A Posteriori Error Estimate of Two Grid Mixed Finite Element Methods for Semilinear Elliptic Equations

In this paper, we present the a posteriori error estimate of two-grid mixed finite element methods by averaging techniques for semilinear elliptic equations. We first propose the two-grid algorithms to linearize the mixed method equations. Then, the averaging technique is used to construct the a posteriori error estimates of the two-grid mixed finite element method and theoretical analysis are given for the error estimators. Finally, we give some numerical examples to verify the reliability and efficiency of the a posteriori error estimator.

Finite element solution based on fast numerical technique for large-scale electromagnetic computation

A numerical technique of the target-region locating （TRL） solver in conjunction with the wave-front method is presented for the application of the finite element method （FEM） for 3-D electromagnetic computation. First, the principle of TRL technique is described. Then, the availability of TRL solver for nonlinear application is particularly discussed demonstrating that this solver can be easily used while still remaining great efficiency. The implementation on how to apply this technique in FEM based on magnetic vector potential （MVP） is also introduced. Finally, a numerical example of 3-D magnetostatic modeling using the TRL solver and FEMLAB is given. It shows that a huge computer resource can be saved by employing the new solver.

Arc-length technique for nonlinear finite element analysis

Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.

NONLINEAR QUASI-CONFORMING FINITE ELEMENT METHOD

The nonlinear quasi-conforming FEM is presented based on the basic concept of the quasi- -conforming finite element. First, the incremental principle of stationary potential energy is discussed, Then, the formulation process of the nonlinear quasi-conforming FEM is given. Lastly, two computational examples of shells are given.

Innovative Techniques Unveiled in Advanced Sheet Pile Curtain Design

This thorough review explores the complexities of geotechnical engineering, emphasizing soil-structure interaction (SSI). The investigation centers on sheet pile design, examining two primary methodologies: Limit Equilibrium Methods (LEM) and Soil-Structure Interaction Methods (SSIM). While LEM methods, grounded in classical principles, provide valuable insights for preliminary design considerations, they may encounter limitations in addressing real-world complexities. In contrast, SSIM methods, including the SSI-SR approach, introduce precision and depth to the field. By employing numerical techniques such as Finite Element (FE) and Finite Difference (FD) analyses, these methods enable engineers to navigate the dynamics of soil-structure interaction. The exploration extends to SSI-FE, highlighting its essential role in civil engineering. By integrating Finite Element analysis with considerations for soil-structure interaction, the SSI-FE method offers a holistic understanding of how structures dynamically interact with their geotechnical environment. Throughout this exploration, the study dissects critical components governing SSIM methods, providing engineers with tools to navigate the intricate landscape of geotechnical design. The study acknowledges the significance of the Mohr-Coulomb constitutive model while recognizing its limitations, and guiding practitioners toward informed decision-making in geotechnical analyses. As the article concludes, it underscores the importance of continuous learning and innovation for the future of geotechnical engineering. With advancing technology and an evolving understanding of soil-structure interaction, the study remains committed to ensuring the safety, stability, and efficiency of geotechnical structures through cutting-edge design and analysis techniques.

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.

A TRIANGULAR QUASI-CONFORMING FINITE ELEMENT FOR TRANSIENT DYNAMIC ANALYSIS

A type of 3 node triangular element is constructed by the Quasi-conforming method, which may be used to solve the equation of a type of inverse problem of wave propagation after Laplace transformation △u-A^2u=0. The strains in the element are approximated by an expohential function and the string-net function between neigh- bouring elements is apporoximated by one dimensional general solution of the equation. Furthermore the strain field satisfies the equation, and therefore in the derivation of the element formulation, no shape function is needed. In this sense, it is a kind of hybrid element. Compared with the ordinary linear triangular element, the new one features higher precision with coarse meshes. Some numerical tests are presented.

DIRECT SOLUTION BY 2-D AND 3-D FINITE ELEMENT METHOD ON FORWARD PROBLEM OF LOW FREQUENCY CURRENT FIELDS IN INHOMOGENEOUS MEDIA

The paper adopts finite element method to analyze the forward problem of low-frequency current fields in inhomogeneous media. Firstly, the direct solution of 2-D and 3-D scalar potential is given. Secondly, the technique of covering finite elements for problems with movement has been presented; namely, when the place of testing point moved, the meshing data will be produced automatically to avoid re-meshing and distortion of the mesh. Thirdly the free and prescribed potential method is used to make the finite element coefficient matrices. Then this paper provides the result of a validity test obtained by simulating the laterolog-3 logging, compared with the numerical model-matching method. Finally, the MLL response is calculated.

