Buckling of steel bars with Lüders bands

Experiments and simulations are presented for the study of interaction between material and structural instabilities that occur in mild steel bars under axial compression. The material instability consists of Lüders bands that nucleate and propagate along the specimens. The structural instability involves lateral deflections of the bar leading to collapse. The study includes an investigation of bars of several different lengths. The mechanical response in the experiments were monitored through measurements of axial load, axial and midspan lateral displacements, and full field imaging of a brittle coating showing the Lüders deformation. Interesting interactions exist between the localized deformation due to the material-level instabilities and the global collapse of the bars. Finite element simulations, using a constitutive model with a nonmonotonic stress–strain behavior, showed good agreement with the experiments and helped to explain the variety of collapse modes seen in the experiments. The symmetry of imperfections and/or loading misalignments have dramatic effects on the evolution of Lüders deformation and the eventual collapse mode. Certain imperfections lead to deformation modes that delay structural collapse.     

Dynamic modeling and modal truncation approach for a high-speed rotating elastic beam

Summary  In the classical finite element analysis of beams, the nonlinear terms of deformation are ignored due to the linearization of deformation based on the assumptions of structural dynamics. Since the number of generalized coordinates is large in flexible bodies when using the finite element method (FEM), the modal truncation approach (MTA) is usually used for improving computational efficiency, and only lower-order transverse modes are chosen. In this paper, dynamic modeling and application of the MTA to a high-speed rotating beam are studied. The foreshortening displacement is included in the longitudinal displacement, therefore the dynamic modeling takes account of the effect of geometric nonlinearity. Equations of a rotating beam are obtained and the FEM and MTA are used for discretization. The applicability of the MTA to a high-speed rotating elastic beam is verified. The comparison of the results obtained by the FEM and MTA shows that in the case of a high-speed rotation, the centrifugal force can excite high-order transverse modes. Since using lower-order transverse modes for modal truncation obviously can cause error, addition of more transverse modes may improve the result. Furthermore, a coupling effect between axial and transverse displacements is revealed. It is shown that in the case of a sudden change of the axial displacement, the inclusion of the axial modes can significantly improve the response. Received 10 April 2001; accepted for publication 26 March 2002 This work was supported by the National Science Foundation of China (19832040) and the National Education Ministry of China (2000024818), for which the authors are grateful.     

火灾后钢筋混凝土异形板的极限均布荷载

本文基于塑性铰线理论确定了钢筋混凝土异形板的破坏机构，并利用有限差分法计算了火灾时板内的温度场，根据高温后钢筋和混凝土的力学性能对塑性铰线截面的弯矩及灾后极限均布荷载进行了分析，为钢筋混凝土板火灾后的评估和维修提供依据．     

Three-dimensional finite element modeling of a vibrating beam with a breathing crack

This paper develops a full three-dimensional finite element model in order to study the vibrational behavior of a beam with a non-propagating surface crack. In this model, the breathing crack behavior is simulated as a full frictional contact problem between the crack surfaces, while the region around the crack is discretized into three-dimensional solid finite elements. The governing equations of this non-linear dynamic problem are solved by employing an incremental iterative procedure. The extracted response is analyzed utilizing either Fourier or continuous wavelet transforms to reveal the breathing crack effects. This study is applied to a cracked cantilever beam subjected to dynamic loading. The crack has an either uniform or non-uniform depth across the beam cross-section. For both crack cases, the vertical, horizontal, and axial beam vibrations are studied for various values of crack depth and position. Coupling between these beam vibration components is observed. Conclusions are extracted for the influence of crack characteristics such as geometry, depth, and position on the coupling of these beam vibration components. The accuracy of the results is verified through comparisons with results available from the literature.     

