Large bending of pipes

The computer model developed has been used successfully for studying the large pipe-bending problem frequently encountered in offshore structural engineering. The pipe-soil interaction is modelled by using the Coulomb friction law. The modified finite element approach coupled with a modified tangent stiffness procedure is used to handle the nonlinearities (geometric and material, etc.) in the problem. The material nonlinearity has been considered both by the plastic-hinge method and by an elastic-plastic method. Before studying the practical problems, sufficient check problems were analysed and a good agreement was found between theoretically exact solutions and the results obtained from the developed computer model.     

Instability of a cylindrical shell under three-point bending

The instability of a cylindrical shell under three point bending is considered. The problem has application to the industrial pipe ram bending process. The loading is idealized as a set of pads of uniform radial pressure in the regions of die-shell contact. A theoretical solution for the smallest buckling load is developed, using the Donnell and Sanders linearized stability equations. A finite element solution is also presented. The paper concludes with a discussion of results, from the two methods.     

Numerical solution of curved pipes submitted to in-plane loading conditions

An alternative formulation to current meshes dealing with finite shell elements is presented to solve the problem of stress analysis of curved pipes subjected to in-plane bending forces. The solution is based on finite curved elements, where displacements are defined from a total set of trigonometric functions or a fifth-order polynomial, combined with Fourier series. Global shell displacements are achieved through the one associated with curved arch bending and the other referred to the toroidal thin-walled shell distortion. Beam-type displacement and in-plane rotation are uncoupled and separately formulated, using trigonometric shape functions, as in Timoshenko or Mindlin beam theory. To build up the solution, a simple deformation model was adopted, based on the semi-membrane concept of the doubly curved shells behaviour. Several studies are presented and compared with experimental and numerical analyses reported by other authors.     

Experimental and numerical investigation of masonry under three-point bending (in-plane)

The aim of this study is to investigate the failure and post-peak behaviour of masonry panels with low bond strength mortar under three-point bending (TPB) both experimentally and numerically. Full-scale masonry panels with two different mortar strengths were tested under TPB. The material parameters were obtained from compression, TPB and shear tests on bricks and brick–mortar interfaces. The experimental results are detailed. Adopted for the numerical study was a micro-model finite element formulation in which masonry is modelled using expanded brick units with zero thickness brick–mortar interfaces. The simulation of the masonry TPB tests compared well with the experimental results. Investigations were the crack propagation through the masonry and the effects of dilatancy on the post peak response.     

Fabrication of unsymmetrical curved plate girders by cold bending

A proprietary cold bending method was recently developed for the fabrication of the steel girders in the Miami Metromover. In an earlier paper, the authors developed a simplified analysis for this system that could be used for curving symmetrical girders. This paper extends this analysis to unsymmetrical girders typically used in bridge construction where the top flange is smaller than the bottom flange. Guidelines are proposed that set limits on the maximum load and permanent residual strains that develop during the curving operation to ensure they are within acceptable norms. These are integrated in a standardized procedure based on actual practice. A comprehensive numerical example is included to illustrate this procedure. This uses design aids specially developed to simplify calculations in the steel shop.     

低碳钢线割裂缝三点弯曲梁的阻裂电测过程分析

为探寻低碳钢三点弯曲试样断裂过程与承载能力,分别对不同尺寸的带裂缝试件进行加载试验,并对其中的典型试件进行应变片电测跟踪测试,得到了一系列关系曲线,其中有载荷与加载点位移关系曲线,中性层位置随载荷变化曲线,塑性段卸载再加载关系曲线等;且计算了各试件失稳时的应力强度因子．同时测量了该试样的塑性变形,并结合黏聚裂纹应力强度因子计算式与断裂准则,得到计算此材料结构承载力的理论值,并与试验值进行对比,两者比较符合．     

Nonlinear elastic analysis of composite beams curved in-plan

A novel 3D elastic total Lagrangian formulation is developed for the numerical analysis of steel–concrete composite beams which are curved in-plan. Geometric nonlinearities are considered in the derivation of the strain expressions, and the partial interaction at the interface in the tangential direction as well as in the radial direction due to flexible shear connectors is incorporated in the unique proposed formulation, which is derived from considerations of fundamental engineering mechanics. Examples are presented to illustrate the effects of initial curvature, geometric nonlinearity and partial interaction on the behaviour of composite curved beams, which are compared with those based on more sophisticated but computationally less efficient ABAQUS shell element models and experiments reported in the literature. The results demonstrate that the developed formulation is accurate and effective in capturing the behaviour of composite beams curved in-plan, providing a highly efficient finite element.     

