A Full Predictor-Corrector Finite Element Method for the One-Dimensional Heat Equation with Time-Dependent Singularities

The energy norm convergence rate of the finite element solution of the heat equation is reduced by the time-regularity of the exact solution. This paper presents an adaptive finite element treatment of time-dependent singularities on the one-dimensional heat equation. The method is based on a Fourier decomposition of the solution and an extraction formula of the coefficients of the singularities coupled with a predictor-corrector algorithm. The method recovers the optimal convergence rate of the finite element method on a quasi-uniform mesh refinement. Numerical results are carried out to show the efficiency of the method.

A Deep Learning Approach to Shape Optimization Problems for Flexoelectric Materials Using the Isogeometric Finite Element Method

A new approach for flexoelectricmaterial shape optimization is proposed in this study.In this work,a proxymodel based on artificial neural network(ANN)is used to solve the parameter optimization and shape optimization problems.To improve the fitting ability of the neural network,we use the idea of pre-training to determine the structure of the neural network and combine different optimizers for training.The isogeometric analysis-finite element method(IGA-FEM)is used to discretize the flexural theoretical formulas and obtain samples,which helps ANN to build a proxy model from the model shape to the target value.The effectiveness of the proposed method is verified through two numerical examples of parameter optimization and one numerical example of shape optimization.

Contribution to the Full 3D Finite Element Modelling of a Hybrid Stepping Motor with and without Current in the Coils

The paper presents our contribution to the full 3D finite element modelling of a hybrid stepping motor using COMSOL Multiphysics software. This type of four-phase motor has a permanent magnet interposed between the two identical and coaxial half stators. The calculation of the field with or without current in the windings (respectively with or without permanent magnet) is done using a mixed formulation with strong coupling. In addition, the local high saturation of the ferromagnetic material and the radial and axial components of the magnetic flux are taken into account. The results obtained make it possible to clearly observe, as a function of the intensity of the bus current or the remanent induction, the saturation zones, the lines, the orientations and the magnetic flux densities. 3D finite element modelling provide more accurate numerical data on the magnetic field through multiphysics analysis. This analysis considers the actual operating conditions and leads to the design of an optimized machine structure, with or without current in the windings and/or permanent magnet.

Earth Pressure of the Trapdoor Problem Using Three-Dimensional Discrete Element Method

Load transformation from the yielding part of the soil to the adjacent part is known as the soil arching effect,which plays an important role in the design of various geotechnical infrastructures.Terzaghi’s trapdoor test was an importantmilestone in the development of theories on soil arching.The research on earth pressure of the trapdoor problem is presented in this paper using the three-dimensional(3D)discrete element method(DEM).Five 3D trapdoor models with different heights are established by 3DDEMsoftware PFC 3D.The variation of earth pressure on the trapdoor with the downward movement of the trapdoor,the distribution of vertical earth pressure along the horizontal direction,the distribution of vertical earth pressure along the vertical direction,the distribution of lateral earth pressure coefficient along the depth direction,the magnitude and direction of contact force chain are studied,respectively.Related research results show that the earth pressure on the trapdoor decreases rapidly after the downward movement of the trapdoor,and then reaches the minimum earth pressure.After that,the earth’s pressure will rise slightly,and whether this phenomenon occurs depends on the depth ratio.For the bottom soil,due to the stress transfer caused by the soil arching effect,the ratio of earth pressure in the loose area decreases,while the ratio of earth pressure in the stable area increases.With the trapdoor moving down,the vertical earth pressure along the depth in the stable zone is basically consistent with the initial state,which shows an approximate linear distribution.After the trapdoor moves down,the distribution of earth pressure along with the depth in the loose area changes,which is far less than the theoretical value of vertical earth pressure of its self-weight.Because of the compression of the soil on both sides,the lateral earth pressure coefficient of most areas on the central axis of the loose zone is close to the passive earth pressure coefficient Kp.The existence of a‘soil arch’can be observed intuitively from the distribution diagram of the contact force chain in the loose zone.

