考虑损伤累积及杆件失稳效应的网壳结构极限承载力分析

为准确分析地震作用下网壳结构的极限承载力,推导了适用于网壳结构常用杆件圆钢管的考虑损伤累积的混合强化本构模型;引入了杆件失稳判别条件和杆件失稳后的力学模型;编写了考虑损伤累积和杆件失稳效应的基于有限元软件ABAQUS 空间梁单元的材料子程序VUMAT-DMB。通过与理论计算结果和已有试验结果进行比较,验证了所编程序的正确性和准确性。算例分析表明:考虑损伤累积对网壳结构极限承载力影响不大,杆件失稳效应将明显降低网壳结构极限承载力。     

基于损伤演化的杆件断裂模拟方法及其应用

建立了钢材的弹塑性损伤本构模型,将其与有限单元法中分段纤维梁模型结合,实现了杆件不同位置损伤程度评估,根据评估结果实时修正杆件特性,建立了杆件断裂数值模拟方法。将所建立的杆件断裂模拟方法应用于单调递增荷载作用下的梁系结构和地震作用下的单层网壳结构,结果表明,所建立方法可有效地模拟杆件断裂;杆件断裂突然,与其相连的节点位移及杆件应变能突增,可能导致与其相连杆件破坏;强震作用下单层网壳结构可能发生杆件断裂,导致结构局部刚度降低,引起结构倒塌破坏。     

粗粒土路基循环荷载试验及累积变形模型研究

为了探讨粗粒土路基在往复列车荷载作用下产生的累积变形和动力特性,开展了粗粒土的室内动三轴试验,分析了不同循环应力比、不同围压对粗粒土路基累积变形的影响。根据动三轴试验结果,提出了考虑围压和循环应力比影响的粗粒土路基累积变形模型。研究结果表明:循环应力比为0.3时是加载次数-累积动应变曲线由稳定型向破坏型演化的起点,随着循环应力比的增大,软化指数不断增大;当循环应力比小于0.3时,软化指数随着围压的增大而减小,当循环应力比大于0.3时,软化指数随着围压的增大而增大。累积变形模型反映循环应力比和围压对累积动应变的影响,能较好地预测累积动应变的发展趋势,且模型参数有明确的物理意义,能为粗粒土路基的设计和养护提供参考。     

罕遇地震下双层球面网壳的弹塑性动力响应分析

对54个双层球面网壳模型在罕遇地震下的弹塑性响应进行了计算。网壳模型中杆件截面按非地震工况下的满应力设计确定,并满足小震作用下的结构验算。计算时考虑网壳和下部结构的协同工作。杆单元采用能够同时考虑受拉屈服和受压屈曲的等效弹塑性滞回模型。根据计算结果,考察了网壳跨度、矢跨比、支座连接条件、下部结构形式以及地震波选取对结构塑性区域、塑性发展程度以及残余变形的影响。研究表明,罕遇地震下双层球面网壳的薄弱区域不全出现在临支座区域。当网壳受下部结构约束较强或跨度和矢跨比均较大时,发生残余塑性应变的杆件大多出现在网壳中间圈层区域。跨度、矢跨比和支座条件是影响塑性杆件分布和塑性应变大小的三个敏感因素。但所有模型并没有在罕遇地震下出现倒塌。     

复杂循环路径下钢材弹塑性屈曲行为研究

复杂强震荷载作用下钢管混凝土柱中的钢管受压屈服后易发生局部屈曲,在杆系有限元模型中采用不考虑屈曲影响的钢材本构模型无法准确模拟钢结构构件的地震响应。为研究复杂循环荷载作用下钢材的屈曲行为,该文设计了强度等级分别为Q235和LYP160的30个钢材试件,并设计了多种复杂循环加载路径进行加载,获得了不同复杂循环荷载作用下钢材的弹塑性屈曲行为和应力-应变滞回关系。基于已有文献中的3种钢材循环本构模型:Légeron模型、GA模型和DM模型对试验结果进行对比分析和评价,结果表明:Légeron模型无法模拟钢材受压区服后的屈曲效应,GA模型中受压屈曲时的应力-应变规律与试验结果较为吻合,DM模型中受拉和受压卸载刚度与试验结果较为吻合。     