Q345低周疲劳性能与疲劳寿命预测分析

本文对结构用钢Q345的低周疲劳性能进行了试验研究。试验在常温下岛津电液伺服疲劳试验机上进行,采用轴向应变控制方法,恒定应变速率为0.005s-1,应变比为-1。试验结果表明,初始阶段,Q345在高应变幅值(0.6%)循环作用下出现循环硬化效应,而在低应变幅值(0.6%)作用下出现循环软化效应;随着加载应变幅的增加,硬化和软化率呈直线上升趋势。Q345疲劳裂纹萌生阶段占其整个寿命的60%以上,其裂纹萌生寿命与应变幅存在幂函数关系。根据Coffin-Manson公式得到了Q345的应变-寿命关系公式;采用能量预测法得到了材料的塑性应变能与疲劳寿命的关系表达式。上述结果对钢结构的设计、评估具有重要的工程应用参考价值。     

Effect of crack-tip shape on the near-tip field in glassy polymer

The physical nature of a crack tip is not absolutely sharp but blunt with finite curvature. In this paper, the effects of crack-tip shape on the stress and deformation fields ahead of blunted cracks in glassy polymers are numerically investigated under Mode I loading and small scale yielding conditions. An elastic–viscoplastic constitutive model accounting for the strain softening upon yield and then the subsequently strain hardening is adopted and two typical glassy polymers, one with strain hardening and the other with strain softening–rehardening are considered in analysis. It is shown that the profile of crack tip has obvious effect on the near-tip plastic field. The size of near-tip plastic zone reduces with the increase of curvature radius of crack tip, while the plastic strain rate and the stresses near crack tip enhance obviously for two typical polymers. Also, the plastic energy dissipation behavior near cracks with different curvatures is discussed for both materials.     

Bounds for finite deflections of impulsively loaded structures with time-dependent plastic behaviort

The paper shows that upper bounds on deflections of an impulsively loaded structure whose behavior in the plastic range is strain rate dependent may be obtained by an application of the theorem of minimum potential energy, with results valid for finite deflections and strains. The concepts of extremal path behavior in strain-time space, due to Ponter, are used in order to provide unique definitions of strain energy and complementary energy for the path dependent material. The theorems are illustrated by examples of fully constrained beams in which deflections of the order of the beam thickness lead to large forces of membrane type.     

Nonlinear dynamics of an inclined beam subjected to a moving load

In this paper, the nonlinear dynamic response of an inclined pinned-pinned beam with a constant cross section, finite length subjected to a concentrated vertical force traveling with a constant velocity is investigated. The study is focused on the mode summation method and also on frequency analysis of the governing PDEs equations of motion. Furthermore, the steady-state response is studied by applying the multiple scales method. The nonlinear response of the beam is obtained by solving two coupled nonlinear PDEs governing equations of planar motion for both longitudinal and transverse oscillations of the beam. The dynamic magnification factor and normalized time histories of mid-pint of the beam are obtained for various load velocity ratios and the outcome results have been illustrated and compared to the results with those obtained from traditional linear solution. The appropriate parametric study considering the effects of the linear viscous damping, the velocity of the traveling load, beam inclination angle under zero or nonzero axial load are carried out to capture the influence of the effect of large deflections caused by stretching effects due to the beam’s immovable ends. It was seen that quadratic nonlinearity renders the softening effect on the dynamic response of the beam under the act of traveling load. Also in the case where the object leaves the inclined beam, its planar motion path is derived and the targeting accuracy is investigated and compared with those from the rigid solution assumption. Moreover, the stability analysis of steady-state response for the modes equations having quadratic nonlinearity was carried out and it was observed from the frequency response curves that for the considered parameters in the case of internal-external primary resonance, both saturation phenomenon and jump phenomenon can be predicted for the longitudinal excitation.     