Three-dimensional Finite Element Analysis of the Mechanical Properties of Helical Thread Connection

Conventional analytical and numerical methods for the mechanical properties of helical threads are relied on many assumptions and approximations and thus hardly yield satisfied results. A parameterized 3D finite element model of bolted joints with real helical thread geometry is established and meshed with refined hexahedral elements. The Von Mises plasticity criterion, kinematic hardening rule of materials and interfacial contacts are employed to make it possible for the suggested model be able to approach real assembly conditions. Then, the mechanical properties of bolted joints with different thread pitches, thread numbers and modular ratios are investigated, including the contact pressure distribution at joint interfaces, the axial load distribution and stress concentration in screw threads during the loading and unloading process. Simulation results indicate that the load distribution in screw threads produced by the suggested model agrees well the results from CHEN’s photoelastic tests. In addition, an interesting phenomenon is found that tightening the bolt with a large preload first and then adjusting the clamping force by unloading can make the load distribution more uniform and reduce the maximum residual equivalent stress in thread roots by up to 40%. This research provides a simple and practical approach to constructing the 3D finite element model and predicting the mechanical properties of helical thread connection.

Three-dimensional Finite Element Modeling of a Maxillary Premolar Tooth Based on the Micro-CT Scanning: A Detailed Description

This study describes the details of how to construct a three-dimensional （3D） finite element model of a maxillary first premolar tooth based on micro-CT data acquisition technique, MIMICS soft- ware and ANSYS software. The tooth was scanned by micro-CT, in which 1295 slices were obtained and then 648 slices were selected for modeling. The 3D surface mesh models of enamel and dentin were created by MIMICS （STL file）. The solid mesh model was constructed by ANSYS. After the material properties and boundary conditions were set, a loading analysis was performed to demonstrate the ap- plicableness of the resulting model. The first and third principal stresses were then evaluated. The re- suits showed that the number of nodes and elements of the finite element model were 56 618 and 311801, respectively. The geometric form of the model was highly consistent with that of the true tooth, and the deviation between them was ~）.28%. The loading analysis revealed the typical stress patterns in the contour map. The maximum compressive stress existed in the contact points and the maximum tensile stress existed in the deep fissure between the two cusps. It is concluded that by using the micro-CT and highly integrated software, construction of the 3D finite element model with high quality will not be difficult for clinical researchers.

Three-dimensional finite element analysis with different internal fixation methods through the anterior approach

BACKGROUND With the modernization of society and transportation in the last decades in China,the incidence of high-energy trauma increased sharply in China,including that of acetabular fractures.AIM To establish different finite element models for acetabular posterior column fractures involving the quadrilateral area of the acetabulum.METHODS The three-dimensional models of the normal and fractured pelvis and the five internal fixations were established using the computed tomography data of the pelvis of a living volunteer.After the vertebral body model was inserted in the way of origin matching and all cancellous bones were copied using the duplicated cancellous bone model as the subtractive entity,the Boolean operation was performed on the pelvis model to obtain the model of the complete pelvis cortical and cancellous bones.RESULTS In the standing position,the maximum stress was 46.21 MPa.In the sitting position,the sacrum bore the simulated gravity load at the upper end.When comparing the five fixations,there were no significant differences in the stress mean values among groups(sitting:P=0.9794;standing:P=0.9741).In terms of displacement,the average displacement of the internal iliac plate group was smaller than that of the spring plate group(P=0.002),and no differences were observed between the other pairs of groups(all P>0.05).In the standing position,there were no significant differences in the mean value of displacement among the groups(P=0.2985).It can be seen from the stress nephogram of the internal fixations in different positions that the stress of the internal fixation was mainly concentrated in the fracture segment.CONCLUSION There were no significant differences among the fixations for acetabular posterior column fractures involving the quadrilateral area of the acetabulum.

