VISCOPLASTIC COLLAPSE OF SHARP-NOTCHED CIRCULAR TUBES UNDER CYCLIC BENDING

This study discusses the experimental result of the viscoplastic response and col- lapse of sharp-notched 316L stainless steel tubes with different notched depths subjected to cyclic bending. The tube bending machine and curvature-ovalization measurement apparatus were used for conducting the symmetric curvature-controlled cyclic bending. To highlight the viscoplastic behavior, three different curvature-rates, 0.0035, 0.035 and 0.35 m-1s-1, were controlled. Ob- servations of a certain curvature-rate reveal that five almost parallel lines corresponding to five different notch-depth （0.2, 0.4, 0.6, 0.8 and 1.0 mm） tubes were presented in the experimental relationship between the cyclic controlled curvature and the number of cycles needed to pro- duce buckling on a log-log scale. However, the slopes for the three different curvature-rates are different. An empirical formulation was proposed to simulate the aforementioned relationship. When comparing with the experimental findings, the simulation was in good agreement with the experimental data.     

Elastic buckling of rectangular plates under linearly varying in-plane normal load with a circular cutout

The elastic buckling behavior of rectangular perforated plates was studied by using the finite element method in this study. Circular cutout was chosen at different locations along the principal x-axis of plates subjected to linearly varying loading in order to evaluate the effect of cutout location on the buckling behavior of plates. The results show that the center of a circular hole should not be placed at the end half of the outer panel for all loading patterns. Furthermore, the presence of a circular hole always causes a decrease in the elastic buckling load of plates subjected to bending, even if the circular hole is not in the outer panel.     

Transition from progressive buckling to global bending of circular shells under axial impact––Part I: Experimental and numerical observations

The influence of impact velocity and material characteristics on the dynamic buckling response of circular shells subjected to axial impact loads is studied. It is shown experimentally that the critical buckling length, which marks the transition between progressive and global buckling of aluminium alloy circular tubes, is significantly influenced by the axial impact velocity. A finite element analysis is undertaken to further explore the effects of material yield stress, strain hardening and strain rate sensitivity on the transition phenomenon. It is observed that circular tubes made of ductile alloys with a high yield stress and low strain hardening characteristics have a better performance as energy absorbers than tubes made of alloys with a low yield stress and high strain hardening characteristics. Theoretical analysis of some particular features of the dynamic buckling transition is presented in Part II [International Journal of Solids and Structures (2004)].     

基于双剪统一强度理论的复式钢管混凝土轴压承载力计算

考虑内、外钢管对混凝土的双重约束作用, 分析复式钢管混凝土的轴压应力状态, 采用双剪统一强度理论分析混凝土和钢管各自的极限轴压强度, 得出复式钢管混凝土轴压承载力公式; 通过推导钢管在极限状态的强度折减系数及钢管与混凝土之间的紧箍力值, 计算出的轴压承载力与试验数据进行对比, 吻合较好, 验证了双剪统一强度理论在复式钢管混凝土轴压承载力计算中的适用性; 并给出了内圆钢管的径厚比和直径与轴压承载力提高系数的关系, 为复式钢管混凝土的优化设计提供理论依据.     

Buckling behaviour of elliptical cylindrical shells and tubes under compression

This paper presents several issues that characterize the buckling behaviour of elliptical cylindrical shells and tubes under compression. First, a formulation of Generalised Beam Theory (GBT) developed to analyse the elastic buckling behaviour of non-circular hollow section (NCHS) members is presented. Since the radius varies along the cross-section mid-line, the main concepts involved in the determination of the deformation modes are adapted to account for the specific aspects related to elliptical cross-section geometry. After that, two independent sets of fully orthogonal deformation modes are determined: (i) local-shell modes satisfying the null membrane shear strain but exhibiting transverse extension and (ii) shell-type modes satisfying both assumptions of null membrane shear strain and null transverse extension. In order to illustrate the application, capabilities and versatility of the formulation, the local and global buckling behaviour of elliptical hollow section (EHS) members subjected to compression is analysed. In particular, in-depth studies concerning the influence of member length on the variation of the critical load and corresponding buckling mode shape are presented. Moreover, the GBT results are compared with estimates obtained by means of shell finite element analyses and are thoroughly discussed. The results show that short to intermediate length cylinders buckle mostly in local-shell modes, exhibiting only transverse extension, while intermediate length to long cylinders buckle mostly in shell-type modes (distortional and global modes), which are characterized by transverse bending and primary warping displacements. It is also shown that the present formulation is very efficient from the computational point of view since only three deformation modes (one local-shell, one distortional and one global) are required to evaluate the buckling behaviour of EHS cylinders for a wide range of lengths.     

