Sensitivity of inelastic response to numerical integration of strain energy

The exact solution to the quasi-static, inelastic response of a cantilever beam of rectangular cross-section subjected to a bending moment at the tip is obtained. The material of the beam is assumed to be linearly elastic-linearly strain-hardening. This solution is then compared with three different numerical solutions of the same problem obtained by minimizing the total potential energy using Gaussian quadratures of two different orders and a Newton-Cotes scheme for integrating the strain energy of deformation. Significant differences between the exact dissipative strain energy and its numerical counterpart are emphasized. The consequence of this on the non-linear transient responses of a beam with solid cross-section and that of a thin-walled beam on elastic supports under impulsive loads are examined.     

机电耦合载荷下的压电层合板瞬态响应分析

针对压电层合板在机电耦合激振下的瞬态响应问题, 提出一种高效混合数值计算方法。经过位移场、 电势场在厚度方向的离散, 利用机电耦合理论和哈密顿原理, 推导出结构的运动方程。引入傅里叶变换, 得到波数域内运动控制方程。应用模态分析方法求解波数域内的位移场和电势场, 对结果进行傅里叶逆变换, 得到空间域内的瞬态响应。以PZT-5A/0° PVDF铺层两相材料复合压电层合板为算例, 分析了力、 电耦合线载荷激励下, 位移场和电势场的瞬态响应历程与分布规律, 计算结果给出了该结构的动力学基本特征。该方法结合了有限元法、 傅里叶变换和模态分析法, 计算高频载荷激振下的压电层合板瞬态响应较一般有限元法大幅减少了单元的划分。该方法可推广至分析任意机电载荷下的各类铺层材料压电层合板瞬态响应问题。      

Proposed design chart of mechanical joints on steel-PHC composite piles

A fundamental study of a mechanical joint in a steel-PHC composite pile subjected to combined loads was done using three-point bending tests and 3D finite element analyses. The three-point bending tests were conducted to evaluate load-deformation response, strain distribution on the pile, ultimate bending moment and failure mode of the mechanical joint on steel-PHC composite piles. In addition, 3D finite element analysis for the mechanical joint was performed and then, the stress distributions and the maximum load resistances of each parts of the joint were estimated by comparing the calculated stresses to the yielding stresses of the joint materials. The 3D numerical methodology in the present study represents a realistic mechanism of mechanical joints. Through detailed numerical analysis, it is found that the behaviour of mechanical joint of composite piles shows safe side under working load. Based on these results, the design chart for steel-PHC piles has been proposed to be convenient for preliminary design stage which can be used to evaluate the safety of mechanical joints.     

含剪力销(锥)螺栓法兰连接结构弯剪扭耦合振动研究

大型工业装备中的连接结构,往往处于复杂多样的外载荷环境中,其振动特性分析尤为重要。针对含剪力销(锥)的螺栓法兰连接结构的振动特性开展研究,根据该类结构在实际工况中受弯、剪、扭组合作用的特点,建立了两种多自由度的质量-非线性弹簧系统,分别讨论了系统在弯剪组合作用以及扭转作用下的振动特性、耦合关系。在此基础上,研究锥角不同、装配间隙不同对螺栓最大拉力的影响,并给出相应关系图;指出在两种工况下剪力销最佳设计角度区间及相应的装配间隙。     

Testing structural concrete beam elements

A method for testing structural concrete beam and column elements subjected to axial load, bending moment and shear is described. The information presented includes: the test set-up, with particular emphasis on how the loads are applied using a combination of hydraulic actuators and rigid links connected to a yoke at each end of the specimen; the specimen boundary conditions which were designed to reduce the shear transferred by strut action; as well as highlights from the first 17 tests which involved monotonic shear, reverse cyclic shear and reverse cyclic axial load on beam elements up to 350 mm×700 mm in cross-section.     