锁脚锚管受力分析的双参数弹性地基梁模型

 针对Winkler地基梁模型的固有缺陷,将能够反映地基连续性的Pasternak双参数地基梁模型引入到锁脚锚管–钢拱架的联合承载分析中,考虑锁脚锚管与钢拱架之间的变形协调与荷载传递,采用结构力学和弹性地基梁理论推导锁脚锚管挠度、剪力、弯矩和地基反力的解析表达式。分别通过算例和工程实例考察不同地基基床系数和剪切刚度对锁脚锚管力学行为的影响规律,并与Winkler地基梁模型进行比较。结果表明：基床系数越小,2种模型计算所得锁脚锚管剪力、弯矩以及地基反力等的差异越明显;由双参数模型所得的地基反力数值较大,而且分布范围更小,主要集中在锁脚锚管端部附近区域;由双参数模型所得的隧道下沉量要小于Winkler模型的计算值。给出了适当减小锁脚锚管长度,并增大其直径的建议。研究成果可为软弱围岩隧道支护设计提供理论参考。     

四种不同形式的弹性悬索静力解答

首先回顾了悬索静力分析的研究历史,收集整理了国际上常用的不同坐标系下的两种解答及国内近年来推导的不同坐标系下的两种解答,通过同种坐标下国内、外解答的一致性和不同坐标系下国际上流行的两种解答一致性的证明,表明该四种解答是一致的,建议使用竖坐标轴正方向向上的解答,用国际上的相应解答建立悬索分析的有限元方法,用本文作者推导的解答进行索的设计与计算。     

Numerical analysis of elastic-plastic bending of curved beams with thin-walled cross-section

It is well known that, when a curved beam is subject to bending, the shape of its cross-section is flattened and collapse occurs as the rigidity is reduced. It is important for design to determine the nonlinear behavior of such beams. This paper describes the elastic-plastic large deformation analysis of a curved beam with a thin-walled cross-section by the finite element method. The analytical formulation is developed by extending the kinematic work hardening model proposed by Ziegler. Several representative cases are computed.     

Benchmark symplectic solutions for bending of corner-supported rectangular thin plates

This work presents the first ever analytical solutions for bending of a rectangular, thin plate supported only at its four corners. This breakthrough analysis employs a new symplectic elasticity approach that extends beyond the limitation of the classical plate bending methods such as Timoshenko's method, Navier method, Levy method and the polynomial approximation analysis of Lee and Ballesteros (Int J Mech Sci 1960;2:206). The classical methods are, in fact, special cases of this symplectic approach in the real eigenvalue regime for wavenumber with at least one pair of opposite sides of plates simply supported. For plate problems that do not fall into this category, the classical methods fail to yield any analytical solutions, but the symplectic approach does because in these cases the plate bending problems enter the complex eigenvalue regime for wavenumber. Another distinctive feature of this new approach is its necessity to pose an eigenvalue problem even for plate bending. In short, this innovative approach establishes the relationship between eigenvalue problem and bending. The novelty of this approach lies in the use of the Hamiltonian principle in a symplectic geometry space to derive a Hamiltonian system and a full state vector. The free boundaries with corner supports are dealt with using the variational principle. Analytical bending modes are then derived by expansion of eigenfunctions. The solutions are compared with other known (approximate) results and numerical finite element solutions but some of the results are not in agreement. Because the analytical bending moment and shear force solutions thus derived fulfill all natural and geometric boundary conditions, it leaves ample room for authentication of the benchmarks in the future. In addition, the twisting moment at the corners satisfies the condition for static bending equilibrium, in which the finite element solutions fail.     

冻融循环作用下砂岩三点弯曲断裂性能试验及其破坏形态研究

针对不同初始缝高比砂岩试样的三点弯断裂性能展开冻融循环试验研究,分析砂岩试样断裂破坏面的三维形貌随冻融循环作用的变化规律;同时,探讨试样破坏面的三维粗糙度系数与其起裂荷载、峰值荷载、断裂韧度、断裂能等参数的关系。研究结果表明:冻融循环作用对砂岩试样起裂荷载、峰值荷载、断裂韧度和断裂能有不同程度的劣化作用,其劣化作用的程度又受试样初始缝高比的影响。砂岩试样断裂面的粗糙度系数随冻融循环次数、初始缝高比的增大呈增大的趋势。当初始缝高比一定时,粗糙度系数与冻融循环次数呈较为明显的指数函数关系。冻融循环作用下,砂岩试样断裂峰值荷载的损伤因子、断裂韧度的损伤因子与粗糙度系数的增量有着较为显著的线性递增关系。     

Elasto-plastic response of orthotropic pipes under bending, pressure and axial force

An elasto-plastic analysis of circular thin-walled pipes in the non-buckled configuration subjected to bending moment, pressure and axial loads is presented. Plastic stress-strain relationships based on Drucker's postulates, Hill's yield criterion and the deformation theory are utilized. The analysis includes orthotropic behaviour with the assumption of a linear strain-hardening material. Results are presented for both isotropic and orthotropic materials.     

