Highly efficient H^1-Galerkin mixed finite element method (MFEM) for parabolic integro-differential equation

A highly efficient H1-Galerkin mixed finite element method （MFEM） is presented with linear triangular element for the parabolic integro-differential equation. Firstly, some new results about the integral estimation and asymptotic expansions are studied. Then, the superconvergence of order O（h^2） for both the original variable u in H1 （Ω） norm and the flux p = u in H（div, Ω） norm is derived through the interpolation post processing technique. Furthermore, with the help of the asymptotic expansions and a suitable auxiliary problem, the extrapolation solutions with accuracy O（h^3） are obtained for the above two variables. Finally, some numerical results are provided to confirm validity of the theoretical analysis and excellent performance of the proposed method.

ELASTIC-PLASTIC FINITE ELEMENT ANALYSIS OF THREE-DIMENSIONAL CONTACT-IMPACT AT RAIL JOINT

Using the finite element code ANSYS/LS-DYNA, a dynamic finite element modelwith an elastic-linear-kinematic-hardening plastic material is established to analyzeelastic-plastic stresses in the railhead in the impact process of wheel and rail occurring at thegap of rail joint. The model is based on the discrete elastic support condition of the rails, whichis suitable for the actual situation of wheel/track rolling contact. In the analysis the influencesof axle load, yield stress and tangent modulus of rail material on the stresses and strains areinvestigated in detail. The distribution of stresses and strains in the jointed railhead are given.It is found that the axle load, yield stress and tangent modulus of rail material greatly affect thestresses and strains in the railhead during impacting. The study provides a reliable method anduseful datum for the further research on fatigue and wear of railhead and improving the rail jointmode.

Finite Element Numerical Simulation and PIV Measurement of Flow Field inside Metering-in Spool Valve

The finite element method （FEM） and particle image velocimetry （PIV） technique are utilized to get the flow field along the inlet passage, the chamber, the metering port and the outlet passage of spool valve at three different valve openings. For FEM numerical simulation, the stream function ψ-vorticity ω forms of continuity and Navier-Stokes equations are employed and FEM is applied to discrete the equations. Homemade simulation codes are executed to compute the values of stream function and vorticity at each node in the flow domain, then according to the correlation between stream function and velocity components, the velocity vectors of the whole field are calculated. For PIV experiment, pulse Nd： YAG laser is exploited to generate laser beam, cylindrical and spherical lenses are combined each other to produce 1.0 mm thickness laser sheet to illuminate the object plane, Polystyrene spherical particle with diameter of 30-50 μm is seeded in the fluid as a tracing particles, Kodak ES 1.0 CCD camera is employed to capture the images of interested, the images are processed with fast Fourier transform （FFT） cross-correlation algorithm and the processing results is displayed. Both results of numerical simulation and PIV experimental show that there are three main areas in the spool valve where vortex is formed. Numerical results also indicate that the valve opening have some effects on the flow structure of the valve. The investigation is helpful for qualitatively analyzing the energy loss, noise generating, steady state flow forces and even designing the geometry structure and flow passage.

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.

Three Dimension Rigid-plastic Finite Element Simulation for Two-Roll Cross-wedge Rolling Process

Cross-wedge rolling (CWR) is a metal process of ro ta ry forming. To produce a part, one cylindrical billet should be placed between t wo counterrotating and wedge-shape dies, which move tangentially relative each other. The billet suffers plastic deformation (essentially, localized compressio n) during its rotation between the rotating dies. Compared to other numerical si mulation methods, the finite element method (FEM) has advantages in solving gene ral problems with complex shapes of the formed parts. In cross-wedge rolling, t here are four stages in the workpiece deformation process, namely knifing, guidi ng, stretching and sizing stage. It is time-consuming and expensive to design t he CWR process by trial and error method. The application of numerical simul ation for the CWR process will help engineers to efficiently improve the process development. Tselikov, Hayama, Jain and Kobayashi, and Higashimo applied the sl ip-line theory in study of CWR process analysis. Zb.pater studied CWR process i ncluding upsetting by upper-bound method. The above numerical simulation were b ased on the two-dimensional plain-strain assumption ignored the metal flow in workpiece axial direction. Therefore, the complex three-dimensional stress and deformation involved in CWR processes were not presented. Compared to other nume rical simulation methods, the finite element method (FEM) has advantages in solv ing general problems with complex shapes of the formed parts. As yet, a few 3-D finite element simulation studies on CWR process have been reported in literatu res. In this paper, the process of cross wedge rolling (CWR) has been simulated and analyzed by 3D rigid-plastic finite element method. Considering the charact eristic of CWR, the static implicit FEM program is selected. The models proposed in this study uses the commercial code DEFORM 3D to simulate the CWR process. T his is an implicit Lagrangian finite element code, which includes many new enhan cements functions. A new method of utilizing multiple processors using the MPI s tandard has been implemented. Automatic switching between the two different defo rmation solvers (Sparse Solver and Conjugate Gradient Solver) has also been impl emented in order to increase the speed of simulations. In this paper, all stages in CWR process are simulated to be able to closely understand and analyze the a ctual CWR process. For simulating all forming stages in CWR process, the dynam ic adaptive remeshing technology for tetrahedral solid elements was applied. T he stress distributions in cross section of forming workpiece are analyzed to in terpret fracture or rarefaction in the center of workpiece. Authors also analyze d the time-torque curve and the laws of load changing.