Plastic strains and the macroscopic critical plane orientations under combined bending and torsion with constant and variable amplitudes

Round cross-section specimens made of 18G2A steel were subjected to different combinations of constant- and variable-amplitude bending and torsion. The fatigue tests were performed under bending and torsion with moment control in the high cycle fatigue regime. Two approaches were used to calculate stress courses from moment histories. In one approach, stresses and strains were computed using simple elastic beam theory (nominal stresses). In the other approach, time courses of moments were used to calculate stress and strain histories taking into account plastic strains and non-linear stress distribution along the specimen cross-section on the basis of the algorithm described in the paper. The loading histories computed according the two methods were used to calculate the critical plane orientations. It was assumed that the orientation of the critical plane is controlled only by shear or tensile fatigue mechanism. Moreover, the theoretical critical plane positions were compared to the experimental macroscopic fatigue fracture plane orientations.     

A NEW CRITERION OF FATIGUE STRENGTH OF A ROUND BAR SUBJECTED TO COMBINED STATIC AND REPEATED BENDING AND TORSION

Abstract Criteria of fatigue strength of a round bar subjected to combined static and repeated bending and torsion have already been published by Findley and Sines together with empirical formulas by Gough. However, it is only Sines'criterion, by which the fatigue limit under combined bending and torsion is calculated, when completely reversed and pulsating fatigue limits and mean stresses are known. The authors show that Sines'criterion does not conform strictly with experimental results and they correct Sines'criterion so that fatigue failure occurs when the octahedral shearing stress amplitude attains a material constant value which decreases not only in proportion to the octahedral normal mean stress, but also in proportion to the octahedral normal stress amplitude. Applying the authors'criterion to combined repeated bending and torsion, plus coexistent static bending and torsion, a design formula was derived. The formula was compared with experimental results of Gough.     

The elasticity problem for a thick-walled cylinder containing a circumferential crack

The elasticity problem for a long hollow circular cylinder containing an axisymmetric circumferential crack subjected to general nonaxisymmetric external loads is considered. The problem is formulated in terms of a system of singular integral equations with the Fourier coefficients of the derivative of the crack surface displacement as density functions. The stress intensity factors and the crack opening displacement are calculated for a cylinder under uniform tension, bending by end couples, and self-equilibrating residual stresses.     

Analysis of local bending effects in sandwich plates with orthotropic face layers subjected to localised loads

This paper presents a method for the approximate analysis of local bending effects in sandwich plates with specially orthotropic face layers subjected to localised external loads. The local bending analysis is based on the assumption that the relative deflection of the loaded face against the deflection of the face not loaded can be modelled by application of an elastic foundation model. This is achieved by introducing a two-parameter elastic foundation model which takes into account the shearing interaction effects between the loaded face and the core material. An approximate solution to the complete problem is achieved by superposition of the local solution and an overall solution derived by application of classical sandwich plate theory. The results obtained are compared with finite element analysis results, and a good match between the solutions is observed. Finally a brief parametric study shows that the local bending effects are strongly influenced by the modular ratio and the thickness of the loaded face.     

Probabilistic analysis of delamination onset in linear anisotropic elastic and viscoelastic composite columns

Previously developed deterministic and stochastic combined load invariant failure criteria are used to determine the onset of delamination in elastic and viscoelastic columns. The analysis includes the effects of initial imperfections as well as offset column loads and transverse shear contributions. The delamination predictions are found to be sensitive to the magnitude of applied loads and of initial imperfections. Illustrative numerical examples are presented for elastic and viscoelastic columns with random combined failure stresses in bending, shear, compression and with normal interlaminar stresses. Probabilities of delamination onset are established for various axial loads and initial imperfections and in the viscoelastic columns additionally as a function of lifetime. Since the failure theories consider the combined effects of bending, shear, compression and normal interlaminar stresses, delamination onset is predicted at smaller axial loads than the critical buckling loads in the elastic case and at shorter viscoelastic lifetimes compared to equivalent columns with no delamination effects.     

