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.

Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

Seismic Wavelet Analysis Based on Finite Element Numerical Simulation

The practice of exploration and production has proved that explosives are excited in different surrounding rocks and the seismic wavelets collected have different characteristics. In this paper, by establishing a numerical model of the explosion in the well, using finite element analysis technology for numerical simulation, the simulation calculated the stress structure in the near-source area of the earthquake excitation, and extracted the seismic wavelet. The results show that the simulation seismic wavelet characteristics of different thin interbedded sand and mudstone structures have changed significantly. Through excitation simulation, the amplitude and spectrum information of seismic wavelets can be compared and analyzed, and the excitation parameters can be optimized. .

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Numerical simulation of tire/soil interaction using a verified 3D finite element model

The compaction and stress generation on terrain were always investigated based on empirical approaches or testing methods for tire/soil interaction.However,the analysis should be performed for various tires and at different soil strengths.With the increasing capacity of numerical computers and simulation software,finite element modeling of tire/terrain interaction seems a good approach for predicting the effect of change on the parameters.In this work,an elaborated 3D model fully complianning with the geometry of radial tire 115/60R13 was established,using commercial code Solidwork Simulation.The hyper-elastic and incompressible rubber as tire main material was analyzed by Moony-Rivlin model.The Drucker-Prager yield criterion was used to model the soil compaction.Results show that the model realistically predicts the laboratory tests outputs of the modeled tire on the soft soil.