Hermite Finite Element Method for Vibration Problem of Euler-Bernoulli Beam on Viscoelastic Pasternak Foundation

Viscoelastic foundation plays a very important role in civil engineering. It can effectively disperse the structural load into the foundation soil and avoid the damage caused by the concentrated load. The model of Euler-Bernoulli beam on viscoelastic Pasternak foundation can be used to analyze the deformation and response of buildings under complex geological conditions. In this paper, we use Hermite finite element method to get the numerical approximation scheme for the vibration equation of viscoelastic Pasternak foundation beam. Convergence and error estimation are rigourously established. We prove that the fully discrete scheme has convergence order O(τ2+h4), where τis time step size and his space step size. Finally, we give four numerical examples to verify the validity of theoretical analysis.

Application of Wavelet Finite Element Method to Simulation of the Temperature Field of Copier Paper

Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copier paper is moving through the fusing rollers. By means of conventional shaft elements, the high gradient temperature variety causes the oscillation of the numerical solution. Based on the Daubechies scaling functions, a kind of wavelet based element is constructed for the above problem. The temperature field of the copier paper moving through the fusing rollers is simulated using the two methods. Comparison of the results shows the advantages of the wavelet finite element method, which provides a new method for improving the copier properties.

Nonlinear simulation of arch dam cracking with mixed finite element method

This paper proposes a new, simple and efficient method for nonlinear simulation of arch dam cracking from the construction period to the operation period, which takes into account the arch dam construction process and temperature loads. In the calculation mesh, the contact surface of pair nodes is located at places on the arch dam where cracking is possible. A new effective iterative method, the mixed finite element method for friction-contact problems, is improved and used for nonlinear simulation of the cracking process. The forces acting on the structure are divided into two parts： external forces and contact forces. The displacement of the structure is chosen as the basic variable and the nodal contact force in the possible contact region of the local coordinate system is chosen as the iterative variable, so that the nonlinear iterative process is only limited within the possible contact surface and is much more economical. This method was used to simulate the cracking process of the Shuanghe Arch Dam in Southwest China. In order to prove the validity and accuracy of this method and to study the effect of thermal stress on arch dam cracking, three schemes were designed for calculation. Numerical results agree with actual measured data, proving that it is feasible to use this method to simulate the entire process of nonlinear arch dam cracking.

Modeling and Simulation of Valve Cycle in Vein Using an Immersed Finite Element Method

A vein model was established to simulate the periodic characteristics of blood flow and valve deformation in blood-induced valve cycles.Using an immersed finite element method which was modified by a ghost fluid technique,the interaction between the vein and blood was simulated.With an independent solid solver,the contact force between vein tissues was calculated using an adhesive contact method.A benchmark simulation of the normal valve cycle validated the proposed model for a healthy vein.Both the opening orifice and blood flow rate agreed with those in the physiology.Low blood shear stress and maximum leaflet stress were also seen in the base region of the valve.On the basis of the healthy model,a diseased vein model was subsequently built to explore the sinus lesions,namely,fibrosis and atrophy which are assumed stiffening and softening of the sinus.Our results showed the opening orifice of the diseased vein was inversely proportional to the corresponding modulus of the sinus.A drop in the transvalvular pressure gradient resulted from the sinus lesion.Compared to the fibrosis,the atrophy of the sinus apparently improved the vein deformability but simultaneously accelerated the deterioration of venous disease and increased the risk of potential fracture.These results provide understandings of the normal/abnormal valve cycle in vein,and can be also helpful for the prosthesis design.