考虑剪切变形时薄壁箱梁的挠曲分析

为分析剪切效应对薄壁箱梁受力特性的影响,利用微板的面内剪切及平衡微分方程,分别推导出不考虑和考虑薄壁箱梁各板面内剪切效应的弯曲位移函数。选取剪切效应引起的附加挠度作为广义位移,通过定义的剪切广义力矩及剪切翘曲位移函数,将剪切变形状态从全梁挠曲变形状态中分离出来,作为独立的变形状态进行分析。为满足全截面翘曲应力的自平衡条件,引入两个截面特性参数对广义剪切翘曲位移函数进行了修正。数值算例表明,按该文推导的薄壁箱梁剪切弯曲位移函数计算的两跨连续梁跨中截面应力与实测值及有限元值吻合良好。挠度计算表明:剪切效应使得该箱梁在集中和均布荷载作用下跨中挠度分别增大27%和24%。     

Creep and shrinkage analysis of composite systems under axial load and biaxial bending

The instantaneous and creep and shrinkage behaviour of composite steel-concrete sections subjected to axial load and biaxial bending is examined analytically using the age-adjusted effective modulus method and a stress relaxation procedure. Any cross-section that can be discretized in rectangular elements can be analysed using the approach described in this study. Material non-linearities (concrete cracking and crushing as well as steel yielding) are included in the formulation by empolying an interative numerical procedure. The analytical method was implemented in a computer program and case studies demonstrate that composite columns under complex loads experience a considerable redistribution of stresses and strains, causing the degree of cracking and the secondary load effects (P-delta) to increase.     

Closed-form solution for crushing response of three-dimensional thin-walled “S” frames with rectangular cross-sections

The crushing behavior of thin-walled rectangular cross-section “S” shaped frames subjected to complex loading cases was analyzed. The results of the biaxial bending collapse of prismatic beams and the collapse under combined bending and compression developed earlier by the present authors were applied to a practical problem of a three-dimensional S frame. The analytical solution of the crushing resistance was derived and the two types of deformation modes were identified using the analysis of the fully plastic bending moment with different orientation angle of bending axis. It was shown that the critical aspect ratio of the rectangular cross-section separating the two deformation modes is 1.366. The analytically derived crushing force gave excellent correlation with the finite element results. The simplified calculation routines derived through this study can be applied to an early design stage of a car body.     

A non-equilibrium approach to processing Hopkinson Bar bending test data: Application to quasi-brittle materials

The aim of this paper was to describe a method of analysing the test data recorded during a Hopkinson Bar bending test. This three-point dynamic bending test was designed for testing the strength of materials under dynamic loads. It is carried out on a specimen consisting of a beam placed on two supports, which is subjected to an impact. The use of Hopkinson Bar as supports makes it possible to determine the forces and displacements at these points. An analytical solution for the transient response of a long beam subjected to a transverse impact was used to determine the impact force and the displacement. This procedure applies for the first few instants when the motions generated by the impact have not yet reached the supports, and the mechanical state of the specimen is identical to that of an unsupported beam. It is suitable for use with quasi-brittle materials for which failure occurs at the very beginning of the test. The material strength is determined at the time of failure, which is characterised by a sudden decrease in the bending moment. The results of a test in which a quasi-brittle material was loaded up to failure are presented and analysed as outlined above. The results obtained confirm the relevance of the present method.     

外露式钢柱脚恢复力特性分析

该文在外露式柱脚拟静力试验的基础上总结了柱脚在压弯和拉弯状态下的受力机理,提出了两种受力状态下柱脚的屈服承载力、极限承载力及转动刚度的计算公式。该文提出的承载力及转动刚度计算结果与试验结果的误差在10%左右,具有较高的计算精度。在试验研究的基础上还提出了两种状态下柱脚的恢复力模型:在压弯状态下,柱脚的滞回曲线呈"旗帜型",骨架曲线由不考虑强度退化的双折线模拟;在拉弯状态下,柱脚的承载力大幅度下降,滞回曲线为饱满曲线,骨架曲线为不考虑锚栓屈服后强度增加的理想弹塑性模型。恢复力模型与试验曲线吻合较好,可有效地反映出不同受力状态及不同锚栓布置下的外露式柱脚的弯矩转角行为,可有效用于分析整体框架的抗震性能。     

冷剪机刀架拉杆疲劳断裂研究

扭杆是剪切机中的关键零件,在剪切过程中受交变裁荷作用,在实际生产中常出现疲劳断裂现象。本文利用有限元对某厂冷剪机的拉杆进行疲劳分析,结果表明,在剪切力发生倾斜条件下,拉杆强度不能满足疲劳寿命长时间运行要求,有可能引起疲劳断裂。     

