应用Daubechies条件小波有限元法求解弹性地基梁

为提高弹性地基梁的计算精度,将Daubechies条件小波有限元法应用于弹性地基梁的计算中。以受集中力作用的弹性地基梁为例,基于传统的Daubechies小波Galerkin法,结合广义变分原理进行改进,将边界条件直接引入求解方程,可以避免小波系数与单元内部节点位移之间的转换,提高计算精度。并分别针对中间单元、左端单元及右端单元构造求解矩阵,进一步组装总体求解矩阵,形成Daubechies条件小波有限元法。最后,通过典型算例,验证Daubechies条件小波有限元法计算弹性地基梁的精度。     

基于UL列式的两节点悬链线索元非线性有限元分析

从UL列式的虚功增量方程和索的悬链线方程出发,建立起了一套完整的对索进行精确分析的非线性有限元法。在该方法中,索的自重影响未作任何的近似予以考虑;导出的索单元切线刚度阵是显示表达式;索单元的节点力可以精确计算。本文方法可以方便地应用于大跨度悬索桥、斜拉桥以及张拉结构等的非线性有限元分析计算。     

国际期刊导读

具有不确定材料性能的壳结构非线性有限元分析;冷弯钢构件残余应力和应变的预测;薄壁开口构件的屈曲分析——有限元公式;薄壁梁的非线性有限元分析;通宽剥离时复合板材的后屈曲性能     

Nachweis der erforderlichen Ankerlänge mit der Finite‐Elemente‐Methode

Verification of a sufficient anchor length on basis of the Finite Element Method. At first the present article analyses the structural mechanism of the anchorage for excavation walls and the subsequent requirement for a minimal anchor length. The accompanying verification of stability has to be carried out according to DIN 1054:2005‐01 by an analysis of the ‘lower failure plane’ on basis of classical earth statics. The Finite Element Method (FEM) normally is not used to verify the stability and the German codes of practise do not recommend this approach. However, it may be possible to proceed in that way. This article shows in the light of an example the mechanical meaning of the verification of the sufficiency of the anchor length. Furthermore it compares the classical approach with a lower failure plane after Kranz with verification on basis of the Finite Element Method. The article will be closed by a variation of the bending stiffness and the bending strength of the excavation wall. It can be shown, that the mechanical behaviour of the wall has a significant effort on the calculated safety factor of an anchored excavation wall.     

考虑衬砌接头的土-盾构隧道有限元模型初探

本文作者详细推导了由梁单元和衬砌接头单元组成的混合单元的刚度矩阵,形成了考虑衬砌拉头的土－盾构隧道有限元模型。利用有限元法计算了考虑衬砌接头和不考虑衬砌接头两种情况下衬砌的内力和衬砌的变形。由计算可知,衬砌接头对衬砌的轴力和位移影响相对较小,但对衬砌的弯矩影响较大,因此在盾构隧道的抗震设计中必须考虑衬砌接头的影响,否则将使设计趋于保守。     

Zur Berechnung von Holzstabtragwerken mit mehrlagigen nachgiebigen Verbundquerschnitten

Calculation of timber structures made of multilayered beam elements with flexible composite sections. The board rib construction technology offers owners, engineers, and architects the opportunity to realise efficient, economic and aesthetical shell‐like buildings. Board rib shells are relatively under‐utilized in spite of their advantages. The reason for this is the lack of a suitable computation method for these complex structural systems made of flexible composite cross‐sections. The solution methods used so far are restricted to just special cases or they represent only approximations. With an efficient, user‐friendly and reliable computation method, such structures will be realised more frequently than at present. Applicability and limitations of the derived method are given in order to avoid inexact solutions. This work presents a finite beam element with a quadratic formulation for the longitudinal displacements for almost any multilayered flexible composite cross‐sections with spatial structural behaviour at geometrical nonlinear theory of 2^nd order. The composite elements are verified with the help of analytical solutions depending on the ratio of the element length and of the joint stiffness. The element is also capable, for example, to calculate wood‐concrete‐composite floors including the effects of creep and shrinkage in sub‐sections.     