Autologous nerve graft repair of different degrees of sciatic nerve defect:stress and displacement at the anastomosis in a three-dimensional finite element simulation model

In the repair of peripheral nerve injury using autologous or synthetic nerve grafting, the mag- nitude of tensile forces at the anastomosis affects its response to physiological stress and the ultimate success of the treatment. One-dimensional stretching is commonly used to measure changes in tensile stress and strain; however, the accuracy of this simple method is limited. There- fore, in the present study, we established three-dimensional finite element models of sciatic nerve defects repaired by autologous nerve grafts. Using PRO E 5.0 finite element simulation software, we calculated the maximum stress and displacement of an anastomosis under a 5 N load in 10-, 20-, 30-, 40-mm long autologous nerve grafts. We found that maximum displacement increased with graft length, consistent with specimen force. These findings indicate that three-dimensional finite element simulation is a feasible method for analyzing stress and displacement at the anas- tomosis after autologous nerve grafting.

Three-dimensional Finite Element Analysis of the Mechanical Stress on Root from Orthodontic Tooth Movement by Sliding Mechanics

In order to study mechanical stress on root from orthodontic tooth movement by sliding mechanics, a 3-dimensional finite element model incorporating all layers of a human mandibular dental arch with orthodontic appliance has been developed to simulate mechanical stress on root from the orthodontic tooth movement. Simulated orthodontic force of 2 N at 0, 30 and 45 degree from the horizontal axis was applied to the crown of the teeth. The finite element analysis showed when orthodontic forces were applied to the tooth, the stress was mainly concentrated at the neck of the tooth decreasing uniformly to the apex and crown. The highest stress on the root was 0.621 N/mm^2 for cervical margin of the canine, and 0.114 N/mm^2 for apical region of the canine. The top of canine crown showed the largest amount of displacement （2.417 μm）, while the lowest amount of displacement was located at the apical region of canine （0.043 μm）. In conclusion, this model might enable one to simulate orthodontic tooth movements clinically. Sliding force at 2 N is ideal to ensure the bodily orthodontic tooth movement. The highest stress concentration in the roots was always localized at the cervical margin when orthodontic force of 2 N at 0, 30 and 45 degree from the horizontal axis, so there may be the same risk of root resorption when orthodontic force of 2 N at 0, 30 and 45 degree was used in clinic cases.

STUDY ON THREE-DIMENSIONAL FINITE BODIES CONTAINING CRACKS USING THE FINITE ELEMENT METHOD OF LINES

The three-dimensional finite element method of lines is presented, and the basic processing description of 3D FEMOL in cracking questions is given in detail. Applications to 3D bodies with cracks indicate that good accuracy can be obtained with relatively coarse girds. In particular, application to the tension specimen shows very good agreement with the evaluation of stress intensity factors, which is better than the results of other methods. This implies a considerable potential for using this method in the 3D analysis of finite geometry solids and suggests a possible extension of this technique to nonlinear material behavior.

Three-Dimensional Thermo-Elastic-Plastic Finite Element Method Modeling for Predicting Weld-Induced Residual Stresses and Distortions in Steel Stiffened-Plate Structures

The objective of the present paper is to develop nonlinear finite element method models for predicting the weld-induced initial deflection and residual stress of plating in steel stiffened-plate structures. For this purpose, three-dimensional thermo-elastic-plastic finite element method computations are performed with varying plate thickness and weld bead length (leg length) in welded plate panels, the latter being associated with weld heat input. The finite element models are verified by a comparison with experimental database which was obtained by the authors in separate studies with full scale measurements. It is concluded that the nonlinear finite element method models developed in the present paper are very accurate in terms of predicting the weld-induced initial imperfections of steel stiffened plate structures. Details of the numerical computations together with test database are documented.