Stability assessment of landslide-prone road cut rock slopes in Himalayan terrain:A finite element method based approach

Large-scale slope destabilization could be aggravated due to swift urbanization and ever-rising demands of geoengineering projects such as dams,tunnels,bridges and widening roads.National Highway-58 connects Delhi to Badrinath in India,which passes through complex geomorphological and geological terrain and often encounters cut slopes susceptible to slope failures.In the present investigation,a detailed geotechnical appraisal is conducted along the road cut slopes from Rishikesh to Devprayag in the Himalayas.Twenty vulnerable road cut slopes were demarcated for detailed slope stability analysis using Phase2D finite element modeling simulator.Nonlinear generalized Hoek-Brown(GHB)criterion was adopted for stability analyses.Out of 20 slopes,five slopes(S6,S7,S18,S19 and S20)are unstable with factor of safety(FoS)less than or equal to 1,and thus needs immediate attention.The FoS values of four slopes(S2,S9,S13 and S17)lie between 1 and 1.3,i.e.marginally stable,and slopes S1,S3,S4,S5,S8,S10,Sll,S12,S14,S15 and S16 are stable.Mohr-Coulomb(MC)criterion was also adopted to compare the slope stability analysis with GHB criterion.The FoS calculated from GHB criterion is close to that using MC criterion for lower values of FoS whereas for higher values,the difference is marked.For the jointed rock in the Himalayan region,the nonlinear GHB criterion gives better results as compared to MC criterion and matches with the prevailing field conditions.Accordingly,some suggestions are proposed to strengthen the stability of cut slopes.

Runge-Kutta method, finite element method, and regular algorithms for Hamiltonian system

The symplectic algorithm and the energy conservation algorithm are two important kinds of algorithms to solve Hamiltonian systems. The symplectic Runge- Kutta （RK） method is an important part of the former, and the continuous finite element method （CFEM） belongs to the later. We find and prove the equivalence of one kind of the implicit RK method and the CFEM, give the coefficient table of the CFEM to simplify its computation, propose a new standard to measure algorithms for Hamiltonian systems, and define another class of algorithms --the regular method. Finally, numerical experiments are given to verify the theoretical results.

Numerical well test for well with finite conductivity vertical fracture in coalbed

A new well test model is developed for the hydraulic fractured well in coalbed by considering the following aspects： methane desorption phenomena, finite conductivity vertical fractures, and asymmetry of the fracture about the well. A new parameter is introduced to describe the storage of the fracture, which is named as a combined fracture storage. Another new concept called the fracture asymmetry coefficient is used to define the asymmetry of the fracture about the well. Finite element method （FEM） is used to solve the new mathematical model. The well test type curves and pressure fields are obtained and analyzed. The effects of the combined fracture storage, desorption factor, fracture conductivity, and fracture asymmetry coefficient on the well test type curves are discussed in detail. In order to verify the new model, a set of field well test data is analyzed.

Finite Element Modeling and Modal Analysis of Complicated Structure with Bolted Joints

A contact bolt model is proposed as a new modeling technique to investigate the complex structure with bolted joints for modal analysis and compared with the coupled bolt model, and the test results are given. Among these models, the coupled bolt model provides the best accurate responses compared with the experimental results. The contact bolt model shows the best effectiveness and usefulness in view of operational time. The bolt models proposed in this study are adopted for a dynamic characteristic analysis of a large diesel engine consisting of several parts which are connected by many bolts. The dynamic behavior of the entire engine structure was investigated by experiment. The coupled bolt model and the contact bolt model were applied to model the assembly of engine with high preload. The experimental results are in good agreement with the finite element method （FEM） results. Compared with the other models, the contact bolt model presented in this paper is more effective and useful in view of operational time and experience of analysts.

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method （FEM） and the differential quadrature method （DQM） to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.

A refined finite element method for bending analysis of laminated plates integrated with piezoelectric fiber-reinforced composite actuators

This research presents a finite element formulation based on four-variable refined plate theory for bending analysis of cross-ply and angle-ply laminated composite plates integrated with a piezoelectric fiber-reinforced composite actuator under electromechanical loading. The four-variable refined plate theory is a simple and efficient higher-order shear deformation theory, which predicts parabolic variation of transverse shear stresses across the plate thickness and satisfies zero traction conditions on the plate free surfaces. The weak form of governing equations is derived using the principle of minimum potential energy, and a 4-node non-conforming rectangular plate element with 8 degrees of freedom per node is introduced for discretizing the domain. Several benchmark problems are solved by the developed MATLAB code and the obtained results are compared with those from exact and other numerical solutions, showing good agreement.