型钢混凝土异形柱框架结构平扭振动反应及地震内力分析

通过对5层实腹式型钢混凝土异形柱空间框架结构模型进行三向地震模拟振动台试验,获得了结构平动、扭转、平扭耦合动力特性,并对结构的多维地震反应、耗能能力、损伤程度、地震内力及平扭振动规律进行了综合分析。结果表明:模型结构前4阶自振频率对应的振型形态依次为X向平动、Y向平扭、扭转和Y向平动;随着地震强度的增加,型钢混凝土异形柱框架结构的自振频率不断下降,加速度放大系数逐渐减小,结构塑性变形不断发展,结构内部损伤逐渐累积,地震能量耗散不断增加,整体累积滞回耗能时程曲线呈台阶势跃迁;在历经0.80g地震作用后,模型结构平扭耦合引起的层间位移角最大值为1/39,超过弹塑性层间位移角限值要求,模型结构的变形和能量双参数模型损伤指数达到0.56;对比模型结构扭转效应发现,偶然偏心平扭耦合作用对模型结构的抗震性能影响较小,其偶然相对偏心距小于0.1;分析计算模型抗扭刚度、地震内力可知,在加载后期,随着水平侧移的增大,楼层的等效抗扭刚度退化并不明显,表明结构具有良好的抗震性能和抗扭变形能力。     

大跨度空间结构多维多点非平稳随机地震反应分析

对大跨度空间结构进行三向正交地震动多点激励下的非平稳随机地震反应分析。建立了多维多点随机非平稳地震动激励下的地震反应分析方法,并针对大跨度空间结构引入了波前法进行简化计算。数值仿真分析了天津奥林匹克中心体育场屋盖结构分别在一维随机地震动或三维随机地震动的一致激励、行波激励以及考虑部分相干效应和地震非平稳性的多点激励下的地震反应,结果表明:考虑地震动空间效应会使结构控制杆件内力增大约30%;考虑部分相干效应会使结构杆件内力变化约10%;考虑多维地震输入会使结构控制内力增大约15%;考虑地震动的非平稳性会使结构杆件内力减小约35%。由此可以得出结论,对于大跨度空间结构的地震反应分析,必须考虑地震动的多维输入和多点激励;然而不考虑地震动的非平稳性,其抗震设计偏于安全。     

饱和软粘土地基的损伤模型与震陷计算

基于各向同性弹塑性损伤和Prevost模型的基本理论,把弹塑性等向硬化、运动硬化和各向同性损伤结合起来,推导了循环荷载作用下不排水饱和软粘土弹塑性动力损伤本构模型.考虑到地震作用下土体应力的不规则性,对循环三轴试验获得的粘土残余应变经验计算公式进行了修正,最后将该残余应变引入到损伤演化方程中.通过对地基的震陷计算并与不考虑损伤的模型进行对比,结果表明,该模型能合理地考虑屈服面内应力循环对地基残余塑性应变的贡献.     

采空区基础变形过程中输电铁塔结构动力冲击效应分析

在通用有限元软件ANSYS中建立了220 k V猫头塔有限元模型,分别采用静力和动力方法分析了基础不均匀沉降、倾斜和水平滑移工况的铁塔杆件内力,计算了基础突然变形时输电铁塔结构的动力冲击系数。结果表明,基础变形过程中输电铁塔塔腿斜材应力变化幅度最大并最先发生破坏。铁塔杆件轴力峰值发生在基础沉降的初始时刻附近,而阻尼比对峰值影响不大,阻尼比分别为0.01和0.05时,塔腿主材轴力峰值仅相差约3.5%。对于经过地表变形剧烈的采空区输电线路,基础突然变形对输电铁塔结构的动力冲击效应显著。考虑基础变形动力冲击效应后,不均匀沉降工况下塔腿斜材应力比增大50%以上,单侧倾斜和水平滑移工况的塔腿斜材应力增大幅度超过100%。     

多维多点输入下大跨度连体高层结构地震反应振动台阵试验研究

利用振动台阵在多维多点激励下对大跨度连体高层结构的地震响应进行了试验研究. 试验中分别对结构输入了单维及多维、一致及不同视波速的行波激励以考察多维地震分量以及行波效应对结构地震响应的影响程度. 试验结果表明:多维地震分量将增大结构地震响应;行波效应可能使连接部位关键杆件的应力有明显增大;同时考虑多维多点时结构沿强轴向加速度响应有所减小, 而沿弱轴向加速度响应明显增大;连廊结构在考虑多维多点地震输入时其竖向地震响应将有明显放大. 因此在对此类结构进行抗震设计时应考虑多维多点地震激励的 影响.     