Out-of-plane behaviour of partially composite or sandwich beams by exact and Finite Element Methods

The out-of-plane vibrations of composite beams with interlayer slip or three-layer sandwich beams are theoretically and numerically investigated in this paper for general boundary conditions. The governing dynamics equations are derived by applying the Hamilton's principle. A Finite Element Resolution is presented for general boundary conditions, and compared to the exact solution based on the resolution of a tenth-order differential equation. The Finite Element Method may exhibit slip locking phenomenon for very stiff connection, a phenomenon widely investigated in the past for the in-plane behaviour of partially composite beams or sandwich beams. This slip locking, analogous to the shear locking for Timoshenko beams, can be faced with some relevant interpolation shape functions of the same order for each kinematics variables, namely the deflections and the torsion angle. The numerical results are presented for layered wood beams and laminated glass beams, with particular emphasis on the rate of convergence of the natural frequencies with respect to the number of Finite Elements. It is theoretically and numerically shown that the elastic spectra of the symmetrical composite beam are composed of two independent spectrums. One spectrum is independent of the connection parameter and can be studied using the solution of the non-composite action, whereas the second spectrum can be obtained from the resolution of a third-order polynomial equation using the Cardano's method. We show the phenomenon of cut-on frequency for this out-of-plane problem, a phenomenon already noticed for the in-plane Timoshenko beam vibrations. The exact method associated to a 10 degrees-of-freedom shape function can be formally associated with the dynamics stiffness method. The numerical and the exact approaches lead to the same dimensionless spectra, up to four digits.     

平端板拼接节点初始刚度的有限元分析

过去30多年来,对现有钢结构设计方法的修正,使其能在结构设计中考虑到连接的半刚性性能。连接的初始转动强度对于结构整体的弹性分析很重要。采用有限元方法得到螺栓连接的平端板梁连接(BFEB)的初始转动刚度(IRS)参数结果。建模中考虑了材料特性、几何非连续性和大位移,同时进行试验分析,并与数值分析进行对比。这些模型显示:对于连接性能的研究,有限元建模与试验研究具有一致性。由于影响参数众多,基于EC3的分量法,提出BFEB连接性能的分析模型。此外,对弯矩-转动曲线的初始斜率进行了数值计算和数据的对比。同时对能准确评估BFEB的初始转动刚度的方法进行了讨论。     

Einsatz von hochfesten Stählen und Betonen bei Hohlprofil‐Verbundstützen

Composite columns made of high‐strength steel and high‐strength concrete. The paper deals with the use of composite columns made of high‐strength steel and high‐strength concrete. Based on the design methods in Eurocode 4‐1‐1 and DIN 18800‐5 a simplified design method is presented for composite columns with high strength concrete and high strength steel in combination with massive inner steel core‐profiles. The ultimate strength of these special type of columns is significantly influenced by the residual stresses in the core profiles resulting from the cooling process during fabrication. Based on Finite Element studies new models are presented for the determination of the distribution of residual stress taking into account the steel grade, the dimensions of the core profiles and the cooling conditions during fabrication.     

题解有限元法和无网格伽辽金法

采用无网格伽辽金法和有限元法对一维问题进行了数值模拟,对结构体离散、刚度矩阵、等效节点荷载、边界条件、计算精度和效率等进行了比较,数值模拟结果表明,同样的节点划分,无网格伽辽金法得到的数值解精度较高、与解析解吻合较好,但是计算量大于有限元法。     