Parametric study of frost-induced bending moments in buried cast iron water pipes

While the features of frost susceptible soils have been examined in various studies, the mechanisms by which volume changes due to ground freezing can influence cast iron water pipes buried below the frost line have not been explained, and the hypothesis that frost-induced ground deformations can induce ring fractures due to longitudinal bending of these pipes has not been proven. Therefore, a parametric study employing three dimensional finite element analysis is reported, where the soil–pipe interaction associated with a pipe crossing under an intersection of a major arterial road with a residential street are examined. The arterial road is modeled as having non-frost susceptible sub-base and the local street is represented as having a lower grade pavement with frost susceptible sub-base. One specific frost loading case featuring both isotropic pore water expansion and orthotropic ice lens formation is modeled.The analysis demonstrates how volume changes due to ground freezing in soil strata above the buried pipe can induce bending moments sufficient to cause ring fracture. Changes in the relative axial stiffness of the pipe were found to have only a small effect on pipe moments. Decreases in the relative flexural stiffness of the pipe resulting from reductions in pipe modulus also had only a small effect on pipe deflections and normalized moments. Changes due to soil modulus had a significant effect on deformations, but little influence on moments. Decreases in pavement stiffness decrease pipe deflections and moments. Trench backfill conditions greatly affect deflection and moment. Reduction in burial depth from 2 m to 1.5 m increases deflections, and increases moments beyond the failure capacity of the grey, cast iron pipe considered in the study, and this computational result is directly supported by field evidence.     

木 - 混凝土组合梁弹性抗弯承载力研究

为了研究相对滑移对木-混凝土组合梁弹性抗弯承载力的影响,结合对木-混凝土组合梁的梁截面受力特点的分析,建立了木-混凝土组合梁弹性抗弯承载力计算模型,提出了考虑滑移后组合梁简化弹性抗弯承载力公式,使组合梁承载力公式得到优化。同时为验证公式正确性,利用Ansys有限元分析软件进行有限元分析。通过有限元分析与理论公式进行比较,结果表明:理论推导公式与有限元分析吻合良好,可以适用于木-混凝土组合梁弹性抗弯承载力计算。     

滑移效应对型钢混凝土梁弹性抗弯强度的影响

指出了由于滑移效应的影响,型钢混凝土梁的抗弯承载力有所降低,采用弹性分析理论,考虑型钢和混凝土交接面滑移影响,建立了考虑滑移效应的弹性抗弯强度计算公式,以提高型钢混凝土梁弹性抗弯强度计算的准确性。     

底面为曲面基础地基极限承载力上限解

为了解决曲面基础作用于土体的极限承载力问题,改进了 Prandtl 机构和 Hill 机构,利用极限分析理论,得到了底面为曲面基础地基极限承载力的上限解;通过两者的比较,以及与底面为平面基础地基极限承载力的比较,所得的上限解大于处于地基表面的平面基础地基极限承载力的上限解,小于埋深为基础宽度一半的平面基础地基极限承载力的上限解,研究结果可供地基承载力设计及计算参考。     

Dynamic elastic instability of long circular cylindrical shells under pure bending

The present paper studies the responses and instabilities of long circular cylindrical shells subjected to dynamic pure bending. The dynamic instability characteristics of the shells subjected to a sudden step bending load of infinite duration are explored. Analysis is performed using nonlinear finite element numerical methods. Critical dynamic moments are determined through the use of Budiansky and Routh's stability criterion. Numerical predictions for the dynamic instability are compared with those static results given earlier by Brazier. The effects of shell geometry on the dynamic stability of the shells are shown. It is found that the dominating factor to affect the shell stability is the ovalization of the shell cross-section in the centre of the shell.     

浅谈玻璃热弯炉的构成、种类和常见问题的解决方法

本文介绍了热弯玻璃工艺制作流程及热弯炉的主要分类等,并分析了影响热弯玻璃质量的因素,提出了解决办法。     

连续曲线双箱钢-混组合梁弯扭性能试验研究

为研究连续曲线双箱钢-混组合梁的弯扭性能,以实际工程为背景,以曲线半径和横隔板连接方式为参数,设计了3根1∶10的缩尺模型,并对其进行静力加载试验,研究试验梁跨中截面的荷载-挠度曲线、横向挠度分布和钢梁与混凝土板间的相对滑移规律。结果表明,3根梁的破坏形式一致,均为弯扭破坏,负弯矩区在0.1P;(P;为极限荷载)时就会开裂;极限荷载时,试验梁跨中截面外侧挠度达内侧的1.37倍;试验梁的抗弯刚度和抗扭刚度均随着曲线半径的增大而提高,横隔板连接方式对其弯扭性能影响不大;混凝土板与钢梁结合面切向滑移随着曲线半径的增大而减小,横向栓接试验梁的滑移量小于横向焊接试验梁的;切向滑移量最大值出现在跨度的3/4处,径向滑移量最大值出现在中支点附近处。