the manufacturing process. It is suitable for （100〉/ 〈110） channel nMOSFETs under biaxial or （100〉/〈 110 ） uniaxial stress and can be implemented in conventional device simulation tools .

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.

An analytical model for estimating rock strength parameters from small-scale drilling data

The small-scale drilling technique can be a fast and reliable method to estimate rock strength parameters. It needs to link the operational drilling parameters and strength properties of rock. The parameters such as bit geometry, bit movement, contact frictions and crushed zone affect the estimated parameters.An analytical model considering operational drilling data and effective parameters can be used for these purposes. In this research, an analytical model was developed based on limit equilibrium of forces in a Tshaped drag bit considering the effective parameters such as bit geometry, crushed zone and contact frictions in drilling process. Based on the model, a method was used to estimate rock strength parameters such as cohesion, internal friction angle and uniaxial compressive strength of different rock types from operational drilling data. Some drilling tests were conducted by a portable and powerful drilling machine which was developed for this work. The obtained results for strength properties of different rock types from the drilling experiments based on the proposed model are in good agreement with the results of standard tests. Experimental results show that the contact friction between the cutting face and rock is close to that between bit end wearing face and rock due to the same bit material. In this case,the strength parameters, especially internal friction angle and cohesion, are estimated only by using a blunt bit drilling data and the bit bluntness does not affect the estimated results.

Submerged flexible vegetation impact on open channel flow velocity distribution: An analytical modelling study on drag and friction

In this paper,an analytical model that represents the streamwise velocity distribution for open channel flow with submerged flexible vegetation is studied.In the present vegetated flow modelling,the whole flow field has been separated into two layers vertically: a vegetated layer and a non-vegetated free-water layer.Within the vegetated layer,an analysis of the mechanisms affecting water flow through flexible vegetation has been conducted.In the non-vegetated layer,a modified log-law equation that represents the velocity profile varying with vegetation height has been investigated.Based on the studied analytical model,a sensitivity analysis has been conducted to assess the influences of the drag (CD) and friction (Cf ) coefficients on the flow velocity.The investigated ranges of CD and Cf have also been compared to published values.The findings suggest that the CD and Cf values are non-constant at different depths and vegetation densities,unlike the constant values commonly suggested in literature.This phenomenon is particularly clear for flows with flexible vegetation,which is characterised by large deflection.

A study of the load transfer behavior of fully grouted rock bolts with analytical modelling

Fully grouted rock bolts have been used in mining industry for many years.Much research has been conducted to evaluate the load transfer behavior of fully grouted rock bolts with experimental programs.However,compared with that,less work has been conducted with analytical modelling.Therefore,in this paper,the authors used an analytical model to study the load transfer behavior of fully grouted rock bolts.To confirm the credibility of this analytical model,an in-situ pull-out test was used to validate this model.There was a close match between the experimental result and the analytical result.Following it,a parametric study was conducted with this analytical model.The influence of coefficients,Young’s modulus of the rock bolt and the diameter of the rock bolt on the load transfer performance of rock bolts was studied.Furthermore,the load distribution along the fully grouted rock bolt was analytically studied.The results show that the axial load in the rock bolt decayed from the loaded end to the free end independent of the pull-out load.However,the trend of the load distribution curve was influenced by the pull-out load.This paper was beneficial for better understanding the load transfer mechanism of fully grouted rock bolts.

Numerical Investigation of Penetration in Ceramic/Aluminum Targets Using Smoothed Particle Hydrodynamics Method and Presenting a Modified Analytical Model

Radius of ceramic cone can largely contribute into final solution of analytic models of penetration into ceramic/metal targets.In the present research,a modified model based on radius of ceramic cone was presented for ceramic/aluminum targets.In order to investigate and evaluate accuracy of the presented analytic model,obtained results were compared against the results of the Florence’s analytic model and also against numerical modeling results.The phenomenon of impact onto ceramic/aluminum composites were modeled using smoothed particle hydrodynamics(SPH)implemented utilizing ABAQUS Software.Results indicated that,with increasing initial velocity and ceramic thickness and decreasing support layer thickness,the radius of ceramic cone decreases;this ends up increasing residual velocity of the projectile and penetration time and extending the area across which the pressure is distributed.These findings indicate enhanced levels of target energy absorption and the required energy for bending and tensioning the target.As such,it can be observed that,at the same thickness and areal density,the ceramic target has its efficiency enhanced with increasing ceramic thickness and decreasing the support layer thickness.Finally,the results revealed that the associated data with SPH confirm the modified analytic model at higher accuracy than the Florence’s analytic model.

