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.

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.

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.

Nonlinear finite element analysis of three implant-abutment interface designs

The objective of this study was to investigate the mechanical characteristics of implant-abutment interface design in a dental implant system, using nonlinear finite element analysis （FEA） method. This finite element simulation study was applied on three commonly used commercial dental implant systems： model I, the reduced-diameter 3i implant system （West Palm Beach, FL, USA） with a hex and a 12-point double internal hexagonal connection; model II, the Semados implant system （Bego, Bremen, Germany） with combination of a conical （45° taper） and internal hexagonal connection; and model III, the Br,~nemark implant system （Nobel Biocare, Gothenburg, Sweden） with external hexagonal connection. In simulation, a force of 170 N with 45°oblique to the longitudinal axis of the implant was loaded to the top surface of the abutment. It has been found from the strength and stiffness analysis that the 3i implant system has the lowest maximum yon Mises stress, prirlcipal stress and displacement, while the Br^nemark implant system has the highest. It was concluded from our preliminary study using nonlinear FEA that the reduced-diameter 3i implant system with a hex and a 12-point double internal hexagonal connection had a better stress distribution, and produced a smaller displacement than the other two implant systems.

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.

Analysis of the Influence of Parafunctional Loads on the Bone-Prosthesis System: A Non-Linear Finite Element Analysis

The present study evaluates the effects of occlusal loading on an implant-supported dental implant with external hexagon dental implant-abutment systems, using the finite element method analysis. Tensile analyses were performed to simulate different axial and obliquous masticatory loads. The influence of the variations in the contouring conditions of the interfaces was analyzed to weigh the osseointegration with linear and non-linear cases, by means of a parametric design. The geometry selected to place the prostheses was a jaw section, considering the properties of the set of cortical and trabecular bones. The results show that for non-linear contour conditions, the stress presents smaller value distributions and signals a different place in the screw-implant interface as the factor of the greater weight in this study. The location indicated that von Mises stress concentrations are not exclusive to the contact regions studied, moving to an area that is not in direct contact with the non-linear contact interfaces. In addition, the direction of load with an angle of 15 degrees presented the highest values of von Mises stress.

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 ram/s, maximal thrust of 27.5 N, maximal efficiency of 43%, and thrust-weight ratio of 45.8.

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.

Multiple linear system techniques for 3D finite element method modeling of direct current resistivity

The strategies that minimize the overall solution time of multiple linear systems in 3D finite element method (FEM) modeling of direct current (DC) resistivity were discussed. A global stiff matrix is assembled and stored in two parts separately. One part is associated with the volume integral and the other is associated with the subsurface boundary integral. The equivalent multiple linear systems with closer right-hand sides than the original systems were constructed. A recycling Krylov subspace technique was employed to solve the multiple linear systems. The solution of the seed system was used as an initial guess for the subsequent systems. The results of two numerical experiments show that the improved algorithm reduces the iterations and CPU time by almost 50%, compared with the classical preconditioned conjugate gradient method.

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.

Finite Element Analysis and Linear Regression of Maximum Temperature for Inner Wall of Chimney Foundation

The uniform design method was adopted and the twenty-four groups of different geometric and physical pa-rameters were chosen. The finite element model was built. Comparisons between the simulation results and the test re-sults prove that the simulation results are correct. The distribution of the temperature field of the chimney foundationwas analyzed. The multivariate linear regression of the hightest tomperature was performed on the inner wall of thechimney foundation by the numerical calculated results. The fitting property of the highest temperature with six influ-ence factors was obtained. A simple method for the calculation of the temperature field of the chimney foundation wasprovided.

Finite element analyses of slope stability problems using non-associated plasticity

In recent years, finite element analyses have increasingly been utilized for slope stability problems. In comparison to limit equilibrium methods, numerical analyses do not require any definition of the failure mechanism a priori and enable the determination of the safety level more accurately. The paper compares the performances of strength reduction finite element analysis(SRFEA) with finite element limit analysis(FELA), whereby the focus is related to non-associated plasticity. Displacement-based finite element analyses using a strength reduction technique suffer from numerical instabilities when using non-associated plasticity, especially when dealing with high friction angles but moderate dilatancy angles. The FELA on the other hand provides rigorous upper and lower bounds of the factor of safety(FoS) but is restricted to associated flow rules. Suggestions to overcome this problem, proposed by Davis(1968), lead to conservative FoSs; therefore, an enhanced procedure has been investigated. When using the modified approach, both the SRFEA and the FELA provide very similar results. Further studies highlight the advantages of using an adaptive mesh refinement to determine FoSs. Additionally, it is shown that the initial stress field does not affect the FoS when using a Mohr-Coulomb failure criterion.