Multiaxial cyclic deformation and non-proportional hardening employing discriminating load paths

Some novel discriminating multiaxial cyclic strain paths with incremental and random sequences were used to investigate cyclic deformation behavior of materials with low and high sensitivity to non-proportional loadings. Tubular specimens made of 1050 QT steel with no non-proportional hardening and 304L stainless steel with significant non-proportional hardening were used. 1050 QT steel was found to exhibit very similar behavior under various multiaxial loading paths, whereas significant effects of loading sequence were observed for 304L stainless steel. In-phase cycles with a random sequence of axial-torsion cycles on an equivalent strain circle were found to cause cyclic hardening levels similar to 90° out-of-phase loading of 304L stainless steel. In contrast, straining with a small increment of axial-torsion on an equivalent strain circle results in higher stress than for in-phase loading of 304L stainless steel, but the level of hardening is lower than for 90° out-of-phase loading. Tanaka’s non-proportionality parameter coupled with a Armstrong–Fredrick incremental plasticity model, and Kanazawa et al.’s empirical formulation as a representative of such empirical models were used to predict the stabilized stress response of the two materials under variable amplitude axial-torsion strain paths. Consistent results between experimental observations and predictions were obtained by employing the Tanaka’s non-proportionality parameter. In contrast, the empirical model resulted in significant over-prediction of stresses for 304L stainless steel.     

An experimental investigation of T-beam stability under bending

This paper presents an experimental setup used to study the response and stability of T-beams subjected to pure bending. The setup consists of a four-point bending device instrumented to measure the moment and curvature in the beam. Special grips are used to attach the specimens to the bending device and enforce a no-twist condition at the ends of the beams. A special instrument is used to measure deformations induced by buckling along the axis of the beam. Results are presented for the cases of monotonic and cyclic bending of short beams that buckle in a local mode. The results indicate that the lateral deflection of the web of the beams develops a ripple relatively early in the bending process. Local buckles arise from localization of the amplitude of the ripple at a given point along the specimen.     

Buckling and post-buckling of long pressurized elastic thin-walled tubes under in-plane bending

The present paper focuses on the structural stability of long uniformly pressurized thin elastic tubular shells subjected to in-plane bending. Using a special-purpose non-linear finite element technique, bifurcation on the pre-buckling ovalization equilibrium path is detected, and the post-buckling path is traced. Furthermore, the influence of pressure (internal and/or external) as well as the effects of radius-to-thickness ratio, initial curvature and initial ovality on the bifurcation moment, curvature and the corresponding wavelength, are examined. The local character of buckling in the circumferential direction is also demonstrated, especially for thin-walled tubes. This observation motivates the development of a simplified analytical formulation for tube bifurcation, which considers the presence of pressure, initial curvature and ovality, and results in closed-form expressions of very good accuracy, for tubes with relatively small initial curvature. Finally, aspects of tube bifurcation are illustrated using a simple mechanical model, which considers the ovalized pre-buckling state and the effects of pressure.     

不同失效模式下轴压管状结构的吸能特性比较

圆管、方管等管状结构受轴向的压缩作用,是工程上常见的一种结构受力形式.由于几何尺寸、边界条件和材料特性的不同,管状结构可以发生5种不同的失效模式:渐进屈曲、整体失稳、翻转、膨胀和劈裂.本文综述了近年来管状结构在轴压作用下不同失效模式的理论建模、实验测试和数值仿真研究结果,并对5种失效模式的力学响应、能量吸收特性进行了对比与分析.     

Low-endurance fatigue behavior under combined bending and torsion

Specimens made of thin-walled low-carbon steel tubes are subjected to combined bending and twisting moments of such magnitudes as to lead to fatigue failure within some one-thousand loading cycles. Tests are run, at room temperature, under conditions of controlled angle of twist and constant rate of loading. Experimental results show that the fatigue life is best expressed in terms of the amplitude of equivalent stress and ultimate strength of the material in potential form. For same maximum stress amplitude, test results show, within the scope of present investigations, that conditions of combined bending and torsion lead to lower fatigue life than those of reversed torsion.     

