The enhancement of the efficacy of patient orthodontic treatment based on the mathematical modelling of prospective implant designs

Opportunities to increase prosthetic treatment efficiency by means of applying osseointegrated implants of traditional and prospective types are analysed. A technique of mathematical modelling of the interaction between implants and jaw bone is exposed. The numerical model and applied program, developed on the basis of finite element method, enabling to analyse a stress strain state of the bone and to determine extreme safe loads on implants are described. It is shown, that the most loaded zone is a layer of the compact bone directly contiguous to the neck of the implant. That is in good agreement with the results of clinical research, according to which just this zone has the highest percentage of complications. Methods for further optimisation of implants and prosthetic structures for the purpose to perfect the techniques of prosthetic treatment are discussed.     

A novel equivalent circuit model for gap-connected cells

Gap junctions connect neighbouring cells, providing the intercellular communication that is essential for cell growth regulation, for example. There is some evidence that gap communication changes upon exposure to electromagnetic (EM) fields. In previous work, we performed detailed finite element method (FEM) modelling of gap junction connected cells exposed to EM fields. For cell configurations, the presence of gap junctions influences the transmembrane potential and its frequency behaviour. The relaxation frequency cannot be accurately predicted by previously developed simplified models. We present a novel equivalent circuit model (ECM) that incorporates more detailed models of the gaps, and compare results obtained with this ECM to finite element and leaky cable (LC) model results. Our ECM provides more accurate estimates of the frequency behaviour of cells than the leaky cable model. Also, our ECM results suggest limitations of the application of simple models to gap-connected cells: with higher gap resistivity, the current flow in the cell interiors becomes increasingly complex and is not well represented by simple models. In this case, techniques such as the finite element method are required to model accurately cell behaviour.     

Realistic modelling and optimisation of steel section cooling process

Abstract

The cooling process in the manufacture of long steel products generates residual stresses and bending in the section. This initial state, arising from the cooling bed, influences the final residual stresses and bending at the end of the subsequent processes. Owing to the importance of the cooling process, this paper presents realistic modelling and optimisation using computational fluid dynamics (CFD) and finite element analysis. Computational fluid dynamics rendered it possible to accurately overcome two main problems common to previous cooling models: the realistic modelling of the heat transfer coefficient (especially important when modelling outdoor cooling beds because of the implications of forced convection) and the precise view factor modelling of the different section surfaces (useful when modelling a complex section). After decoupled CFD thermo‐analysis, the temperature record of each node in the section was loaded into the finite element stress displacement model. The relevant influence of steel phase transformation was considered applying a combined methodology, involving an ABAQUS user subroutine. Accordingly, accurate residual stresses and bending were obtained. After establishing the models, several strategies were analysed for reducing the residual stresses during the cooling process. Results were successfully validated with experimental data from structural section producers.     

Matrix Analysis of Shear Lag and Shear Deformation in Thin-Walled Box Beams

This paper presents an initial value solution of the static equilibrium differential equations of thin-walled box beams, considering both shear lag and shear deformation. This solution was used to establish the related finite element stiffness matrix and equivalent nodal forces vector. In the procedure a special shear-lag-induced bimoment is introduced, so that the analysis of shear lag and shear deformation of thin-walled box beams is admitted into the program system of the matrix-displacement method. The present procedure can be used to analyze accurately the shear lag and shear deformation effects for thin-walled box beams, especially for some complex structures (such as continuous box girders and box beams with varying cross section, etc.). The numerical results obtained by the present procedure are consistent with the results of model tests and predictions of the finite shell element method or finite difference approach.     

Distribution of plastic strain and negative pressure in necked steel and copper bars

The distributions of plastic strain and negative pressure (hydrostatic tensile stress) have been computed both by an approximate method based on an extension of the Bridgman development and by a finite element analysis in inhomogeneously deforming bars after necking. The computations have been made for both initially smooth bars as well as bars having machined initial natural neck profiles, for two types of stress-strain behavior, modelling a spheroidized 1045 steel and a fully aged Cu-0.5 pct Cr alloy. The results of the finite element analysis show that the approximate method based on an extension of the Bridgman development is good only for slightly necked bars. In more acutely necked bars the Bridgman development is good only near the center of the neck. Some experimental results on strain distribution and on neck profiles are also presented.     

3D‐FE Modelling and Simulation of Multi‐way Loading Process for Multi‐ported Valves

Multi‐ported valves are widely used in the marine, sanitary, petrochemical and power industry. Multi‐way loading forming technology provides an efficient approach for integral forming of high strength multi‐ported valves, such as tee pipe coupling, high‐pressure cross valves, large‐scale complex valves, and so on. Since the multi‐way loading process is a very complicated plastic forming process due to the complexity of loading path, finite element numerical simulation is adopted to investigate the multi‐way loading process in order to predict and control the multi‐ported valve forming process. A reasonable model of the process is developed under DFEORM‐3D environment based on the coupled thermo‐mechanical finite element method. Then the reliability of the model is validated with respect to geometry development and forming defects. Numerical simulations of multi‐way loading forming for a tee valve and a cross valve have been carried out via using the developed model. Further, the forming processes of tee valve and cross valve have been compared. Moreover, the modelling method is also suitable for multi‐way loading processes of other complex components.     