三向类网架结构弯曲和振动分析的分解刚度法

把三向类网架结构简化为夹层板,采用考虑剪切变形的具有三个广义位移的平板弯曲理论进行分析。基于分解刚度思想提出了三向类网架(三角锥网架、三向网架)静力分析和固有振动分析的方法,给出了简便实用的计算公式。通过有限元法的验证,表明了分解刚度法作为一种简化的计算方法,其精度是比较高的,绝大多数的误差都小于5%。可以应用于工程结构设计,便于快速得出网架结构挠度和内力的计算结果及分布规律。此外,与其它的计算方法相比其计算公式大大简化了。     

Iterative univariate optimization of nonlinear trusses with fuzzy strain constraints

A univariate iterative method for the optimization of nonlinear trusses with fuzzy constraints is proposed. The method is based on the control of elemental strains rather than stresses and hence it is called the desirable strain design criteria method. The objective of the fuzzy optimization is to find a design so that the weight or volume of the truss as well as all of the constraints on the elemental strains and joint deflections are desirable and satisfactory according to the fuzzy designer expressions. Such expressions are made in the form of fuzzy membership functions. Two illustrative examples, a 3- and a 10-bar truss, are optimized by the proposed method, where it is shown that in both cases the method monotonically converges to the highest desirability.     

Damage and failure in low energy impact of fiber-reinforced polymeric composite laminates

We analyze the damage initiation, damage progression, and failure during 3-dimensional (3-D) elasto-plastic deformations of a fiber reinforced polymeric laminated composite impacted by a low speed rigid sphere, and compare computed results with experimental findings available in the literature. Damage is assumed to initiate when one of Hashin’s failure criteria is satisfied, and its evolution is modeled by an empirical relation proposed by Matzenmiller, Lubliner and Taylor. The transient nonlinear problem is solved by the finite element method (FEM). Contributions of the work include considering damage in 3-D rather than plane stress deformations of a laminated structure and elasto-plastic deformations of the composite. This has been accomplished by developing a user defined subroutine and implementing it in the FE software ABAQUS. From strains supplied by ABAQUS the material subroutine uses a micro-mechanics approach based on the method of cells and values of material parameters of constituents to calculate average stresses in an FE, and checks for Hashin’s failure criteria. If damage has initiated in the material, the subroutine evaluates the damage developed, computes resulting stresses, and provides them to ABAQUS. The damage evolved at a material point is not allowed to decrease during unloading. The delamination failure mode is simulated by using the cohesive zone model available in ABAQUS. The computed time histories of the axial load acting on the impactor are found to agree well with the experimental ones available in the literature, and various damage and failure modes agree qualitatively with those observed in tests.     

Extended multiscale finite element method for elasto-plastic analysis of 2D periodic lattice truss materials

An extended multiscale finite element method is developed for small-deformation elasto-plastic analysis of periodic truss materials. The base functions constructed numerically are employed to establish the relationship between the macroscopic displacement and the microscopic stress and strain. The unbalanced nodal forces in the micro-scale of unit cells are treated as the combined effects of macroscopic equivalent forces and microscopic perturbed forces, in which macroscopic equivalent forces are used to solve the macroscopic displacement field and microscopic perturbed forces are used to obtain the stress and strain in the micro-scale to make sure the correctness of the results obtained by the downscale computation in the elastic-plastic problems. Numerical examples are carried out and the results verify the validity and efficiency of the developed method by comparing it with the conventional finite element method.     

Behaviour and design of pin connected structures

The feasibility of achieving a preassigned stress state by changing the stiffness of determinate and indeterminate pin connected structures is presented. A new force method with all element forces (or stresses or areas) as independent variables is developed. The possibility but futility of getting the element areas by inverting and pre-multiplying the coefficient matrix with the external load vector when areas are chosen as variables is shown. The relationship existing between the compatibility equations and the plastic strength of pin connected structures is illustrated. Possible design methods for trusses under single or multiplicity of load conditions, the design of truss geometry and the relations between fully stressed and minimum weight structures are examined and illustrated through several examples.     

