组合杆件扭转实验设计与课程教学实践

设计制作了一种比较复杂的弯扭组合变形结构作为实验装置.基于材料力学空间杆件的弯扭组合变形的强度计算,确定施加扭矩载荷的弹性极限值.对该装置进行了两组扭转实验测试,测试结果和理论计算结果比较表明,二者吻合较好.本实验是对材料力学实验改革的有益尝试,可直接应用于材料力学实验教学中.     

齿轮系统传动轴受横向冲击的响应分析

将齿轮传动系统的齿轮轴承简化为具有集中质量的固支梁,将齿轮受到啮合齿轮的意外撞击看成是质量块对梁的冲击。给出弯扭组合的Mises屈服条件,指出传动轴受冲击时不能忽略扭矩作用。分析了弯曲和扭转作用下的结构响应,进行了应变率修正,给出特殊情况下弯扭响应的简化分析。算例表明,弯扭冲击下传动轴的横向位移和扭转角都较大,不可忽略应变率效应;传动轴直径是影响横向位移的重要因素。     

基于弯扭组合梁元的多段折叠翼离散突风响应

基于弯扭组合梁元对大展弦比多段折叠翼的离散突风响应特性进行了研究。首先，将平面一般梁元叠加扭转自由度得到一种新的弯扭组合梁元，建立包含折叠角参数的缩减有限元模型。其次，对片条理论进行修正以得到不同折叠角度下弯扭组合梁元上的气动力，构建多段折叠翼在离散突风作用下的动力学方程。最后，引入Laplace变换处理动力学方程中的积分微分项，得到折叠角对翼尖加速度、翼根弯/扭矩等响应的影响。一个近地面无人机三段式折叠翼的算例结果表明，机翼固有频率会随着折叠角的变化呈现非线性性态，相比舒展状态，折叠角的存在虽不能明显减小翼尖加速度，但能够有效减小翼根弯/扭矩响应。     

发动机叶片扭转和弯曲变形同步测量新方法

扭转和弯曲变形测量可以确定叶片弯扭变形耦合的特征,为叶片弯扭耦合分析提供可用的试验手段。本文提出了一种发动机叶片扭转和弯曲变形同步测量的新方法,其中,扭转角度测量方法能更加灵活地应用于测量叶片类形状不规则构件的扭转变形,而弯曲变形测量方法解决了叶片变形方向未知且存在弯扭耦合时的叶片变形测量问题,从而可实现对叶片截面扭转和弯曲变形的同步测量。对上述测量方法进行了专门的验证试验,结果表明:与传统方法测量结果相比,扭转角度测量偏差小于1%,挠度测量偏差小于2%,满足工程测量精度要求。     

轴向受载的Timoshenko薄壁梁的弯扭耦合动力响应

利用简正模态法研究各种集中载荷和分布载荷作用下单对称轴向受载的Timoshenko薄壁梁的弯扭耦合动力响应。该弯扭耦合梁所受到的载荷可以是集中载荷或沿着梁长度分布的分布载荷。目前研究中采用考虑了轴向载荷、剪切变形和转动惯量影响的Timoshenko薄壁梁理论。首先建立轴向受载的Timoshenko薄壁梁结构的普遍运动微分方程并进行其自由振动的分析。一旦得到轴向受载的Timoshenko薄壁梁的固有频率和模态形状，利用简正模态法计算薄壁梁结构的弯扭耦合动力响应。针对具体算例，提出并讨论了动力弯曲位移和扭转位移的数值结果。     

考虑剪切变形影响的开口薄壁梁约束扭转的扭转角分析

以开口薄壁梁约束扭转分析理论为基础,通过初参数法推导开口薄壁梁在外扭矩作用下产生的扭转角;推导了槽钢扭转剪应力不均匀系数的精确计算公式;为得到与Timoshenko梁理论类似的简化公式,探讨圣维南扭矩可以忽略时的情形,阐述了简化方法与理论解之间的误差来源,定义了剪切变形影响参数。通过具体算例分析跨度、高宽比等参数对扭转角的影响,并与符拉索夫理论、ANSYS壳单元、简化方法的计算结果进行对比。计算结果表明:当弯扭系数、高宽比恒定时,本文方法的解与符拉索夫解的最大误差从跨径为30m的16.15%到跨径为5m的89.5%;当弯扭系数、跨径恒定时,本文方法的解与符拉索夫解的最大误差从高宽比为1的6.9%到高宽比为5的62.44%;随跨径减小或高宽比增大,剪切变形不容忽略。当弯扭系数与跨径的乘积减小到一定值时可以忽略圣维南扭矩从而得到简化公式;高宽比增大,扭转剪应力不均匀系数先减小后增大。     

DNA纳米管的扭转刚度模型

刚度是衡量材料弹性变形难易程度的一个定量表征参数,与DNA纳米管静动力学特性及其结构生物功能密切相关．本文致力于研究DNA纳米管的扭转刚度．首先,在六角形均匀封装条件下,考虑到单个DNA杆件弯扭组合问题的静不定特点,我们利用平衡方程、变形协调方程和弹性本构方程,合理预测了DNA纳米管扭转实验中单个DNA杆件的弯扭组合变形,由此给出了DNA纳米管扭转刚度预测的解析模型．最后的结果表明：随着DNA杆数的增加,DNA纳米管的弯曲刚度显著增加,而其扭转刚度却几乎不变,合理解释了扭转实验中发现的现象．有关结论为DNA折叠结构的设计和应用提供了参考．     

空间曲梁单元的扭转修正系数研究

三维空间曲梁有限单元模型是模拟曲梁结构的有效数值方法,可以考虑曲梁的弯扭耦合特性,最为符合曲梁的几何和受力特征.由于有限元法采用梁理论的平截面假定,空间曲梁单元上的扭转剪应力分布与实际曲梁截面上的扭转剪应力不同,从而会导致扭转刚度和扭转变形的计算失真.本文基于剪切应变能等效原理,推导了不同长宽比的矩形截面空间曲梁单元的...     