Establishment of a three-dimensional finite element model for gunshot wounds to the human mandible

Objective:To investigate the feasibility of a finite element model as an ideal research tool for human maxillofacial gunshot wounds.Methods:Mandible CT scan data on the Chinese Visible Human were imported into MIMICS software to obtain the surface mesh of the mandible.Then,these surface-meshed models were imported into ANSA software for automatic net generation.Elements and nodes were partitioned on the basis of the mesh to obtain a three-dimensional finite element model for the mandible with every internal parameter consistent with those of our previously developed model in the pig mandible.The finite element model was imported into LS-DYNA for computation.Finally,the LS-POST was used to complete the simulation and the measurements.Results:A three-dimensional finite element model was successfully established for gunshot wounds in the human mandible.The stress distribution and the degree of injury were simulated dynamically for shots from two types of projectiles in the mandible at one entry angle and at three impact velocities.Conclusion:Three-dimensional finite element models will become ideal research tools for treatment of ballistic wounds of the human maxillofacial region.Using this human mandibular model as a foundation,we will be able to successfully develop three-dimensional finite element models for human maxillofacial gunshot wounds.

Three-dimensional Finite Element Analysis on the Layer Steel Fiber Reinforced Concrete Pavement:A New Type of Pavement Material

An investigation was conducted on the design of layer steel fiberreinforced concrete (LSFRC) PAVEMENT. Finite element method wasapplied to the analysis on the stress distribution in order todetermine The thickness and segregation distance of LSFRC pavementslabs.

THE CHARACTERISTIC FINITE ELEMENT ALTERNATING-DIRECTION METHOD AND ANALYSIS FOR THREE-DIMENSIONAL NUMERICAL RESERVOIR SIMULATION

Petroleum science has made remarkable progress in organic geochcmistry and in the research into the theories of petroleum origin, its transport and accumulation. In estimating the oil-gas resources of a basin, the knowledge of its evolutionary history and especially the numerical computation of fluid flow and the history of its changes under heat is vital. The mathematical model can be described as a coupled system of nonlinear partial differentical equations with initial-boundary value problems. This thesis, from actual conditions such as the effect of fluid compressibility and the three-dimensional characteristic of large-scale science-engineering computation, we put forward a kind of characteristic finite element alternating-direction schemes and obtain optimal order estimates in L^2 norm for the error in the approximate assumption.

Three-dimensional finite element analysis of hyperbaric oxygen therapy on the optic nerve from a damaged orbit

A middle-aged male patient with a right orbital comminuted fracture underwent computer tomography scanning, and a three-dimensional finite element model of the eyes and relevant tissues was established. Optic nerve stress in a hyperbaric oxygen environment was simulated and analyzed by changing the elastic modulus and external pressure of the skull at the damage side. Results showed that stress maximized at the contact site of the optic nerve and the eyeball in the damaged and intact eye orbits. Optic nerve stress at the damaged orbit significantly increased; however, stress in the intact orbit only slightly changed with decreased elastic modulus of the skull while external pressure remained unchanged. Maximum optic nerve stress increased in the damaged and intact side, along with increased external pressure, while elastic modulus remained unchanged. These experimental findings suggested that the optic nerve was compressed under hyperbaric oxygen and optic nerve stress was greater in the damaged orbit than in the intact orbit.

Finite element analysis of three-dimensional laser-induced transient thermal grating in diamond/ZnSe system

This paper uses finite element method to obtain the three-dimensional temperature field of laser-induced transient thermal grating （TTG） for two-layered structure of diamond film on ZnSe substrate. The numerical results indicate that unique two-times heating process is gradually experienced in the area between two adjacent grating stripes. However, there is a little change for the temperature field along the depth direction for the diamond film due to its great thermal conductivity. It further finds that the thickness of the diamond film has a significant influence on the temperature field in diamond/ZnSe system. The results are useful for the application of laser-induced TTG technique in film/substrate system.

THE SLIDING SURFACE ALGORITHMSINTHREE－DIMENSIONAL DYNAMIC FINITE ELEMENT CODE

In this paper, the sliding surface algorithms in dynamic finite element analysis ofhigh velocity impact are presented. With these algorithms, the momentum and theangular momentum of the element can be conserved. The calculated examples showthat the calculation using these algorithms in dynamic finite element analysis of highvelocity is valid and stable.