An investigation of the static and dynamic behavior of electrically actuated rectangular microplates

We present an investigation of the static and dynamic behavior of the nonlinear von-Karman plates when actuated by the nonlinear electrostatic forces. The investigation is based on a reduced order model developed using the Galerkin method, which rely on modeshapes and in-plane shape functions extracted using a finite element method. In this study, a fully clamped microplate is considered. We investigate the static behavior and the effect of different non-dimensional design parameters. The static results are validated by comparison with the results calculated by a finite element model. The forced-vibration response of the plate is then investigated when the plate is excited by a harmonic AC load superimposed to a DC load. The dynamic behavior is examined near the primary and secondary (superharmonic and subharmonic) resonances. The microplate shows a strong hardening behavior due to the cubic nonlinearity of mid-plane stretching. However, the behavior switches to softening as the DC load is increased. Finally, near-square plates are studied to understand the effect of geometric imperfections of microplates.     

Elastic–plastic and limit-state analyses of frames with softening plastic-hinge models by mathematical programming

Frames (and more general beam systems) subjected to monotonic loading are modelled by conventional finite elements with the traditional assumption of possible plastic deformations concentrated in pre-selected “critical sections”. The inelastic behaviour of these beam sections, i.e. the development of “plastic hinges”, is described by piece-wise-linear constitutive models allowing for hardening and/or softening, in terms of generalized stresses and conjugate kinematic variables.The following topics are discussed: step-by-step analysis methods, both “exact” and stepwise holonomic; path bifurcations and overall stability; limit and deformation analyses combined, as an optimization problem under complementarity constraints apt to compute the safety factor (with respect to global or local failures); numerical tests of nonconventional algorithms by means of simple representative applications.The objective of the paper is to provide a unified methodology and to propose novel procedures for inelastic analyses of frames up to failure, in the light of recent results in mathematical programming, particularly on complementarity theory.     

Preliminary study on ductile fracture of imperfect lattice materials

The ductile fracture behavior of two-dimensional imperfect lattice material under dynamic stretching is studied by finite element method using ABAQUS/Explicit code. The simulations are performed with three isotopic lattice materials: the regular hexagonal honeycomb, the Kagome lattice and the regular triangular lattice. All the three lattices are made of an elastic/visco-plastic metal material. Two typical imperfections: vacancy defect and rigid inclusion are introduced separately. The numerical results reveal novel deformation modes and crack growth patterns in the ductile fracture of lattice material. Various crack growth patterns as defined according to their profiles, “X”-type, “Butterfly”-type, “Petal”-type, are observed in different combinations of imperfection type and lattice topology. Crack propagation could induce severe material softening and deduce the plastic dissipation of the lattices. Subsequently, the effects of the strain rate, relative density, microstructure topology, and defect type on the crack growth pattern, the associated macroscopic material softening and the knock-down of total plastic dissipation are investigated.     

冲击载荷下软钢梁早期响应的数值模拟和简化模型

冲击载荷作用下，梁的早期响应既有弹性变形也有塑性变形，两者相互耦合．有限元数值模拟的结果表明，弹性弯曲波的传播是梁早期变形的主要机制，刚塑性简化理论预言的初始阶段中梁的“移行塑性铰”实际上是不存在的．本文提出的弹性 理想塑性简化模型可以很好地模拟固支软钢梁的早期响应     

On the elastoplastic cyclic analysis of plane beam structures using a flexibility-based finite element approach

This paper presents the extension of a flexibility-based large increment method (LIM) for the case of cyclic loading. In the last few years, LIM has been successfully tested for solving a range of non-linear structural problems involving elastoplastic material models under monotonic loading. In these analyses, the force-based LIM algorithm provided robust solutions and significant computational savings compared to the displacement-based finite element approach by using fewer elements and integration points. Although in cyclic analysis a step-by-step solution procedure has to be adopted to account for the plastic history, LIM will still have many advantages over the traditional finite element method. Before going into the basic idea of this extension, a brief discussion regarding LIM governing equations is presented followed by the proposed solution procedure. Next, the formulation is specified for the treatment of the elastic perfectly plastic beam element. The local stage for the beam behavior is discussed in detail and the required improvement for the LIM methodology is described. Illustrative truss and beam examples are presented for different non-linear material models. The results are compared with those obtained from a standard displacement method and again highlight the potential benefits of the proposed flexibility-based approach.     

