A non-linear finite element model of human L4-L5 lumbar spinal segment with three-dimensional solid element ligaments

This paper establishes a non-linear finite element model (NFEM) of L4-L5 lumbar spinal segment with accurate three-dimensional solid ligaments and intervertebral disc. For the purpose, the intervertebral disc and surrounding ligaments are modeled with four-nodal three-dimensional tetrahedral elements with hyper-elastic material properties. Pure moment of 10 N·m without preload is applied to the upper vertebral body under the loading conditions of lateral bending, backward extension, torsion, and forward flexion, respectively. The simulate relationship curves between generalized forces and generalized displacement of the NFEM are compared with the in vitro experimental result curves to verify NFEM. The verified results show that: (1) The range of simulated motion is a good agreement with the in vitro experimental data; (2) The NFEM can more effectively reffect the actual mechanical properties than the FE model using cable and spring elements ligaments; (3) The NFEM can be used as the basis for further research on lumbar degenerative diseases.

A symplectic finite element method based on Galerkin discretization for solving linear systems

We propose a novel symplectic finite element method to solve the structural dynamic responses of linear elastic systems.For the dynamic responses of continuous medium structures,the traditional numerical algorithm is the dissipative algorithm and cannot maintain long-term energy conservation.Thus,a symplectic finite element method with energy conservation is constructed in this paper.A linear elastic system can be discretized into multiple elements,and a Hamiltonian system of each element can be constructed.The single element is discretized by the Galerkin method,and then the Hamiltonian system is constructed into the Birkhoffian system.Finally,all the elements are combined to obtain the vibration equation of the continuous system and solved by the symplectic difference scheme.Through the numerical experiments of the vibration response of the Bernoulli-Euler beam and composite plate,it is found that the vibration response solution and energy obtained with the algorithm are superior to those of the Runge-Kutta algorithm.The results show that the symplectic finite element method can keep energy conservation for a long time and has higher stability in solving the dynamic responses of linear elastic systems.

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.

Validation and application of three-dimensional discontinuous deformation analysis with tetrahedron finite element meshed block

In the last decade, three dimensional discontin- uous deformation analyses （3D DDA） has attracted more and more attention of researchers and geotechnical engineers worldwide. The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation, which would cause block expansion under rigid body rotation and thus limit its capability to model block de- formation. In this paper, 3D DDA is coupled with tetrahe- dron finite elements to tackle these two problems. Tetrahe- dron is the simplest in the 3D domain and makes it easy to implement automatic discretization, even for complex topol- ogy shape. Furthermore, element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly. The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested. Valida- tion is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes, i.e., wedge failure. Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases. Finally, a complex rockslide example demon- strates the robustness and versatility of the coupled method.

Three-Dimensional Simulations of RESET Operation in Phase-Change Random Access Memory with Blade-Type Like Phase Change Layer by Finite Element Modeling

An optimized device structure for reducing the RESET current of phase-change random access memory （PCRAM） with blade-type like （BTL） phase change layer is proposed. The electrical thermal analysis of the BTL cell and the blade heater contactor structure by three-dimensional finite element modeling are compared with each other during RESET operation. The simulation results show that the programming region of the phase change layer in the BTL cell is much smaller, and thermal electrical distributions of the BTL cell are more concentrated on the TiN/GST interface. The results indicate that the BTL cell has the superiorities of increasing the heating efficiency, decreasing the power consumption and reducing the RESET current from 0.67mA to 0.32mA. Therefore, the BTL cell will be appropriate for high performance PCRAM device with lower power consumption and lower RESET current.

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.

Alternating Direction Finite Volume Element Methods for Three-Dimensional Parabolic Equations

This paper presents alternating direction finite volume element methods for three-dimensional parabolic partial differential equations and gives four computational schemes, one is analogous to Douglas finite difference scheme with second-order splitting error, the other two schemes have third-order splitting error, and the last one is an extended LOD scheme. The L2 norm and H1 semi-norm error estimates are obtained for the first scheme and second one, respectively. Finally, two numerical examples are provided to illustrate the efficiency and accuracy of the methods.

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.

