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.

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.

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.

Importance of Three-Dimensional Piezoelectric Coupling Modeling in Quantitative Analysis of Piezoelectric Actuators

This paper demonstrates the importance of three-dimensional(3-D)piezoelectric coupling in the electromechanical behavior of piezoelectric devices using three-dimensional finite element analyses based on weak and strong coupling models for a thin cantilevered piezoelectric bimorph actuator.It is found that there is a significant difference between the strong and weak coupling solutions given by coupling direct and inverse piezoelectric effects(i.e.,piezoelectric coupling effect).In addition,there is significant longitudinal bending caused by the constraint of the inverse piezoelectric effect in the width direction at the fixed end(i.e.,3-D effect).Hence,modeling of these effects or 3-D piezoelectric coupling modeling is an electromechanical basis for the piezoelectric devices,which contributes to the accurate prediction of their behavior.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BEDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOW (Ⅱ)

The finite_element_displacement_perturbation method (FEDPM)for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes (Ⅰ) was employed to calculate the stress distributions and the stiffness of the bellows. Firstly, by applying the first_order perturbation solution (the linear solution)of the FEDPM to the bellows, the obtained results were compared with those of the general solution and the initial parameter integration solution proposed by the present authors earlier, as well as of the experiments and the FEA by others.It is shown that the FEDPM is with good precision and reliability, and as it was pointed out in (Ⅰ) the abrupt changes of the meridian curvature of bellows would not affect the use of the usual straight element. Then the nonlinear behaviors of the bellows were discussed. As expected, the nonlinear effects mainly come from the bellows ring plate,and the wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishing of the ring plate, like the C_shaped bellows, the nonlinear effects almost vanish. In addition, when the pure bending moments act on the bellows, each convolution has the same stress distributions calculated by the linear solution and other linear theories, but by the present nonlinear solution they vary with respect to the convolutions of the bellows. Yet for most bellows, the linear solutions are valid in practice.

Finite Element Modelling of Steel Beams with Web Openings

Height limitations are not uncommon in multi-storey buildings due to economic requirements and esthetical considerations. Substantial spaces are normally required to enable the passage of large pipes and ducts beneath steel beams leading to uneconomic floor heights. The most adopted solution for this issue is the use of steel beam web openings to provide the required space for services. These openings could lead to a significant decrease of the beam load carrying capacity depending on the adopted openings shape, size and location. These aspects motivated the present study based on FE simulations calibrated against numerical and test results. The results accuracy enabled a comprehensive parametric analysis of beams with web openings to be made focused on the profile size, web opening location, among others. The study also investigated the efficiency of longitudinal stiffeners welded at the opening region and benefits of using an adequate edge concordance radius in beams with rectangular and square openings. The obtained results showed the need of using welded longitudinal stiffeners in order to increase the beams ultimate load carrying capacity. This adoption can double or even triple the ultimate load of beams with rectangular and square opening heights equal to 0.75 H, respectively.

Virtual Element Formulation for Finite Strain Elastodynamics Dedicated to Professor Karl Stark Pister for his 95th birthday

The virtual element method(VEM)can be seen as an extension of the classical finite element method(FEM)based on Galerkin projection.It allows meshes with highly irregular shaped elements,including concave shapes.So far the virtual element method has been applied to various engineering problems such as elasto-plasticity,multiphysics,damage and fracture mechanics.This work focuses on the extension of the virtual element method to efficient modeling of nonlinear elasto-dynamics undergoing large deformations.Within this framework,we employ low-order ansatz functions in two and three dimensions for elements that can have arbitrary polygonal shape.The formulations considered in this contribution are based on minimization of potential function for both the static and the dynamic behavior.Generally the construction of a virtual element is based on a projection part and a stabilization part.While the stiffness matrix needs a suitable stabilization,the mass matrix can be calculated using only the projection part.For the implicit time integration scheme,Newmark-Method is used.To show the performance of the method,various two-and three-dimensional numerical examples in are presented.

A New Fourth Order Difference Approximation for the Solution of Three-dimensional Non-linear Biharmonic Equations Using Coupled Approach

This paper deals with a new higher order compact difference scheme, which is, O(h4) using coupled approach on the 19-point 3D stencil for the solution of three dimensional nonlinear biharmonic equations. At each internal grid point, the solution u(x,y,z) and its Laplacian Δ4u are obtained. The resulting stencil algo-rithm is presented and hence this new algorithm can be easily incorporated to solve many problems. The present discretization allows us to use the Dirichlet boundary conditions only and there is no need to discretize the derivative boundary conditions near the boundary. We also show that special treatment is required to handle the boundary conditions. Convergence analysis for a model problem is briefly discussed. The method is tested on three problems and compares very favourably with the corresponding second order approximation which we also discuss using coupled approach.