A force-based model for composite steel-concrete beams with partial interaction

This paper presents a new force-based beam-column element for the nonlinear analysis of composite steel-concrete beams with partial interaction. The element is made up of three components: (a) a fiber beam-column element that models the behavior of the steel girder, (b) a fiber beam-column element that models the behavior of the concrete deck, and (c) a bond element that models the transfer of forces between the steel and concrete elements through shear connectors. The model neglects uplift and frictional effects. The fiber beam-columns are force-based elements that depend on force interpolation functions. A linear bending moment and a constant axial force serve as the interpolation functions. An important factor that favors the use of force-based elements in modeling composite structures is their ability to treat any type of distributed element loads. Distributed element loads are applied internally in a continuous manner by force superposition at the control sections. The state determination of these elements is based on an iterative solution that determines the element resisting forces and stiffness matrix. The bond element is a spring-type element that assumes a linear bond stress variation along the length. The nonlinear behavior of the composite element derives entirely from the constitutive laws of the steel, the concrete and the shear connectors. The paper concludes with a correlation study to investigate the validity of the model. Good agreement between analysis and experimental results was observed.     

Effiziente 3‐D numerische Simulation im Tunnel und Kavernenbau

Efficient 3‐D numerical Simulation in Underground Construction Due to several reasons 3‐D analyses of tunnels or caverns are rarely performed in practical applications. The reasons are the high effort of mesh generation and the long computing times. The simulation of a powerhouse cavern reported here it is definitely a 3‐D problem that can not be reduced to a two‐dimensional model. The aim of the numerical simulation reported here was to determine the reasons for the occurrence of cracks in the concrete wall of the powerhouse cavern and to determine the likelihood that these cracks will propagate further. It will be shown that by using a coupled Finite Element/Boundary Element approach the effort in simulation can be reduced considerably.     

Thermisch getrennte Stirnplattenstöße

Beam‐to‐beam splices with thermal separation. In structural engineering and in steel housebuilding there is an increasing architectural interest in positioning walls inside the supporting columns. In order to prevent the formation of thermal bridges between beams and columns, the connection can be separated by a thermal intermediate layer made of fibre composite. Based on the secured state of knowledge a model for the evaluation of resistance and rotational stiffness of bolted beam‐to‐beam splices with extended end‐plates and thermal separation has been developed. This model allows the user‐oriented analysis of the behaviour of such joints.     

Finite‐Elemente‐Berechnungen zum Trag‐ und Verformungsverhalten von Kopfbolzendübeln

Finite Element Calculation of load bearing and deformation behavior of headed studs. In the scope of numerical simulations the composite joint between concrete slab and steel girder is represented by springs or interface elements considering bi‐linear as well as tri‐linear shear‐slip behavior. This method is established to determine the global load bearing behavior for any degree of shear connection. In order to illustrate the concentrated load introduction a three‐dimensional modeling of the shear connector is required. This paper describes a three‐dimensional nonlinear finite element model, which offers the possibility to investigate the local load bearing and deformation behavior of headed studs under shear load. It has been calibrated on shear tests performed by the Institute for Structural Concrete, of University of Technology, Aachen. On the basis of parametrical studies the influence of the concrete strength, the length of the stud as well as the formation of the welded collar have been determined. Furthermore, the limits of the simulation of shear tests are detected.     

集中荷载作用下钢-混凝土组合梁界面滑移及变形

报道了8榀集中荷载作用下钢-混凝土组合简支梁的滑移规律和变形的试验结果。利用Goodman弹性夹层假设,推导了钢-混凝土组合简支梁的界面滑移和挠度变形的理论计算公式。该理论公式既能描述组合梁的界面滑移规律,又可以计算界面滑移对组合梁变形挠度的影响。利用通用有限元软件对钢-混凝土组合梁的界面滑移与变形进行了非线性有限元分析,并将多项计算结果进行了比较。通过大量理论计算,探讨工程设计中合适的剪力连接度。本文所得的理论计算公式,将方便工程设计人员对钢-混凝土组合结构滑移和变形挠度进行计算,并为其极限承载力的有限元计算提供了理论基础。     