Study on Postseismic Impact of Wenchuan Earthquake on the Sichuan-Yunnan Region Based on Three-Dimensional Viscoelastic Finite Element Method

Based on the lateral segmentation and vertical stratification characteristics of the crustal medium in Sichuan-Yunnan region,and the asymmetry of the static dislocations on the coseismic fault plane of the Wenchuan M_S8.0 earthquake,we built a three-dimensional viscoelastic finite element model of the crust in the Sichuan-Yunnan region.The postseismic impact of the Wenchuan M_S8.0 earthquake on the Sichuan-Yunnan region was studied.The results show that:①The far-field horizontal deformation caused by the viscoelastic relaxation of the medium in the 10 years after the earthquake is about 0-20 mm within the Sichuan-Yunnan diamond-shaped block,which has a greater influence on north side and smaller on south side.②In the 10 years after the earthquake,the far-field vertical deformation caused by the viscoelastic relaxation effect of the medium is small,and it shows an increase of about 0-4 mm in most areas of the Sichuan-Yunnan diamond-shaped block.③The Xianshuihe fault and the eastern segment of the East Kunlun fault,which are close to the seismogenic fault,show a high gradient on deformation fields after the earthquake.④In order to compare with the strong earthquake activity in the SichuanYunnan region after the Wenchuan earthquake,the horizontal stress state and the Coulomb failure stress change of the active block boundary are also calculated.From the spatial distribution of the coseismic and postseismic displacement field,the fault activity characteristics reflected by the stress state and the stress loading of the fault layer reflected by the Coulomb failure stress change,there is a certain correlation with the spatial distribution of strong earthquake activity in this region.

THE CLOSED-FORM SOLUTION OF VECTOR FINITE ELEMENT INTEGRAL EQUATIONS FOR THREE DIMENSIONAL ELECTROMAGNETIC ANALYSIS

In this paper,a set of closed-form formulas for vector Finite Element Method(FEM) to analyze three dimensional electromagnetic problems is presented on the basis of Gaussian quadrature integration scheme.By analyzing the open region problems,the first-order Absorbing Boundary Condition(ABC) is considered as the truncation boundary condition and the equation is carried out in a closed-form.Based on the formulas,the hybrid Expanded Cholesky Method(ECM) and MultiFrontal algorithm(MF) is applied to solve finite element equations.Using the closed-form solution,the elec-tromagnetic field of three dimensional targets can be studied sententiously and accurately.Simulation results show that the presented formulas are successfully and concise,which can be easily used to analyze three dimensional electromagnetic problems.

Three-Dimensional Finite Elemental Analysis of Bone Stress near an Implant Placed at the Border between Mandible and Fibular Graft in Mandibular Reconstruction

Purpose: The aim of the present study was to use finite elemental analysis (FEA) to evaluate bone stress near an implant placed at the border between the mandible and fibular graft in mandibular reconstruction. Materials and Methods: A fibular model (FM) and transplantation model (TM) were constructed for FEA. In TM, mandible was on the mesial side and the fibular graft was on the distal side. The implant was positioned at the center of both bone models. In TM, it was placed on the border between the mandible and fibular graft. A 10-mm implant was used in the monocortical model and a 15-mm implant was used in the bicortical model. The loading force was set at 100 N, the angle was set at 90°, and the loading position was set as center, mesial, or distal on the upper surface of the prosthesis. Von Mises equivalent stress values of the bone near the implant collar and apex at the middle line between buccal and lingual side were measured. Results: In all models, stress values were significantly lower with center loading than with distal loading and mesial loading. In center loading, the stress values were significantly lower in the bicortical model than in the monocortical model. There were no significant differences in stress values between FM and TM in all conditions. Conclusions: Bone stress was least with the center loading position, which was further decreased by bicortical fixation. There was no increase in mechanical stress associated with placing an implant at the border between the mandible and the fibular graft.