A coupling cross-section finite element model for torsion analysis of prismatic bars

A general finite element model has been developed for the analysis of prismatic bars subject to torsional loading by modelling only a small slice of the bar. Exact analytical coupling deformation relationships between the artificial cross-sections, which are independent of the position of axis of rotation, have been formulated. Three examples from the range of analyses that have been evaluated have been selected to demonstrate the accuracy and effectiveness of the method. Analyses for an orthotropic elastic square cross-section bar, an elastic–plastic circular cross-section shaft containing a radial crack, and geometrically nonlinear deformation of a thin-walled I-section beam are presented and compared with previous results, where available.     

Chaotic and asymmetrical beam response to impulsive load

Both symmetrical and asymmetrical final displacements are observed for elastic–plastic beams under symmetrical impulsive loading. A three-degree-of-freedom Shanley-type model is developed in this study, which is capable of revealing chaotic and asymmetrical responses of an elastic–plastic beam by introducing initial imperfections. To identify the asymmetrical displacement, the beam response is decomposed into three vibration modes. Corresponding modal participation factors are derived based on the displacement of the three-degree-of-freedom beam model. Phase plane trajectories, Poincaré maps and power spectral density diagrams are derived to illustrate both the symmetrical and asymmetrical chaotic vibrations. Numerical simulations using a general-purpose FE code LS-DYNA are carried out for an elastic–plastic beam subjected to impulsive load. The simulation results indicate that the elastic–plastic beam demonstrates chaotic and asymmetrical vibration when the applied impulsive load exceeds a critical value, which agrees with experimental observations.     

Path dependence and multiaxial behavior of a polycrystalline NiTi alloy within the pseudoelastic and pseudoplastic temperature regimes

Several multiaxial experiments on polycrystalline NiTi have been conducted within a wide temperature range. In this vein, the pseudoelastic as well as the pseudoplastic behavior are investigated within the distinct temperature regimes. Isothermal and temperature varying thermomechanical loading paths are applied by means of an active temperature control in order to characterize the path dependence of pseudoelasticity and the multiaxial one-way effect of the alloy. The main focus is on the determination of the dependence of the loading sequence, the related non-linearity of the material and the combined material interaction, e.g., referring to reorientation processes for complex loading paths with respect to pseudoelasticity and the one-way effect. Isothermal tension/compression/torsion experiments are performed on an austenitic microstructure spanning all four quadrants of the axial/torsional strain subspace. In this regard, it is deduced in the course of this contribution that the apparently qualitatively different material behavior for different strain paths in the pseudoelastic temperature regime might be explained by the axial/torsional and tension/compression asymmetry. Furthermore, some multidimensional axial/torsional stress controlled experiments are realized with loading on a martensitic and unloading being implemented both on martensitic and austenitic microstructures. Here, the peculiarity of the one-way effect referring to apparently different transformation temperatures is ascribed to the loading history of the specimen material and to differently oriented martensite variants. In order to elucidate these effects, potential explanations for the pseudoelastic path dependence and the non-linearity in the material behavior with reference to the multiaxial one-way effect are presented.     

拉─扭复合加载下不锈钢的弹塑性本构关系─I．实验

讨论了１Ｃｒ１８Ｎｉ９Ｔｉ不锈钢薄壁圆管试件沿三段折线、不同曲率的圆形和椭圆应变路径承受拉－扭复合载荷的实验．在塑性应变空间中，观察加载路径的内蕴几何参数对应力矢量大小、方向影响的规律．结果表明：响应的延迟角、瞬时软化和重新强化性质与路径的内蕴几何学密切相关；Ｌｅｎｓｋｙ的“局部确定性”假设不完全符合事实；变形历史和应变分量相互间的耦合效应对响应存在显著的影响．初步的电镜实验表明，材料中的位错组态和塑性应变历史密切相关     