Finite Element Simulation on the Spin-forming of the 3D Non-axisymmetric Thin-Walled Tubes

The roller movement trace for the 3D non-axisymmetric thin-walled tubes is a complex space curve. Besides the roller rotation caused by contact with the blank, the roller rotates around the workpiece together with the main spindle, and also moves simultaneously along the direction of the revolution radius. The method to correctly establish the finite element （FE） models of the metal spinning is based on the MSC. MARC software was introduced. The calculation formulas considering both the revolution and rotation of the roller were obtained by the mathematical deduction. The saving calculation points m should be a multiple of 4 for one revolution of the roller around the workpiece to obtain the maximum forming force for the spinning of the 3D non-axisymmetric thin-walled tubes. The simulation results conform well to the experimental ones for several spinning methods; the maximum error is less than ±15%.

COMPACTLY SUPPORTED NON-TENSOR PRODUCT FORM TWO-DIMENSION WAVELET FINITE ELEMENT

Some theorems of compactly supported non-tensor product form two-dimension Daubechies wavelet were analysed carefully. Compactly supported non-tensor product form two-dimension wavelet was constructed, then non-tensor product form two dimension wavelet finite element was used to solve the deflection problem of elastic thin plate. The error order was researched. A numerical example was given at last.

Quasi-optimal complexity of adaptive finite element method for linear elasticity problems in two dimensions

This paper introduces an adaptive finite element method （AFEM） using the newest vertex bisection and marking exclusively according to the error estimator without special treatment of oscillation. By the combination of the global lower bound and the localized upper bound of the posteriori error estimator, perturbation of oscillation, and cardinality of the marked element set, it is proved that the AFEM is quasi-optimal for linear elasticity problems in two dimensions, and this conclusion is verified by the numerical examples.

Matrix-Free Higher-Order Finite Element Method for Parallel Simulation of Compressible and Nearly-Incompressible Linear Dedicated to Professor Karl Stark Pister for his 95th birthday Elasticity on Unstructured Meshes

Higher-order displacement-based finite element methods are useful for simulating bending problems and potentially addressing mesh-locking associated with nearly-incompressible elasticity,yet are computationally expensive.To address the computational expense,the paper presents a matrix-free,displacement-based,higher-order,hexahedral finite element implementation of compressible and nearly-compressible(ν→0.5)linear isotropic elasticity at small strain with p-multigrid preconditioning.The cost,solve time,and scalability of the implementation with respect to strain energy error are investigated for polynomial order p=1,2,3,4 for compressible elasticity,and p=2,3,4 for nearly-incompressible elasticity,on different number of CPU cores for a tube bending problem.In the context of this matrix-free implementation,higher-order polynomials(p=3,4)generally are faster in achieving better accuracy in the solution than lower-order polynomials(p=1,2).However,for a beam bending simulation with stress concentration(singularity),it is demonstrated that higher-order finite elements do not improve the spatial order of convergence,even though accuracy is improved.

Analysis of Linear Triangular Elements for Convection-diffusion Problems by Streamline Diffusion Finite Element Methods

This paper is devoted to studying the superconvergence of streamline diffusion finite element methods for convection-diffusion problems. In [8], under the condition that ε ≤ h^2 the optimal finite element error estimate was obtained in L^2-norm. In the present paper, however, the same error estimate result is gained under the weaker condition that ε≤h.

A Cell-Based Linear Smoothed Finite Element Method for Polygonal Topology Optimization

The aim of this work is to employ a modified cell-based smoothed finite element method(S-FEM)for topology optimization with the domain discretized with arbitrary polygons.In the present work,the linear polynomial basis function is used as the weight function instead of the constant weight function used in the standard S-FEM.This improves the accuracy and yields an optimal convergence rate.The gradients are smoothed over each smoothing domain,then used to compute the stiffness matrix.Within the proposed scheme,an optimum topology procedure is conducted over the smoothing domains.Structural materials are distributed over each smoothing domain and the filtering scheme relies on the smoothing domain.Numerical tests are carried out to pursue the performance of the proposed optimization by comparing convergence,efficiency and accuracy.

Finite Element Methods Applied to the Tubular Linear Stepping Motor

In this paper proposes a Finite Element Methods analyzing applied to the linear tubular stepping actuator. The linear displacement is modeled by means of a layer of finite elements placed in the air gap. The design of the linear stepper motor for achieving a specific performance requires the choice of appropriate tooth geometry. The magnetic field of the actuator has been analyzed using the finite element method over a current-displacement variation. The magneto static field and electromagnetic force was introduced in order to predict before construction, the inductance values according to the displacement and the currents into the coils. The results were obtained for the magnetic flux density distribution and the electromagnetic force for different positions and current.