CHEBYSHEV PSEUDOSPECTRAL-HYBRID FINITE ELEMENT METHOD FOR THREE-DIMENSIONAL VORTICITY EQUATION

In this paper,Chebyshev pseudospectral-finite element schemes are proposed for solving three dimensional vorticity equation.Some approximation results in nonisotropic Sobolev spaces are given.The generalized stability and the convergence are proved strictly.The numerical results show the advantages of this method.The technique in this paper is also applicable to other three-dimensional nonlinear problems in fluid dynamics.

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 anisotropic induced polarization modeling using finite element method

With the development of geophysical exploration technology,the anisotropy of underground media has got more and more attention.At present,there are few studies on the anisotropy of the induced polarization method.This article explores the effect of anisotropy on the underground media of the induced polarization method under three-dimensional complex terrain.The research work transforms the underground electric field control equation into a variational problem,and use the unstructured finite element method to construct a large linear equation system for solving electric potentials.By the sparse matrix compression technique and symmetric successive over-relaxation preconditioned conjugate gradient algorithm(SSOR-PCG)to solve the equation system.Finally,the article uses the classic central gradient array method to obtain the forward apparent polarizability value.The calculation results of the model find that different anisotropic conditions will significantly affect the forward results which show a strong directional correlation,revealing the importance of considering anisotropy in practical work.

Evaluation value of three-dimensional finite element model analysis for bone mineral density and bone metabolism activity in patients with osteoporosis

Objective: To study the evaluation value of three-dimensional finite element model analysis for bone mineral density (BMD) and bone metabolism activity in patients with osteoporosis. Methods: A total of 218 patients who were diagnosed with osteoporosis in the hospital between February 2014 and January 2017 were collected as observation group, and 100 healthy volunteers who received physical examination in the hospital during the same period were selected as normal control group. The femoral head of the two groups was analyzed by three-dimensional finite element model, and the femoral head BMD levels and serum bone metabolism index contents were measured. Pearson test was used to evaluate the evaluation value of femoral head three-dimensional finite element model for osteoporosis. Results: The cancellous bone and cortical bone Von Mises stress value of observation group were lower than those of normal control group, and femoral neck BMD value of observation group was lower than that of normal control group;serum bone metabolism index BGP content was lower than that of normal control group while NBAP, TRACP-5b and CTX-1 contents were higher than those of normal control group. Pearson test showed that the cancellous bone and cortical bone Von Mises stress value of patients with osteoporosis were directly correlated with BMD value and bone metabolism index contents. Conclusion: The three-dimensional finite element model analysis resultsof patients with osteoporosis can objectively reflect the femoral headBMD value and bone metabolism activity, and is a reliable way to evaluate the risk of long-term fractures.

Three-dimensional finite element analysls for external midface distraction after different osteotomy in patients with cleft lip and palate

Objective To study three - dimensional finite element analysis for external midface distraction after different osteotomy in patients with cleft lip and palate ( Clp) . Methods Three - dimensional Fem models of Le Fort Ⅰ,Ⅱand Ⅲ,osteotomy in Clp patients were estabolished. External midface distraction were simulated. An anteriorly and inferiorly directed 900 g force was

Combined load bearing capacity of rigid piles embedded in a crossanisotropic clay deposit using 3D finite element lower bound

In this study,an iterative-based three-dimensional finite element lower bound in association with the second-order cone programming method is adopted to evaluate the limit load of a single pile embedded in cross-anisotropic soils under general loading condition.The lower bound solutions of the pile embedded in an anisotropic soil deposit can be found by formulating the element equilibrium,equilibrium of shear and normal stresses along discontinuities,boundary conditions,yield function,and optimizing the objective function through the second-order cone programming method in conjunction with an iterative-based update procedure.A general loading condition is considered to profile the expansion of the safe load in the vertical-horizontal-moment(V-H-M)space.The results of this study are compared and validated against three different cases including an isotropic lateral loading,anisotropic end bearing capacity,and a pile embedded in an isotropic soil deposit under general loading condition.A parametric study is conducted to evaluate the impact of different influencing factors.It was found that the effect of anisotropy on the variation of lateral limit load of a single pile is more pronounced than the corresponding vertical and bending moment limit loads,whereas the interface properties have more significant effects on the vertical and bending moment limit loads in comparison to the lateral limit load.