Distribution of plastic strain and negative pressure in necked steel and copper bars

The distributions of plastic strain and negative pressure (hydrostatic tensile stress) have been computed both by an approximate method based on an extension of the Bridgman development and by a finite element analysis in inhomogeneously deforming bars after necking. The computations have been made for both initially smooth bars as well as bars having machined initial natural neck profiles, for two types of stress-strain behavior, modelling a spheroidized 1045 steel and a fully aged Cu-0.5 pct Cr alloy. The results of the finite element analysis show that the approximate method based on an extension of the Bridgman development is good only for slightly necked bars. In more acutely necked bars the Bridgman development is good only near the center of the neck. Some experimental results on strain distribution and on neck profiles are also presented.     

Simulation of the Process Influencing Behaviour of Forming Machines

In the design of sheet metal components and associated tools the use of forming process simulation based on finite element method is state of the art. The modelling of the forming process, however, neglects fundamental influences of the forming machine. But today, the machine behaviour influencing the process can be described with simulation tools sufficiently. The article presented here describes the current state of simulation for forming machines in regard to static and dynamic influences on the forming process. Furthermore, two examples and a proposal for enhancing the model are given.     

Finite Element Response Sensitivity Analysis of Steel-Concrete Composite Beams with Deformable Shear Connection

The behavior of steel-concrete composite beams is strongly influenced by the type of shear connection between the steel beam and the concrete slab. For accurate analytical predictions, the structural model must account for the interlayer slip between these two components. In numerous engineering applications (e.g., in the fields of structural optimization, structural reliability analysis, and finite element model updating), accurate response sensitivity calculations are needed as much as the corresponding response simulation results. This paper focuses on a procedure for response sensitivity analysis of steel-concrete composite structures using displacement-based locking-free frame elements including deformable shear connection with fiber discretization of the cross section. Realistic cyclic uniaxial constitutive laws are adopted for the steel and concrete materials as well as for the shear connection. The finite element response sensitivity analysis is performed according to the direct differentiation method. The concrete and shear connection material models as well as the static condensation procedure at the element level are extended for response sensitivity computations. Two steel-concrete composite structures for which experimental test results are available in the literature are used as realistic testbeds for response and response sensitivity analysis. These benchmark structures consist of a nonsymmetric, two-span continuous beam subjected to monotonic loading and a frame subassemblage under cyclic loading. The new analytical derivations for response sensitivity calculations and their computer implementation are validated through forward finite difference analysis based on the two benchmark examples considered. Selected sensitivity analysis results are shown for validation purposes and for quantifying the effect and relative importance of the various material parameters in regards to the nonlinear monotonic and cyclic response of the testbed structures.     

铜扁线挤压模腔内材料成形的数值模拟

在分析了铜扁线连续挤压机成形部件结构的基础上,运用I-DEAS创建节点和单元,构造出坯料及成形零部件的有限元模型,并用DEFORM软件对其进行有限元分析,建立金属三维空间塑性变形流动模型,得到各场量分布,分析具体现象与结构之间的关系。     

Continuous Dynamic Model for Tapered Beam‐Like Structures

Distributed parameter modeling may offer a viable alternative to the finite‐element approach for modeling large flexible space structures. In addition, the introduction of the transfer matrix method to the continuum modeling process provides a very useful tool to facilitate the distributed parameter model applied to more complex configurations. This paper proposes a piecewise continuous Timoshenko beam model, which was used for the dynamic analysis of a tapered beam‐like structure. Instead of the arbitrarily assumed shape functions used in a finite‐element analysis, the closed‐form solution of the Timoshenko beam equation was used. Application of the transfer matrix method was used to relate all elements as a whole. Using the corresponding boundary conditions and compatibility equations, a characteristic equation for the global tapered beam was produced and natural frequencies derived. The results from this analysis were compared to those obtained from a conventional finite‐element analysis. While comparable results are obtained, the piecewise continuous Timoshenko beam model significantly decreased the number of modal elements required.     

4100mm宽厚板轧机支承辊辊型曲线优化仿真分析

 辊间接触压力分布是影响宽厚板板形质量和轧辊使用寿命的重要因素,为了获得均匀的辊间压力分布,以4100mm宽厚板四辊轧机为对象,考虑轧件弹塑性变形和辊系弹性变形耦合作用,采用弹塑性热-力耦合非线性有限元方法,数值模拟分析了宽厚板轧制过程的辊间接触压力分布规律,并通过仿真分析,对支承辊辊型及其边部卸载曲线进行了选型和优化改进,获得了以二次曲线为辊凸度和抛物线为辊肩部卸载曲线的辊形,延长了轧辊的使用寿命,改善了宽厚板的板型质量。     

3D Finite Element Model for Asphalt Concrete Response Simulation

An extensive experimental, analytical, and numerical investigation on the response of asphalt concrete is currently in progress at Delft University of Technology. The objectives of this Asphalt Concrete Response (ACRe) project are: (a) the formulation and finite element implementation of a three‐dimensional, strain‐rate sensitive, temperature‐ and loading history‐dependent constitutive model, and (b) the development of the necessary experimental set‐ups, testing procedures, and data analysis methods for determination of the model parameters. These objectives are strongly interrelated: on the one hand, the model dictates what should be measured in a test, while on the other hand, the response observed in the tests sets the requirements for the model. As a result, model development/verification and experimental testing have been progressing in parallel throughout the project. In this contribution both the finite element and the experimental aspects of the project will be presented. The constitutive model has been implemented in the finite element system INSAP. The system has been used to simulate the initiation and propagation of damage in two flexible pavement structures due to repeated loading. The simulations illustrate the influence of geometry and material characteristics on the development of damage.     