Elasto-Plastic Analysis of Tubular Joints of Offshore Platforms by Finite Element Method

The plastic node method is reformulated by the variational principle and is applied to elasto-plastic finite element analysis of tubular joints, eventually including the effect of internal and external gussets, stiffener rings, etc., if necessary. Four different joints are studied here in detail for the elasto-plastic behavior, the strain at the hot spot, the strain concentration factor around the intersection line, and the propagation of the plastic region with loading up to collapse in order to determine the ultimate strength, safety factor, and development of the plastic field. The present results are in good agreement with the experimental results.

FINITE ELEMENT DISPLACEMENT PERTURBATION METHOD FOR GEOMETRIC NONLINEAR BEHAVIORS OF SHELLS OF REVOLUTION OVERALL BENDING IN A MERIDIONAL PLANE AND APPLICATION TO BELLOWS (Ⅰ)

In order to analyze bellows effectively and practically, the finite_element_displacement_perturbation method (FEDPM) is proposed for the geometric nonlinear behaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba_ tion that the nodal displacement vector and the nodal force vector of each finite element are expanded by taking root_mean_square value of circumferential strains of the shells as a perturbation parameter. The load steps and the iteration times are not as arbitrary and unpredictable as in usual nonlinear analysis. Instead, there are certain relations between the load steps and the displacement increments, and no need of iteration for each load step. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander's nonlinear geometric equations of moderate small rotation are used, and the shell made of more than one material ply is also considered.

ADAPTIVE FINITE ELEMENT METHOD FOR ANALYSIS OF POLLUTANT DISPERSION IN SHALLOW WATER

A finite element method for analysis of pollutant dispersion in shallow water is presented. The analysis is divided into two parts ： （ 1 ） computation of the velocity flow field and water surface elevation, and （2） computation of the pollutant concentration field from the dispersion model. The method was combined with an adaptive meshing technique to increase the solution accuracy, as well as to reduce the computational time and computer memory. The finite element formulation and the computer programs were validated by several examples that have known solutions. In addition, the capability of the combined method was demonstrated by analyzing pollutant dispersion in Chao Phraya River near the gulf of Thailand.

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.

NONLINEAR FINITE ELEMENT ANALYSIS OF CONCRETE OFFSHORE PLATFORMS

Taking account of the progressive cracking and crushing of the concrete, the full-range nonlinear analysis has been made for a R.C. Structure, from loading to cracking until crushing for some elements. The diagrams showing the distribution of the stresses and the horizontal displacements and the pictures showing the cracking and crushing of the concrete are given. This paper also gives the comparison between the results of nonlinear analysis and linear analysis.

CRITERIA FOR FINITE ELEMENT ALGORITHM OF GENERALIZED HEAT CONDUCTION EQUATION

To eliminate oscillation and overbounding of finite element solutions of classical heat conduction equation, the author and Xiao have put forward two new concepts of monotonies and have derived and proved several criteria. This idea is borrowed here to deal with generalized conduction equation and finite element criteria for eliminating oscillation and overbounding are also presented. Some new and useful conclusions are drawn.

ERROR ESTIMATION AND DOUBLE MESH FOR RIGID-VISCOUS-PLASTIC FINITE ELEMENT ANALYSIS OF UNSTEADY EXTRUSION PROCESSES

Error estimation, double mesh as well as fore-and-aft process program are applied in the rigid-viscous-plastic finite element simulation of tube unsteady extrusions. By the error estimation, mesh can be reasonably divided. The double mesh includes analytical mesh and material mesh. The analytical mesh is used in the finite element analysis. The material mesh is used in the recording of distortion history. The fore-and-aft process program is used in the input-output of data and computer drawing. In the results, analytical meshes, distorted material meshes and strain contours are mapped by computer.

Object-Oriented Finite Element Analysis of Metal Working Processes

Recently an object-oriented approach has been applied in the fields of finite element analysis with a view to treating the various complexities within these. It has been demonstrated that finite element software designed using an object-oriented approach can be significantly more robust than traditional codes. This paper describes a special kind of implementation of object-oriented programming which is rather hybrid in nature, in the development of a finite element code for engineering analysis of metal working problems using C++, and discusses the advantages of this approach.