Self-adaptive strategy for one-dimensional finite element method based on EEP method with optimal super-convergence order

Based on the newly-developed element energy projection （EEP） method with optimal super-convergence order for computation of super-convergent results, an improved self-adaptive strategy for one-dimensional finite element method （FEM） is proposed. In the strategy, a posteriori errors are estimated by comparing FEM solutions to EEP super-convergent solutions with optimal order of super-convergence, meshes are refined by using the error-averaging method. Quasi-FEM solutions are used to replace the true FEM solutions in the adaptive process. This strategy has been found to be simple, clear, efficient and reliable. For most problems, only one adaptive step is needed to produce the required FEM solutions which pointwise satisfy the user specified error tolerances in the max-norm. Taking the elliptical ordinary differential equation of the second order as the model problem, this paper describes the fundamental idea, implementation strategy and computational algorithm and representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

FINITE ELEMENT ANALYSIS FOR MICROSTRUCTURE EVOLUTION IN HOT FINISHING ROLLING OF STEEL STRIPS

A computer model that describes the evolution of microstructures during the hot finishing rolling of SS400 steel has been proposed. It has been found that the microstructure strongly depends on processing of materials and on their parameters, which affected the history of the thermomechanical variables, such as temperature, strain, and strain rate. To investigate the microstructural evolutions during the hot finishing rolling process, the rigid-thermoviscoplastic finite element method （FEM） has been combined with dynamic recrystallization, static recrystallization, and grain growth models. The simulation results show a good agreement with those from the prediction software online.

Experimental and Finite Element Method Studies of J-Lead Solder Joint Reliability

A comprehensive experimental and numerical study of solder joints for plastic leaded chip carrier (PLCC) 84-Pin, 1.27 mm pitch was carried out. The reliability of solder joints was assessed through accelerated thermal cycling at the temperature range of - 55℃-125℃. The samples were taken out to observe the evolution in microstructure, such as grain coarsening, initiation and propagation of cracks. It was found that the Pb-rich phases segregated gradually and formed a continuous layer adjacent to the intermetallic compound (IMC) layer with increasing the number of thermal cycles, resulting in cracks near the solder/lead interface. The response of stress and strain was studied using nonlinear finite element method (FEM), and the results agreed well with the experimental data.

Radial Force Analysis of Polydioxanone Coronary Stent by Finite Element Method

Coronary stent is used to treat stenosis artery by recovering the luminal diameter of artery and maintaining the normal blood flow. The geometry of coronary stent is an important factor for the radial force. In this study,the relation between the radial force of stent and crown angle was discussed. The result showed that there was no particular rule between the radial force of stent and the crown angle. The maximum radial force of stent was obtained when the crown angle was 50. 04° and the minimum radial force was got when the crown angle was 75°.

SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD

Based on the newly-developed element energy projection （EEP） method for computation of super-convergent results in one-dimensional finite element method （FEM）, the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.

P_1-nonconforming triangular finite element method for elliptic and parabolic interface problems

The lowest order Pl-nonconforming triangular finite element method （FEM） for elliptic and parabolic interface problems is investigated. Under some reasonable regularity assumptions on the exact solutions, the optimal order error estimates are obtained in the broken energy norm. Finally, some numerical results are provided to verify the theoretical analysis.

3D FINITE ELEMENT ANALYSIS OF THE DAMAGE EFFECTS ON THE DENTAL COMPOSITE SUBJECT TO WATER SORPTION

The damage effects of water sorption on the mechanical properties of the hydroxyapatite particle reinforced Bis-GMA/TEGDMA copolymer （HA/Bis-GMA/TEGDMA） h-ave been predicted using 3D finite cell models. The plasticizer effect on the polymer matrix was considered as a variation of its Young＇s modulus. Three different cell models were used to determine the influence of varying particle contents, interphase strength and moisture concentration on the debonding damage. The stress distribution pattern has been examined and the stress transfer mode clarified. The Young＇s modulus and fracture strength of the Bis-GMA/TEGDMA composite were also predicted using the model with and without consideration of the damage. ine Iormer results with consideration of the debonding damage are in good agreement with existing literature experimental data. The shielding effect of our proposed model and an alternative approach were discussed. The FCC cell model has also been extended to predict the critical load for the damaged and the undamaged composite subject to the 3-point flexural test.

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.

PREDICTION FOR FORMING LIMIT OF AL2024T3 SHEET BASED ON DAMAGE THEORY USING FINITE ELEMENT METHOD

This paper presents the application of anisotropic damage theory to the study of forming limit diagram of A12024T3 aluminum alloy sheet. In the prediction of limiting strains of the aluminum sheet structure, a finite element cell model has been constructed. The cell model consists of two phases, the aluminum alloy matrix and the intermetallic cluster. The material behavior of the aluminum alloy matrix is described with a fully coupled elasto-plastic damage constitutive equation. The intermetallic cluster is assumed to be elastic and brittle. By varying the stretching ratio, the limiting strains of the sheet under biaxial stretching have been predicted by using the necking criterion proposed. The prediction is in good agreement with the experimental findings. Moreover, the finite element cell model can provide information for understanding the microscopic damage mechanism of the aluminum alloy. Over-estimation of the limit strains may result if the effect of material damage is ignored in the sheet metal forming study.