Analysis of second-order shear-deformable beams with semi-rigid connections

In this paper a new beam finite element is proposed for the solution of framed structures with semi-rigid connections. The element uses the second order Timoshenko's beam model. Power series expansion of kinematic relations is employed to improve solution stability. Effect of flexible and eccentric connections is considered by means of rotational and linear springs plus rigid end-offset. The proposed approach has the same computational cost of a standard beam element since additional degrees of freedom are condensed out. The resulting element stiffness matrix expression is given as the summation of the second order Timohenko's beam stiffness matrix and corrective matrices. The proposed element is readily implementable in existing finite element codes. Some benchmark problems are used to test the efficiency of the proposed procedure.     

Derivation of the exact stiffness matrix for a two-layer Timoshenko beam element with partial interaction

This paper presents the full closed-form solution of the governing equations describing the behaviour of a shear-deformable two-layer beam with partial interaction. Timoshenko’s kinematic assumptions are considered for both layers, and the shear connection is modelled through a continuous relationship between the interface shear flow and the corresponding slip. The limiting cases of perfect bond and no bond are also considered. The effect of possible transversal separation of the two members has been neglected. With the above assumptions, the present work can be considered as a significant development beyond that available from Newmark et al.’s paper [4]. The differential equations derived considering the above key assumptions have been solved in closed form, and the corresponding “exact” stiffness matrix has been derived using the standard procedure basically inspired by the well-known direct stiffness method. This “exact” stiffness matrix has been implemented in a general displacement-based finite element code, and has been used to investigate the behaviour of shear-deformable composite beams. Both a simply supported and a continuous beam are considered in order to validate the proposed model, at least within the linear range. A parametric analysis has been carried out to study the influence of both shear flexibility and partial interaction on the global behaviour of composite beams. It has been found that the effect of shear flexibility on the deflection is generally more important for composite beams characterized by substantial shear interaction.     

Infinite elements for numerical analysis of underground excavations

Infinite elements were developed to overcome an inherent limitation of the Finite Element Method. The technology of infinite elements has been refined to such an extent that the modeling of an unbounded medium is no longer a limitation of the Finite Element Method. This paper shows that the remaining problem associated with a non-uniform and non-zero far-field decay of any one of the problem variables can also be resolved without having to create nodes at infinity. A combined finite-infinite element analysis now matches the power of the Boundary Element Method in handling the unbounded analysis domains while retaining the versatility of the Finite Element Method.     

基于精细梁模型的向量式有限元分析

精细梁不同于Euler梁和Timoshenko梁,该模型在考虑剪切变形的同时还考虑了横向弯曲时截面转动产生的附加轴向位移及横向剪切变形影响截面抗弯刚度后产生的附加横向位移。推导了适用于向量式有限元分析的精细梁单元应变和内力表达式,采用FORTRAN自编了向量式有限元程序。对悬臂梁、两端固支梁和门式框架进行了算例分析,对比了采用不同梁单元模型下结构的竖向位移。结果表明:当高跨比较小时,3种梁单元的竖向位移相差不大;当高跨比较大时,精细梁单元的竖向位移较Euler梁和Timoshenko梁明显增大,表明剪切变形及刚度折减引起的附加轴向位移、附加横向位移不能忽略。精细梁单元模型对高跨比较大的梁进行分析可望得到更精确的结果。     

Probleme bei der Berechnung von Stahlbetonkonstruktionen mittels dreidimensionalen Gesamtmodellen

Design of three‐dimensional Finite Element Models In practice, complex three‐dimensional finite element models of an entire structure are used more and more often to design a reinforced concrete building. As daily experience shows, results from computer analysis are often trusted with blind faith. For reasons of time, the required checking of the model as well as a clear documentation of the main results remain undone. This development raises questions regarding the safety of structures in the future. The various problems of a complex 3‐d finite element analysis will be demonstrated by a simple structure, an arch bridge. It will be shown, that no software is able to design this bridge, at least in parts. An independent checking of the computer results is always required.