Transient analysis of tube rolling processes by a semi-analytical formulation

A semi-analytical formulation is presented for transient metal-forming processes which, being axisymmetric in geometry, are subjected to non-axisymmetric loads and boundary conditions. The problems are described in terms of the flow formulation, and the pseudo-concentration method (two material based) is used to account for time integration and non-axisymmetric free surfaces. Proper Fourier series expansion of both the scalar fields defined to identify the free surfaces and of all the variables of the mechanical problem allows the performance of an advective transport–corresponding to time integration–for a non-axisymmetric velocity field. A block diagonal matrix is obtained for each harmonic component, as it has been achieved for the constant time solution. The new configuration found as a result of this analysis is taken to calculate the velocity field for the incremented time, which in turn is used to perform the following time step.     

Mechanical Behavior of a Partially Encased Composite Girder with Corrugated Steel Web: Interaction of Shear and Bending

The synergistic use of partially encased concrete and composite girders with corrugated steel webs (CGCSWs) has been proposed to avoid the buckling of corrugated steel webs and compression steel flanges under large combined shear force and bending moment in the hogging area. First, model tests were carried out on two specimens with different shear spans to investigate the mechanical behavior, including the load-carrying capacity, failure modes, flexural and shear stress distribution, and development of concrete cracking. Experimental results show that the interaction of shear force and bending moment causes the failure of specimens. The bending-to-shear ratio does not affect the shear stiffness of a composite girder in the elastic stage when concrete cracking does not exist, but significantly influences the shear stiffness after concrete cracking. In addition, composite sections in the elastic stage satisfy the assumption of the plane section under combined shear force and bending moment. However, after concrete cracking in the tension field, the normal stresses of a corrugated web in the tension area become small due to the “accordion effect,” with almost zero stress at the flat panels but recognizable stress at the inclined panels. Second, three-dimensional finite-element (FE) models considering material and geometric nonlinearity were built and validated by experiments, and parametric analyses were conducted on composite girders with different lengths and heights to determine their load-carrying capacity when subjected to combined loads. Finally, an interaction formula with respect to shear and flexural strength is offered on the basis of experimental and numerical results in order to evaluate the load-carrying capacity of such composite structures, thereby providing a reference for the design of partially encased composite girders with corrugated steel webs (PECGCSWs) under combined flexural and shear loads.     

含圆周非贯穿裂纹悬臂管道的振动分析与裂纹识别

摘 要：根据线性断裂力学理论和应变能释放原理,推导了含圆周非贯穿裂纹管道在轴力、剪力和弯矩等荷载作用下的局部柔度系数方程,利用适应性Simpson方法编写了数值积分程序进行局部柔度系数求解,建立了含裂纹管道的二维有限元模型进行含裂纹悬臂管道的振动特性分析,应用等值线图原理进行了悬臂管道的裂纹识别。研究结果表明：本文裂纹模型克服了当前裂纹模型仅针对特定的荷载模式或非空心截面的缺陷,基于等值线图法能有效识别含裂纹悬臂管道的裂纹位置、深度。     

Bending moment and axial force interacting on solid timber beams

This paper describes the results of bending moment (M) and axial force (N) interaction tests on 220 solid spruce specimens with cross-section 80×160 mm. Depending on the timber strength, existing design models for M/N-interaction are fitted to the test results and different analytical approaches for the magnification or reduction of the initial moment due to beam deflections are evaluated. Interaction graphs of timber columns subjected to simultaneous action of bending moment and axial force exhibit convex curvilinearity viewed from the basis of the diagram. The degree of convexity depends on the slenderness of the column and on the strength of the timber. In the case of stocky columns subjected to high bending moments and small axial forces, the highest deviation from linearity can be observed. Design models published in standards and in literature describe the non-linearity of the interaction curve on the basis of an elastic stress-strain relationship in the tension portion of the cross-section and by a non-linear, “plastic” behaviour of the compression zone. Majority of former tests were performed on timber beams with small cross-section. For the case of interaction of bending and tension stress, only a limited number of results are available, because of the difficulty to apply high tension forces.