THE DISPLACEMENT FUNCTION OF QUASI-CONFORMING ELEMENT AND ITS NODE ERROR

Based on the strain formulation of the quasi-conforming finite element, displacement functions are constructed which have definite physical meaning, and a conclusion can be obtained that the coefficients of the constant and the linear strain are uniquely determined, and the quasi-conforming finite element method is convergent to constant strain. There are different methods for constructing the rigid displacement items, and different methods correspond to different order node errors, and this is different from ordinary displacement method finite element.

基于有限元技术的疲劳裂纹扩展方法研究进展

疲劳裂纹是引起工程结构断裂失效的重要因素之一.目前疲劳裂纹扩展的有限元仿真商业软件有ANSYS、ABAQUS、FRANC3D、ZENCRACK等,这些软件为疲劳裂纹扩展过程的研究提供了有力支撑.本文对目前疲劳裂纹扩展的有限元仿真方法进行了综述.阐明了疲劳裂纹的定义以及研究疲劳裂纹扩展行为的必要性;介绍了三种用于模拟疲劳裂纹扩展的有限元方法:扩展有限元法(XFEM)、内聚力模型(CZM)和虚拟裂纹闭合技术(VCCT);分别总结了三种方法的基本理论和核心思想,对三种方法的应用与发展进行了分类归纳;最后对三种有限元方法进行分析,指出每种方法各自的优势及目前存在的局限性,并对疲劳裂纹扩展有限元仿真技术的未来改进方向给出了建议.

深中通道中山大桥主桥超宽大节段钢箱梁吊装匹配技术

深中通道中山大桥主桥为主跨580 m的双塔双索面钢箱梁斜拉桥,主梁采用流线型扁平钢箱梁,梁宽46 m(含风嘴),主梁共划分69个节段,标准段长18 m、最大吊重约429 t,采用桥面吊机双悬臂吊装。由于钢箱梁节段自重大、宽度较大、横桥向竖向刚度较小等,在桥面吊机悬臂吊装过程中,会出现钢箱梁匹配面高差过大(最大约63 mm)的问题。为解决该问题,实现梁段精确匹配安装,提出3种钢箱梁吊装匹配方案:“门架+拉索”方案、“牛腿反力架”方案、“一字梁锁定+C形焊缝+部分张拉斜拉索”方案。经有限元仿真分析综合比选,最终选择“一字梁锁定+C形焊缝+部分张拉斜拉索”方案。该方案以箱梁竖腹板为定位点,提前焊接一字梁,采用法兰连接后锁定待拼梁段,部分焊接拼接面内箱梁形成C形焊缝;通过提前挂索并张拉部分斜拉索,减小匹配面已拼梁段横桥向竖向变形,达到箱梁匹配要求。施工中采取了匹配高差调节、局部应力控制、拼接缝宽控制等关键技术,最终将该桥钢箱梁匹配面高差减小至9.8 mm以内,钢箱梁局部应力可控,斜拉索初张过程中钢箱梁应力增量小于10 MPa,且各箱梁节段拼接缝宽可控制在1 cm以内。

大跨径上承空腹式梁拱组合刚构桥设计关键技术

为克服主跨大于200 m的山区桥梁在桥型选择中采用连续刚构桥易导致的弊端,以及选用上承式钢筋混凝土拱桥由于适用条件存在的局限性,提出了将常规预应力混凝土连续刚构桥和上承式钢筋混凝土拱桥在结构体系上进行组合,形成上承式梁拱组合刚构新桥型。大跨径上承空腹式梁拱组合刚构桥的结构体系和力学特征进行了分析,采用有限元分析方法对该桥型的主要结构参数、合理成桥状态、拱梁汇合段构造、梁拱倒三角区施工和临时扣索的合理拆除时机等设计关键技术开展研究,结果表明:上承空腹式梁拱组合刚构桥利用下弦拱辅助主梁受力并形成自平衡受力体系,显著减小了中跨和边跨主梁长度,使结构力学性能得以优化,具有结构竖向刚度大,对长期挠度变形控制效果好的优点;当结构关键控制点的强度、刚度和线形计算指标符合目标范围时,可达到合理成桥状态;拱梁汇合段的下弦拱顶板与上弦梁底板的交汇构造采用A字形,构造简单,传力效果好,施工质量容易控制;该桥型适宜采用平衡悬浇节段施工,梁拱倒三角区段上弦梁和下弦拱均需采用临时斜拉扣挂辅助结构受力,下弦拱临时扣索宜在拱梁汇合段形成后与中跨常规梁段跨中合龙之前分批拆除,上弦梁临时扣索在全桥合龙后拆除。