不同加载状态下TA2钛合金绝热剪切破坏响应特性

一般认为绝热剪切现象在宏观上表现为材料动态本构失稳,即热软化大于应变硬化.本文采用帽型受迫剪切试样研究TA2钛合金的动态力学特性和本构失稳过程.首先对剪切区加载应力状态进行理论和数值分析,通过合理设计帽型试样,剪切区变形可近似按剪切状态处理;结合二维数字图像相关法(two-dimensional digital image correlation,DIC-2D)直接测试试样剪切区应变演化,给出帽型受迫剪切实验的等效应力-应变响应曲线.进一步,利用Hopkinson压杆对TA2钛合金开展动态压缩及帽型剪切对比试验研究,比较压缩、剪切试验得到的等效应力-应变曲线,采用"冻结"试样方法分析试样中绝热剪切局域化演化过程,探讨不同加载状态下TA2钛合金的绝热剪切破坏现象及其动态力学响应特性.实验结果表明,在塑性变形初始阶段,动态压缩及剪切加载下的等效应力-应变曲线符合较好,但随塑性损伤发展及绝热剪切带形成,两者出现分离,表明损伤及绝热剪切演化过程与应力状态相关.剪切试样实验得到的本构"软化"特性能够反映绝热剪切带起始、破坏演化过程的力学响应特性,而在动态压缩实验中,即使试样中已出现双锥形的绝热剪切带及局部裂纹分布,其表观等效应力-应变曲线并不出现软化特征,动态压缩实验无法得到关于绝热剪切起始、发展以及破坏的本构软化响应特性.     

金属材料在复杂应力状态下的塑性流动特性及本构模型

工程应用中,金属材料和结构往往处于复杂应力状态。材料的塑性行为会受到应力状态的影响,要精确描述材料在复杂应力状态下的塑性流动行为,必须在本构模型中考虑应力状态效应的影响。然而,由于在动态加载下材料的应变率效应和应力状态效应相互耦合、难以分离,给应力状态效应的研究和模型的建立造成很大困难。通过对Ti-6Al-4V钛合金材料开展不同加载条件下的力学性能测试,提出了一个包含应力三轴度和罗德角参数影响的新型本构模型,并通过VUMAT用户子程序嵌入ABAQUS/Explicit软件。分别采用新提出的塑性模型和Johnson-Cook模型对压剪复合试样的动态实验进行了数值模拟。结果表明,新模型不仅在对材料本构曲线的拟合方面具有较强的优势,而且由该模型所得到的透射脉冲和载荷-位移曲线均更加准确。因此,该模型能够更精确地描述和预测金属材料在复杂应力状态下的塑性流变行为。     

剪切流作用下层合梁非线性振动特性研究

针对剪切流中层合梁的大变形非线性振动问题, 采用高阶剪切变形锯齿理论和冯·卡门应变描述层合梁的变形模式和几何非线性效应, 构建了大变形层合梁非线性振动有限元数值模型; 采用基于任意拉格朗日?欧拉方法的有限体积法求解不可压缩黏性流体纳维-斯托克斯方程, 结合层合梁和流体的耦合界面条件建立了剪切流作用下层合梁流固耦合非线性动力学数值模型, 采用分区并行强耦合方法对层合梁的流致非线性振动响应进行了迭代计算. 研究了不同速度分布的剪切流作用下单层梁和多层复合材料梁的振动响应特性, 并验证了本文数值建模方法的有效性. 结果表明: 剪切流作用下单层梁的振动特性与均匀流作用下的情况不同, 梁的运动轨迹受剪切流影响向下偏斜, 随着速度分布系数增加, 尾部流场中的涡结构发生改变; 刚度比对剪切流作用下层合梁的振动特性有显著影响, 随着刚度比的增加, 层合梁振动的振幅增大, 主导频率下降, 运动轨迹由‘8’字形逐渐变得不对称; 发现了不同厚度比和铺层角度情况下, 层合梁存在定点稳定模式、周期极限环振动模式和非周期振动模式三种不同的振动模式, 改变层合梁铺层角度可实现层合梁周期极限环振动模式向非周期振动模式转变.