Stress Distribution in Maxillary Central Incisors without Ferrules: A Finite Element Analysis of Post and Core Systems

Purpose: The purpose of this study was to identify optimal post and core materials for central incisors without ferrules using three-dimensional finite element analysis and three-point bending tests. Methods: Stress analyses were performed with six models: cast metal post and core (MP), composite resin core alone, straight fiber-reinforced post-composite resin core (FSR), tapered fiber-reinforced post-composite resin core, straight titanium post-composite resin core (TSR), and tapered titanium post-composite resin core (TTR). A 100-N load was applied to the lingual surface at a 45° angle to the long axis of the tooth. Maximum von Mises stress distributions were calculated with finite element analysis software. Five samples each of composite resin, straight fiber-reinforced post, straight titanium post, straight fiber-reinforced post and composite resin, and straight titanium post and composite resin were subjected to three-point bending tests, followed by analysis of variance and Tukey’s multiple comparison test. Results: Stress distribution was optimal on TTR. Maximum von Mises stress on the cervical side of the post was greatest in TSR (693 MPa) and TTR (556 MPa). Maximum stress on the apical side of the post was greatest in MP (110 MPa). Maximum stress in surrounding dentin was lowest in MP (203 MPa) and TTR (250 MPa). Gap distance was smallest in MP (0.09 mm) and largest in FSR (0.26 mm). Mean maximum three-point bending force was lowest in composite resin (26.9 N/mm) and highest in titanium post and composite resin (97.1 N/mm). Titanium post bending strength was consistently greater than that of the fiber-reinforced post (p < 0.01). Conclusion: These results revealed optimal stress distribution and high bending strength with the tapered titanium post and resin combination, suggesting that this combination can most effectively prevent root or post fracture in an anterior tooth without a ferrule.

Three-dimensional FDEM numerical simulation of failure processes observed in Opalinus Clay laboratory samples

This study presents the first step of a research project that aims at using a three-dimensional(3D) hybrid finite-discrete element method(FDEM) to investigate the development of an excavation damaged zone(EDZ) around tunnels in a clay shale formation known as Opalinus Clay. The 3D FDEM was first calibrated against standard laboratory experiments, including Brazilian disc test and uniaxial compression test. The effect of increasing confining pressure on the mechanical response and fracture propagation of the rock was quantified under triaxial compression tests. Polyaxial(or true triaxial) simulations highlighted the effect of the intermediate principal stress(s2) on fracture directions in the model: as the intermediate principal stress increased, fractures tended to align in the direction parallel to the plane defined by the major and intermediate principal stresses. The peak strength was also shown to vary with changing σ2.

THREE-DIMENSIONAL ELLIPTIC CRACK UNDER IMPACT LOADING

The dynamic stress intensity factor of a three-dimensional elliptic crack under impact loadingis determined with the finite element method.The computation results can take into account the influence oftime and the ratio of the wave speeds on the stress intensity factor.The present method is suitable not onlyfor three-dimensional dynamic crack,but also for three-dimensional dynamic contact.

Simulation-Based Construction of Three-Dimensional Process Model for Punching Cartridge Cases

A method of constructing three-dimensional process model for the punching cartridge cases is presented based on DEFORM simulation analysis. Using DEFORM software,the finite element simulation models for the punching and forming process of cartridge cases are established,and the corresponding simulation result model of each intermediate procedure is obtained by continuously performing the forming process simulation. The simulation model cannot annotate size and process information due to poor interface between DEFORM software and CAD software. Thus,a 3D annotation module is developed with secondary development technology of UG NX software. Consequently,the final process model with dimension and process information is obtained. Then,with the current 3D process management system,the 3D punching and forming process design of cartridge cases can be completed further. An example is also provided to illustrate that the relative error between the simulation process model and the physical model is less than 2%,which proves the validity and reliability of the proposed method in this study.

Microstructure-based three-dimensional characterization of chip formation and surface generation in the machining of particulate-reinforced metal matrix composites

Particulate-reinforced metal matrix composites(PRMMCs)are difficult to machine due to the inclusion of hard,brittle reinforcing particles.Existing experimental investigations rarely reveal the complex material removal mechanisms(MRMs)involved in the machining of PRMMCs.This paper develops a three-dimensional(3D)microstructure-based model for investigating the MRM and surface integrity of machined PRMMCs.To accurately mimic the actual microstructure of a PRMMC,polyhedrons were randomly distributed inside the matrix to represent irregular SiC particles.Particle fracture and matrix deformation and failure were taken into account.For the model’s capability comparison,a two-dimensional(2D)analysis was also conducted.Relevant cutting experiments showed that the established 3D model accurately predicted the material removal,chip morphology,machined surface finish,and cutting forces.It was found that the matrix-particle-tool interactions led to particle fractures,mainly in the primary shear and secondary deformation zones along the cutting path and beneath the machined surface.Particle fracture and dilodegment greatly influences the quality of a machined surface.It was also found that although a 2D model can reflect certain material removal features,its ability to predict microstructural variation is limited.