Damage constitutive for high strength concrete in triaxial cyclic compression

A constitutive relationship for high strength concrete in triaxial monotonic and cyclic compressions is developed based on the continuum damage mechanics. The bounding surface concept is employed in the formulation of the theoretical model. An experimental program was undertaken in order to establish databases for high strength concrete under triaxial monotonic and cyclic compressions. The stress-strain responses of high strength concrete subjected to triaxial monotonic and cyclic compressions were acquired through an experimental program. Comparison of the stress strain results indicates good agreement between the theoretical model and the experimental data.     

剪切变形对FGM圆板轴对称屈曲的影响

基于一阶剪切变形板理论，推导了功能梯度材料圆形板在边界面内均布压力作用下的轴对称屈曲方程。在推导过程中，忽略了前屈曲耦合变形。利用一阶板理论与经典板理论屈曲方程之间在数学形式上的相似性，得到了一阶板理论下功能梯度材料圆板与经典板理论下均匀圆板临界屈曲载荷之间的解析关系。利用这个解析关系，可以直接从已有的较为简单的经典理论的结果，获得一阶板理论下功能梯度材料板的临界屈曲载荷。     

Moment-curvature models under reverse cyclic straining

The paper describes the development ofM-? models from stress-strain curves resulting from tests on axially loaded mild-steel specimens subjected to cyclic alternating plastic strains. These “push-pull” tests lead to the formulation of a power law which can be used to predict the nonlinear response of sections in bending under similar ambient conditions. These predictions are compared with experiments on beams subjected to pure bending involving strain control. The resulting load-deflection curves, derived directly from experimentalM-? models and indirectly from theoreticalM-? models arising from stress-strain data, are themselves compared with similar experimental data in the case of cantilever beams under tip loads.     

Elastoplastic modeling of circular fiber-reinforced ductile matrix composites considering a finite RVE

A micromechanical elastoplastic damage model considering a finite RVE is proposed to predict the overall elastoplastic damage behavior of circular fiber-reinforced ductile (matrix) composites. The constitutive damage model proposed in our preceding work (Kim and Lee, 2009) considering a finite Eshelby’s tensor (Li et al., 2005, Wang et al., 2005) is extended to accommodate the elastoplastic behavior of the composites. On the basis of the exterior-point Eshelby’s tensor for circular inclusions and the ensemble-averaged effective yield criterion, a micromechanical framework for predicting the effective elastoplastic damage behavior of ductile composites is derived. A series of numerical simulations are carried out to illustrate stress–strain response of the proposed micromechanical framework and to examine the influence of a Weibull parameter on the elastoplastic behavior of the composites. Furthermore, comparisons between the present predictions and experimental data available in the literature are made to further assess the predictive capability of the proposed model.     

功能梯度与均匀圆板静动态解之间的相似转换关系

基于经典板理论,研究了功能梯度材料圆板的轴对称弯曲、屈曲和自由振动解与相应的均匀材料圆板解之间的转换关系.通过消去拉-弯耦合项得到了以挠度函数表示的功能梯度圆板的弯曲、屈曲和自由振动控制方程.分析功能梯度圆板与均匀圆板的控制方程之间的相似性,得到了功能梯度材料圆板与均匀圆板的解之间解的相似转换关系,在假定FGM圆板的材料性质沿厚分别以幂函数和指数函数的度变规律后,给出了相应的转换系数的解析表达式.该系数集中反映了功能梯度圆板的材料非均匀性.在已知均匀材料圆板轴对称解的条件下,可将功能梯度材料圆板轴对称问题的求解转化为相似转换系数的计算问题.这一方法可为非均匀板的求解提供了十分便捷有效的途径,而且便于工程应用.     