DEFORMATION ANALYSIS OF SHEET METAL SINGLE-POINT INCREMENTAL FORMING BY FINITE ELEMENT METHOD SIMULATION

Single-point incremental forming （SPIF） is an innovational sheet metal forming method without dedicated dies, which belongs to rapid prototyping technology. In generalizing the SPIF of sheet metal, the deformation analysis on forming process becomes an important and useful method for the planning of shell products, the choice of material, the design of the forming process and the planning of the forming tool. Using solid brick elements, the finite element method（FEM） model of truncated pyramid was established. Based on the theory of anisotropy and assumed strain formulation, the SPIF processes with different parameters were simulated. The resulted comparison between the simulations and the experiments shows that the FEM model is feasible and effective. Then, according to the simulated forming process, the deformation pattern of SPIF can be summarized as the combination of plane-stretching deformation and bending deformation. And the study about the process parameters＇ impact on deformation shows that the process parameter of interlayer spacing is a dominant factor on the deformation. Decreasing interlayer spacing, the strain of one step decreases and the formability of blank will be improved. With bigger interlayer spacing, the plastic deformation zone increases and the forming force will be bigger.

Flow simulation considering adsorption boundary layer based on digital rock and finite element method

Due to the low permeability of tight reservoirs,throats play a significant role in controlling fluid flow.Although many studies have been conducted to investigate fluid flow in throats in the microscale domain,comparatively fewer works have been devoted to study the effect of adsorption boundary layer(ABL)in throats based on the digital rock method.By considering an ABL,we investigate its effects on fluid flow.We build digital rock model based on computed tomography technology.Then,microscopic pore structures are extracted with watershed segmentation and pore geometries are meshed through Delaunay triangulation approach.Finally,using the meshed digital simulation model and finite element method,we investigate the effects of viscosity and thickness of ABL on microscale flow.Our results demonstrate that viscosity and thickness of ABL are major factors that significantly hinder fluid flow in throats.

Radiation heat transfer model for complex superalloy turbine blade in directional solidification process based on finite element method

For the sake of a more accurate shell boundary and calculation of radiation heat transfer in the Directional Solidification(DS) process, a radiation heat transfer model based on the Finite Element Method(FEM)is developed in this study. Key technologies, such as distinguishing boundaries automatically, local matrix and lumped heat capacity matrix, are also stated. In order to analyze the effect of withdrawing rate on DS process,the solidification processes of a complex superalloy turbine blade in the High Rate Solidification(HRS) process with different withdrawing rates are simulated; and by comparing the simulation results, it is found that the most suitable withdrawing rate is determined to be 5.0 mm·min^(-1). Finally, the accuracy and reliability of the radiation heat transfer model are verified, because of the accordance of simulation results with practical process.

Treatment of discontinuous interface in liquid-solid forming with extended finite element method

Extended finite element method(XFEM) is proposed to simulate the discontinuous interface in the liquid-solid forming process.The discontinuous interface is an important phenomenon happening in the liquid-solid forming processes and it is difficult to be simulated accurately with conventional finite element method(CFEM) because it involves solid phase and liquid phase simultaneously.XFEM is becoming more and more popular with the need of solving the discontinuous problem happening in engineering field.The implementation method of XFEM is proposed on Abaqus code by using UEL(user element) with the flowchart.The key is to modify the element stiffness in the proposed method by using UEL on the platform of Abaqus code.In contrast to XFEM used in the simulation of solidification,the geometrical and physical properties of elements were modified at the same time in our method that is beneficial to getting smooth interface transition and precise analysis results.The analysis is simplified significantly with XFEM.

Sintering zone prediction in direct metal laser sintering by finite element method

A three-dimensional finite element thermal model in direct metal laser sintering(DMLS) including the effect of powder-to-solid transition were established to predict sintering zone, which benefited the determination of suitable process parameters in DMLS. The nonlinear transient model of the metals thermal conductivity for powder-to-solid transition was developed. The model uses solid thermal properties of material in liquid-phase zone, transitional ones in sintering or sintered zone and powder ones in unsintered zones of powder bed to predict, respectively. Sintering zone boundary was estimated by maximum temperature history profile. Experiments were carried out using multi-component Cu-based metal powder. Compared experimental and predicted results, the mean error of sintering depth and width are 7.8% and 14.4%, respectively, which confirms the accuracy of the FEM prediction.