A LOCKING-FREE ANISOTROPIC NONCONFORMING FINITE ELEMENT FOR PLANAR LINEAR ELASTICITY PROBLEM

The main aim of this article is to study the approximation of a locking-free anisotropic nonconforming finite element for the pure displacement boundary value problem of planar linear elasticity. The optimal error estimates are obtained by using some novel approaches and techniques. The method proposed in this article is robust in the sense that the convergence estimates in the energy and L^2-norms are independent-of the Lame parameter λ.

Finite element analysis of the effect of micro-pore defect on linear friction welding of medium carbon steel

Micro-pore is a very common material defect. In the present paper, the temperature fields of medium carbon steel joints with and without micro-pore defect during linear friction welding （LFW） were investigated by using finite element method. The effect of micro-pore defect on the axial shortening of joints during LFW was examined. The x- and y-direction displacements of micro-pore during the LFW process were also studied. In addition, the shape of micro-pore after LFW was observed. The heat conducted from the weld inteace to the specimen interior. The fluctuation range of the temperature curves for the joint with micro-pore is larger than that without micro-pore. Position of micro-pore changes with the change of the friction time. The circular shape of micro-pore becomes oval after welding.

A streamline diffusion nonconforming finite element method for the time-dependent linearized Navier-Stokes equations

A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.

Implementing the Node Based Smoothed Finite Element Method as User Element in Abaqus for Linear and Nonlinear Elasticity

In this paper,the node based smoothed-strain Abaqus user element(UEL)in the framework of finite element method is introduced.The basic idea behind of the node based smoothed finite element(NSFEM)is that finite element cells are divided into subcells and subcells construct the smoothing domain associated with each node of a finite element cell[Liu,Dai and Nguyen-Thoi(2007)].Therefore,the numerical integration is globally performed over smoothing domains.It is demonstrated that the proposed UEL retains all the advantages of the NSFEM,i.e.,upper bound solution,overly soft stiffness and free from locking in compressible and nearly-incompressible media.In this work,the constant strain triangular(CST)elements are used to construct node based smoothing domains,since any complex two dimensional domains can be discretized using CST elements.This additional challenge is successfully addressed in this paper.The efficacy and robustness of the proposed work is obtained by several benchmark problems in both linear and nonlinear elasticity.The developed UEL and the associated files can be downloaded from https://github.com/nsundar/NSFEM.

High-efciency improved symmetric successive over-relaxation preconditioned conjugate gradient method for solving large-scale finite element linear equations

Fast solving large-scale linear equations in the finite element analysis is a classical subject in computational mechanics. It is a key technique in computer aided engineering （CAE） and computer aided manufacturing （CAM）. This paper presents a high-efficiency improved symmetric successive over-relaxation （ISSOR） preconditioned conjugate gradient （PCG） method, which maintains lelism consistent with the original form. Ideally, the by 50% as compared with the original algorithm. the convergence and inherent paralcomputation can It is suitable for be reduced nearly high-performance computing with its inherent basic high-efficiency operations. By comparing with the numerical results, it is shown that the proposed method has the best performance.

Optimal design of butterfly-shaped linear ultrasonic motor using finite element method and response surface methodology

A new method for optimizing a butterfly-shaped linear ultrasonic motor was proposed to maximize its mechanical output. The finite element analysis technology and response surface methodology were combined together to realize the optimal design of the butterfly-shaped linear ultrasonic motor. First, the operation principle of the motor was introduced. Second, the finite element parameterized model of the stator of the motor was built using ANSYS parametric design language and some structure parameters of the stator were selected as design variables. Third, the sample points were selected in design variable space using latin hypercube Design. Through modal analysis and harmonic response analysis of the stator based on these sample points, the target responses were obtained. These sample points and response values were combined together to build a response surface model. Finally, the simplex method was used to find the optimal solution. The experimental results showed that many aspects of the design requirements of the butterfly-shaped linear ultrasonic motor have been fulfilled. The prototype motor fabricated based on the optimal design result exhibited considerably high dynamic performance, such as no-load speed of 873 mm/s, maximal thrust of 27.5 N, maximal efficiency of 43%, and thrust-weight ratio of 45.8.