Finite element analysis of formability of a few kinds of special steel sheets

Deep drawing processes of various special steel sheets are simulated by the rigid-plastic finite element method. To predict the forming limit a criterion for ductile fracture is applied. From the histories of stress and strain in each element calculated by the finite element simulation, the fracture initiation site and the critical stroke are predicted by means of the ductile fracture criterion. The predictions so obtained are compared with experimental observations. The results show that the finite element analysis combined with the ductile fracture criterion is useful to predict the forming limit in a wide range of sheet steels.     

Numerical Cracking and Debonding Analysis of RC Beams Reinforced with FRP Sheet

Bonding a fiber reinforced polymer (FRP) sheet to the tension-side surface of reinforced concrete (RC) structures is often performed to upgrade the flexural capacity and stiffness. Except for upper concrete crushing, FRP sheet reinforcing RC structure may fail in sheet rupture, sheet peeloff failure due to opening of a critical diagonal crack, or concrete cover delamination failure from the sheet end. Accompanying the occurrence of these failure modes, reinforcing effects of the FRP sheet will be lost and load-carrying capacity of the RC structures will be decreased suddenly. This study is devoted to developing a numerical analysis method by using a three-dimensional elasto-plastic finite element method to simulate the load-carrying capacity of RC beams failed in the FRP sheet peeloff mode. Here, the discrete crack approach was employed to consider geometrical discontinuities such as opening of cracks, slipping of rebar, and debonding of the FRP sheet. Comparisons between analytical and experimental results confirm that the proposed numerical analysis method is appropriate for estimating the load-carrying capacity and failure behavior of RC beams flexurally reinforced with a FRP sheet.     

变形金属再结晶过程计算机模拟

通过有限元方法和计算机模拟技术可有效模拟金属热加工和变形金属退火时的再结晶过程，计算金属组织演化和预报材料性能。介绍了目前再结晶计算机模拟的方法和模型-Monte Carlo(MC)法，Cellular Automation(CA)法，纯几何模型模拟，分组模型模拟和杂化模型模拟，重点分析了MC模拟法在均质和非均质形核，二相粒子对再结晶的影响，动态再结晶等方面的研究进展。指出用MC法模拟存在的问题，应用有限元法计算基本变形储存能和织构；建立含速率的再结晶形核和生长模型及耦合温度场模型的研究途径。     

Damage Detection in Composite Materials Using Identification Techniques

The present paper describes an approach for damage detection in composite structures that has its basis in methods of system identification. Response of a damaged structure differs from predictions obtained from a mathematical model of the original structure, where such a model is typically a finite‐element representation of the structure. In the present work dealing with composite materials, two distinct analytical models, one using two‐dimensional (2D) elements in conjunction with the classical lamination theory and another using three‐dimensional (3D) elements were considered. The output error approach of system identification was employed to determine changes in the analytical model necessary to minimize differences between the measured and predicted response. The proposed method is an extension of the stiffness‐reduction approach for damage detection to realistic structures. Numerical simulation of measurements of static deflections, strains, and vibration modes were used in the identification procedure. The methodology was implemented for representative composite structures. Principal shortcomings in the proposed approach and possible methods to circumvent these problems are discussed in the paper.     

冷轧板带残余应力求解分析

冷轧板带残余应力是影响板带质量的重要因素。为了提高板形质量,根据板带轧制前后体积不变原理,推导了残余应力的数学模型,采用有限元法对板带失稳时的临界载荷进行了求解,运用解析法和有限元法相互耦合的计算方法建立了板带失稳后的残余应力修正模型。结果表明:初始残余应力的作用使板带产生了失稳,因此需要对残余应力进行修正计算,修正后的残余应力与现场实测结果有较好的一致性。     

Delamination Characteristics around Hole in Laminates with Softening Strip

Graphite/epoxy laminates with and without a softening strip around a hole were investigated. The softening strip is a portion of the graphite critical ply, which is replaced by a glass/epoxy composite. Analysis was conducted with finite element methods: The in‐plane stress distribution was found using a planform two‐dimensional model and interlaminar stress distributions around a hole were obtained from a through‐thickness quasi‐three‐dimensional model. The variation of strain‐energy release rate for a delamination occurring at the critical interface was investigated. The finite element results indicate that the inplane and interlaminar stress distributions, as well as the strain‐energy release rates, are significantly reduced for laminates with a softening strip.