THEORETICAL PREDICTION OF TOOL-CHIP CONTACT LENGTH IN ORTHOGONAL METAL MACHINING BY COMPUTER SIMULATION

A method for determination of tool-chip contact length is theoreticallypresented in orthogonal metal machining. By using computer simulation and based on the analyses ofthe elastro-plastic deformation with lagrangian finite element method in the deformation zone, theaccumulated representative length of the low layer, the tool-chip contact length of the chipcontacting the tool rake are calculated, experimental studies are also carried out with 0.2 percentcarbon steel. It is shown that the tool-chip contact lengths obtained from computer simulation havea good agreement with those of measured values.

Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method

A novel,highly efficient and accurate adaptive higher-order finite element method(hp-FEM)is used to simulate a multi-frequency resistivity loggingwhile-drilling(LWD)tool response in a borehole environment.Presented in this study are the vector expression of Maxwell’s equations,three kinds of boundary conditions,stability weak formulation of Maxwell’s equations,and automatic hpadaptivity strategy.The new hp-FEM can select optimal refinement and calculation strategies based on the practical formation model and error estimation.Numerical experiments show that the new hp-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom,which provides more accurate results than those obtained using the adaptive h-FEM.The numerical results illustrate the high efficiency and accuracy of the method at a given LWD tool structure and parameters in different physical models,which further confirm the accuracy of the results using the Hermes library(http://hpfem.org/hermes)with a multi-frequency resistivity LWD tool response in a borehole environment.

Large eddy simulation for wind field analysis based on stabilized finite element method

In this paper,a stabilized finite element technique,actualized by streamline upwind Petrov-Galerkin(SUPG) stabilized method and three-step finite element method(FEM),for large eddy simulation(LES) is developed to predict the wind flow with high Reynolds numbers.Weak form of LES motion equation is combined with the SUPG stabilized term for the spatial finite element discretization.An explicit three-step scheme is implemented for the temporal discretization.For the numerical example of 2D wind flow over a square rib at Re=4.2×105,the Smagorinsky's subgrid-scale(SSGS) model,the DSGS model,and the DSGS model with Cabot near-wall model are applied,and their results are analyzed and compared with experimental results.Furthermore,numerical examples of 3D wind flow around a surface-mounted cube with different Reynolds numbers are performed using DSGS model with Cabot near-wall model based on the present stabilized method to study the wind field and compared with experimental and numerical results.Finally,vortex structures for wind flow around a surface-mounted cube are studied by present numerical method.Stable and satisfactory results are obtained,which are consistent with most of the measurements even under coarse mesh.

Numerical simulation of single roller melt spinning for NdFeB alloy based on finite element method

The numerical simulation model of single roller melt spinning for rapid quenching process of NdFeB alloy was built,and the vacuum chamber,cooling roller and sample were taken into account as a system.The existing mature technology was in order to verify the correctness of simulation.The rapid quenching ribbons with different roll speeds were used as the simulation objects.The results of the numerical simulation and experiments show that the validity of the model has been testified and the reasons of the formation of complete quenching ribbons and by-product have been explained.The experimental thickness of the ribbons is proportional to the theoretical thickness.In the same spray condition,with the roll speed increasing,the thickness decreases linearly.At the speed range of25-30 m·s^(-1),the simulated calculation date is close to the experimental date,which can be considered as an ideal technological parameter.

Numerical simulation of isothermal chemical vapor infiltration process in fabrication of carbon-carbon composites by finite element method

The chemical vapor infiltration process in fabrication of carbon-carbon composites is highly inefficient and requires long processing time. These limitations add considerably to the cost of fabrication and restrict the application of this material. Efforts have been made to study the CVI process in fabrication of carbon-carbon composites by computer simulation and predict the process parameters, density, porosity, etc. According to the characteristics of CVI process, the basis principle of FEM and mass transport, the finite element model has been established. Incremental finite element equations and the elemental stiffness matrices have been derived for the first time. The finite element program developed by the authors has been used to simulate the ICVI process in fabrication of carbon-carbon composites. Computer color display of simulated results can express the densification and distributions of density and porosity in preform clearly. The influence of process parameters on the densification of preform has been analyzed. The numerically simulated and experimental results give a good agreement.