Constitutive model and finite element formulation for large strain elasto-plastic analysis of shells

This contribution presents a refined constitutive and finite element formulation for arbitrary shell structures undergoing large elasto-plastic deformations. An elasto-plastic material model is developed by using the multiplicative decomposition of the deformation gradient and by considering isotropic as well as kinematic hardening phenomena in general form. A plastic anisotropy induced by kinematic hardening is taken into account by modifying the flow direction. The elastic part of deformations is considered by the neo-Hookean type of a material model able to deal with large strains. For an accurate prediction of complex through-thickness stress distributions a multi-layer shell kinematics is used built on the basis of a six-parametric shell theory capable to deal with large strains as well as finite rotations. To avoid membrane locking in bending dominated cases as well as volume locking caused by material incompressibility in the full plastic range the displacement based finite element formulation is improved by means of the enhanced assumed strain concept. The capability of the algorithms proposed is demonstrated by various numerical examples involving large elasto-plastic strains, finite rotations and complex through-thickness stress distributions.     

Application of the finite element–difference method to vibration problems

The so-called finite element–difference method introduced in References 1 and 2 yields a continuous stress field by finite difference operations and finite element interpolations. In the present paper, applications of the method to vibration problems are discussed. The inverse iteration procedure is modified for this method. Numerical results show that the accuracy of solutions depends strongly on the type of finite difference operator chosen: for reliable and accurate solutions in modal analysis problems, element internal strains must be included in the strain field used to compute nodal forces associated with element deformations.     

A TORSIONAL SPRING-LIKE BEAM ELEMENT FOR THE DYNAMIC ANALYSIS OF FLEXIBLE MULTIBODY SYSTEMS

A new finite element beam formulation for modelling flexible multibody systems undergoing large rigid-body motion and large deflections is developed. In this formulation, the motion of the ‘nodes’ is referred to a global inertial reference frame. Only Cartesian position co-ordinates are used as degrees of freedom. The beam element is divided into two subelements. The first element is a truss element which gives the axial response. The second element is a torsional spring-like bending element which gives the transverse bending response. D'Alembert principle is directly used to derive the system's equations of motion by invoking the equilibrium, at the nodes, of inertia forces, structural (internal) forces and externally applied forces. Structural forces on a node are calculated from the state of deformation of the elements surrounding that node. Each element has a convected frame which translates and rotates with it. This frame is used to determine the flexible deformations of the element and to extract those deformations from the total element motion. The equations of motion are solved along with constraint equations using a direct iterative integration scheme. Two numerical examples which were presented in earlier literature are solved to demonstrate the features and accuracy of the new method.     

A structural experimental technique to characterize the viscoelastic behavior of concrete under restrained deformations

An innovative variable restraint frame is proposed to characterize the viscoelastic behavior of concrete under tensile stresses induced by restraints to shrinkage deformations (mainly due to drying). Two concrete specimens with the same cross section are used, subjected to equal thermal and moisture conditions: one is made of plain concrete, to assess the “free” deformations due to shrinkage and temperature; the other is reinforced with two steel threaded rods, which induce a manually controlled axial restraint to shrinkage. The restrained specimen is installed on a reaction frame, being stretched in force control mode. The concrete and the rods are instrumented with strain gauges and temperature sensors, which allow separation of the different components of concrete strains with the aid of equations based on equilibrium and compatibility conditions. This permits identifying the elastic and tensile creep concrete strains, as well as the concrete tensile stresses induced by the restrained shrinkage. The device also allows assessing the concrete modulus of elasticity during the test and remains operational even upon concrete cracking, features of great interest for the intended material characterization.     

Safety factor maximization for trusses subjected to fatigue stresses

This article presents a mathematical model for sizing optimization of undamped trusses subjected to dynamic loading leading to fatigue. The combined effect of static and dynamic loading, at steady state, is considered. An optimization model, whose objective is the maximization of the safety factor of these trusses, is developed. A new quantity (equivalent fatigue strain energy) combining the effects of static and dynamic stresses is presented. This quantity is used as a global measure of the proximity of fatigue failure. Therefore, the equivalent fatigue strain energy is minimized, and this seems to give a good value for the maximal equivalent static stress. This assumption is verified through two simple examples. The method of moving asymptotes is used in the optimization of trusses. The applicability of the proposed approach is demonstrated through two numerical examples; a 10-bar truss with different loading cases and a helicopter tail subjected to dynamic loading.