拱暨索拱面内稳定性研究的传递矩阵法

为探究拱桥面内稳定问题求解的新途径,应用传递矩阵法对径向均布荷载作用下的圆拱面内屈曲微分方程进行解答,利用边界条件导出其特征方程,从而求得其屈曲荷载。同时,结合力法以及拱上荷载集度与轴力的关系,将该理论方法推广到承受集中荷载的变截面拱以及索拱组合结构的稳定分析中,并和有限元ANSYS计算结果进行对比,验证了本文理论和方法的正确性。最后,研究了不同荷载工况下的边界条件、圆心角和截面惯性矩对拱结构面内稳定性的影响。结果表明,索拱结构的面内稳定性优于纯拱结构。     

Stability experiments on the strongest columns and circular arches

Recent theories predict the cross-sectional shapes for the strongest, end-loaded column and the radially loaded arch whose neutral axis is circular. These tapered shapes have higher predicted load-carrying capacities than uniform columns or arches of equal weight and length or span. The purpose of the present experimental investigation was to study the stability of these configurations, modified so that no experimental model had the predicted cross-sectional area of zero where the bending moments vanished. Precise buckling loads were measured on metal models of tapered, pinned-end columns using strain gages and a unique modification of Southwell's method. The dynamic stability of these end-loaded columns under transverse vibrations was observed. Static stability tests were also performed on Plexiglas models of the strongest shaped circular arch and on the uniform circular arch of equal weight and span. The predicted buckling loads for the strongest shapes agreed reasonably well with measurements. The shaped circular arch, however, was found to be an inefficient design for loading applied uniformly across the span rather than in the radial direction.     

Bending instabilities of elastic tubes

The present paper examines instabilities of long thin elastic tubes. Both initially straight and initially bent tubes are analyzed under in-plane bending. Tube response, a combination of ovalization instability and bifurcation instability (buckling), is investigated using a nonlinear finite element (FE) technique, which employs polynomial functions in the longitudinal tube direction and trigonometric functions to describe cross-sectional deformation. It is demonstrated that the interaction between the two instability modes depends on the value and the sign of the initial tube curvature. The ovalization of initially bent tubes is examined in detail and, in particular, the case of opening moments. Furthermore, the paper emphasizes on bifurcation instability. It is shown that buckling may occur prior to or beyond the ovalization limit point, depending on the value of the initial curvature. Using the nonlinear FE formulation, the location of bifurcation on the primary path is detected, post-buckling equilibrium paths are traced, and the corresponding wavelengths of the buckled configurations are calculated. Moreover, results over a wide range of initial curvature values are presented, extending the findings of previous works. Finally, several analytical approaches, introduced in previous research works, are also employed to estimate the moments causing ovalization and bifurcation instability. These approaches are based on nonlinear flexible shell theory or simplified ring analysis. The efficiency and accuracy of those analytical methods with respect to the nonlinear FE formulation are examined.     

Non-linear buckling and postbuckling behavior of thin-walled beams considering shear deformation

The static stability of thin-walled composite beams, considering shear deformation and geometrical non-linear coupling, subjected to transverse external force has been investigated in this paper. The theory is formulated in the context of large displacements and rotations, through the adoption of a shear deformable displacement field (accounting for bending and warping shear) considering moderate bending rotations and large twist. This non-linear formulation is used for analyzing the prebuckling and postbuckling behavior of simply supported, cantilever and fixed-end beams subjected to different load condition. Ritz's method is applied in order to discretize the non-linear differential system and the resultant algebraic equations are solved by means of an incremental Newton-Rapshon method. The numerical results show that the beam loses its stability through a stable symmetric bifurcation point and the postbuckling strength is in relation with the buckling load value. Classical predictions of lateral buckling are conservative when the prebuckling displacements are not negligible and the non-linear buckling analysis is required for reliable solutions. The analysis is supplemented by investigating the effects of the variation of load height parameter. In addition, the critical load values and postbuckling response obtained with the present beam model are compared with the results obtained with a shell finite element model (Abaqus).     

Torsional buckling of an elastic thick-walled tube made of rubber-like material

The elastic stability of a rubber-like, thick-walled tube which is subjected to finite torsional deformation is investigated both theoretically and experimentally. The analysis is based on the theory of finite elastic deformations, in cojunction with the method of small displacements superposed on large elastic deformations. The governing field equations are solved by a numerical scheme which determines the critical buckling torque and the associated buckling mode of the tube. The predicted results compare closely with the experimental measurements of the buckling of thick-walled silicone rubber tubes tested under finite twist.