Dynamic response of clamped sandwich beams: analytical modeling

An improved analytical model is developed to predict the dynamic response of clamped lightweight sandwich beams with cellular cores subjected to shock loading over the entire span.The clamped face sheets are simplified as a single-degree-of-freedom(SDOF)system,and the core is idealized using the rigid-perfectly-plastic-locking(RPPL)model.Reflection of incident shock wave is considered by incorporating the bending/stretching resistance of the front face sheet and compaction of the core.The model is validated with existing analytical predictions and FE simulation results,with good agreement achieved.Compared with existing analytical models,the proposed model exhibits superiority in two aspects:the deformation resistance of front face sheet during shock wave reflection is taken into account;the effect of pulse shape is considered.The practical application range of the proposed model is therefore wider.

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.

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.

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.

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.

Application of Artificial Neural Networks Model as Analytical Tool for Groundwater Salinity

The main source of water in Gaza Strip is the shallow coastal aquifer. It is extremely deteriorated in terms of salinity which influenced by many variables. Studying the relation between these variables and salinity is often a complex and nonlinear process, making it suitable to model by Artificial Neural Networks (ANN). Initially, it is assumed that the salinity (represented by chloride concentration, mg/l) may be affected by some variables as: recharge rate, abstraction, abstraction average rate, life time and aquifer thickness. Data were extracted from 56 municipal wells, covering the area of Gaza Strip. After a number of modeling trials, the best neural network was determined to be Multilayer Perceptron network (MLP) with four layers: an input layer of 6 neurons, first hidden layer with 10 neurons, second hidden layer with 7 neurons and the output layer with 1 neuron which gives the final chloride concentration. The ANN model generated very good results depending on the high correlation between the observed and simulated values of chloride concentration. The correlation coefficient (r) was 0.9848. The high value of (r) showed that the simulated chloride concentration values using the ANN model were in very good agreement with the observed chloride concentration which mean that ANN model is useful and applicable for groundwater salinity modeling. ANN model was successfully utilized as analytical tool to study influence of the input variables on chloride concentration. It proved that chloride concentration in groundwater is reduced by decreasing abstraction, abstraction average rate and life time. Furthermore, it is reduced by increasing recharge rate and aquifer thickness.

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.

Analytical modeling for rapid design of bistable buckled beams

Double-clamped bistable buckled beams demonstrate great versatility in various fields such as robotics,energy harvesting,and microelectromechanical system(MEMS).However,their design often requires time-consuming and expensive computations.In this work,we present a method to easily and rapidly design bistable buckled beams subjected to a transverse point force.Based on the Euler–Bernoulli beam theory,we establish a theoretical model of bistable buckled beams to characterize their snapthrough properties.This model is verified against the results from a finite element analysis(FEA)model,with maximum discrepancy less than 7%.By analyzing and simplifying our theoretical model,we derive explicit analytical expressions for critical behavioral values on the force-displacement curve of the beam.These behavioral values include critical force,critical displacement,and travel,which are generally sufficient for characterizing the snapthrough properties of a bistable buckled beam.Based on these analytical formulas,we investigate the influence of a bistable buckled beam's key design parameters,including its actuation position and precompression,on its critical behavioral values,with our results validated by FEA simulations.Our analytical method enables fast and computationally inexpensive design of bistable buckled beams and can guide the design of complicated systems that incorporate bistable mechanisms.

CONSTANT ELASTICITY OF VARIANCE MODEL AND ANALYTICAL STRATEGIES FOR ANNUITY CONTRACTS

The constant elasticity of variance（CEV） model was constructed to study a defined contribution pension plan where benefits were paid by annuity. It also presents the process that the Legendre transform and dual theory can be applied to find an optimal investment policy during a participant＇s whole life in the pension plan. Finally, two explicit solutions to exponential utility function in the two different periods （before and after retirement） are revealed. Hence, the optimal investment strategies in the two periods are obtained.