Numerical simulation of hydraulic fracturing and associated microseismicity using finite-discrete element method

Hydraulic fracturing （HF） technique has been extensively used for the exploitation of unconventional oiland gas reservoirs. HF enhances the connectivity of less permeable oil and gas-bearing rock formationsby fluid injection, which creates an interconnected fracture network and increases the hydrocarbonproduction. Meanwhile, microseismic （MS） monitoring is one of the most effective approaches to evaluatesuch stimulation process. In this paper, the combined finite-discrete element method （FDEM） isadopted to numerically simulate HF and associated MS. Several post-processing tools, includingfrequency-magnitude distribution （b-value）, fractal dimension （D-value）, and seismic events clustering,are utilized to interpret numerical results. A non-parametric clustering algorithm designed specificallyfor FDEM is used to reduce the mesh dependency and extract more realistic seismic information.Simulation results indicated that at the local scale, the HF process tends to propagate following the rockmass discontinuities; while at the reservoir scale, it tends to develop in the direction parallel to themaximum in-situ stress. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

A Finite Element Method Solver for Time-Dependent and Stationary Schrodinger Equations with a Generic Potential

A general finite element solution of the Schrodinger equation for a onedimensional problem is presented.The solver is applicable to both stationary and time-dependent cases with a general user-selected potential term.Furthermore,it is possible to include external magnetic or electric fields,as well as spin-orbital and spinmagnetic interactions.We use analytically soluble problems to validate the solver.The predicted numerical auto-states are compared with the analytical ones,and selected mean values are used to validate the auto-functions.In order to analyze the performance of the time-dependent Schrodinger equation,a traveling wave package benchmark was reproduced.In addition,a problem involving the scattering of a wave packet over a double potential barrier shows the performance of the solver in cases of transmission and reflection of packages.Other general problems,related to periodic potentials,are treated with the same general solver and a Lagrange multiplier method to introduce periodic boundary conditions.Some simple cases of known periodic potential solutions are reported.

Finite element method simulation for tensile process of sintered iron-base material

Different material properties leads to different metal fracture behaviors. Even if the powder material is composed of plastic metal, the fracture still does not show macroscopic plastic deformation characteristics if the material contains a large number of voids. Eight node isoparametric elastic plastic finite element method was used to simulate the tensile process of sintered powder material. By setting a number of voids in the analyzed metal cuboid, the initial density was taken into consideration. The material properties of the three dimensional solid for the tensile simulation were defined with reference to the known pure iron material parameters. The load displacement curves during elongation were obtained with a universal testing machine, and then the simulated curves were compared with the experimental results. The factors that cause the stress concentration and strength decrease were analyzed according to the simulated equivalent von Mises stress distribution.

Finite element method simulation of shotpeening wing skin panel

Finite element method(FEM) was used to simulate the forming process of shotpeening the wing skin panel. Experiment of shotpeeing the wing skin panel was carried out. The results show that equivalent deformation in shotpeening process can be obtained using the elongation and bending result caused by thermal stress that is induced by applying temperature load on the surface of the part. Deformation of the part in the shotpeeing process can be analyzed using this method. The parameters and their relationships are identified.

3D Finite Element Simulation of Tunnel Boring Machine Construction Processes in Deep Water Conveyance Tunnel

Applying stiffness migration method,a 3D finite element mechanical model is established to simulate the excavation and advance processes.By using 3D nonlinear finite element method,the tunnel boring machine(TBM) excavation process is dynamically simulated to analyze the stress and strain field status of surrounding rock and segment.The maximum tensile stress of segment ring caused by tunnel construction mainly lies in arch bottom and presents zonal distribution.The stress increases slightly and limitedly in the course of excavation.The maximum and minimum displacements of segment,manifesting as zonal distribution,distribute in arch bottom and vault respectively.The displacements slightly increase with the advance of TBM and gradually tend to stability.