确定性载荷作用下Timoshenko薄壁梁的弯扭耦合动力响应

建立了一种普遍的解析理论用于求解确定性载荷作用下Timoshenko薄壁梁的弯扭耦合动力响应。首先通过直接求解单对称均匀Timoshenko薄壁梁单元弯扭耦合振动的运动偏微分方程，给出了计算其自由振动的精确方法，并导出了Timoshenko弯扭耦合薄壁梁自由振动主模态的正交条件。然后利用简正模态法研究了确定性载荷作用下单对称Timoshenko薄壁梁的弯扭耦合动力响应，该弯扭耦合梁所受到的荷载可以是集中载荷或沿着梁长度分布的分布载荷。最后假定确定性载荷是谐波变化的，得到了各种激励下封闭形式的解，并对动力弯曲位移和扭转位移的数值结果进行了讨论。     

开闭裂纹转子的弯扭耦合振动研究

以水平放置的Jeffcott裂纹转子为研究对象，建立了开闭裂纹转子弯扭耦合振动的非线性运动微分方程，并用数值方法分析了纯弯曲振动与弯扭耦合振动情况下转子的动力响应。结果表明：弯扭耦合振动是由转子质量的偏心和转子自重的共同作用而产生的，当质量偏心很小时可以不考虑扭转振动的影响，当偏心较大时，扭转对弯曲振动的影响主要体现在高转速部分，且由于裂纹开闭的作用，使扭转的耦合作用存在一个范围，随裂纹深度的增加，扭振影响的转速下限就会越低，但当裂纹较深、转速较快时，扭转对弯曲振动在作用范围内有明显的影响，使频谱图和轴心轨迹都发生较大的变化，且对转速的变化极为敏感，因此在故障诊断时必须对扭转的耦合作用高度重视。     

用边界元法求一般截面的弯曲中心

使用Saint-Venant弯曲理论,将一般截面柱体的横向弯曲问题,归结为解两个同类型的边界积分方程,并用此求得了柱体的弯曲函数和附加扭转函数,在此基础上,可用边界元法确定一般截面的弯曲中心。最后为了说明方法的应用,给出了一个数值算例。     

Bending analysis of magnetoelectroelastic nanoplates resting on Pasternak elastic foundation based on nonlocal theory

Based on the nonlocal theory and Mindlin plate theory, the governing equations (i.e., a system of partial differential equations (PDEs) for bending problem) of magnetoelectroelastic (MEE) nanoplates resting on the Pasternak elastic foundation are first derived by the variational principle. The polynomial particular solutions corresponding to the established model are then obtained and further employed as basis functions with the method of particular solutions (MPS) to solve the governing equations numerically. It is confirmed that for the present bending model, the new solution strategy possesses more general applicability and superior flexibility in the selection of collocation points. The effects of different boundary conditions, applied loads, and geometrical shapes on the bending properties of MEE nanoplates are evaluated by using the developed method. Some important conclusions are drawn, which should be helpful for the design and applications of electromagnetic nanoplate structures.     

弹性薄板弯曲问题的等价的直接变量边界积分方程

建立平面弹性薄板弯曲问题理论中具有直接变量的等价边界积分方程，传统的直接变量边界积分方程，它们都不是等价的，对此进行了深入的讨论。     

复合受力下焊接栓钉SRC柱抗扭承载力计算

为研究压、弯、剪、扭复合受力下焊接栓钉型钢混凝土(SRC)柱的抗扭承载力计算方法,基于滞回性能试验结果,分析了试验过程和破坏形态,利用了空间桁架理论与叠加原理,提出了复合受力下焊接栓钉SRC柱抗扭计算模型和强度统一方程.结果表明:所提出的强度统一方程和抗扭承载力计算方法的计算结果与试验结果均值误差均在3％内,吻合较好.     

A thin-sheet, combined tension and bending specimen

Validating stress intensity factor solutions for combined tension and bending is an arduous task because the necessary experimental data are not readily available. Toward this end, a tension and bending test specimen was designed to produce controllable levels of both tension stress and bending stress at the crack location. The specimen was made from 2024-T3 clad aluminum, which is commonly used in aircraft structures. The need for testing multiple specimens of various geometries and stress levels prompted the development of an analytical tool for specimen design. An extention of the Schijve line model, based on simple beam theory, was developed to calculate the stress distributions of tension and bending through the length of the specimen. A comparison of measured static strain levels with those predicted by the model showed the model to be accurate to within 5 percent, confirming its efficacy for specimen design. As expected, for the same remote stress (100 MPa), cracks in the tension and bending specimens grew faster than those in middle-cracked tension specimens.     

Optimization of a metal honeycomb sandwich beam-bar subjected to torsion and bending

In this paper, we analyze a metal honeycomb sandwich beam/torsion bar subjected to combined loading conditions. The cell wall arrangement of the honeycomb core is addressed in the context of maximizing resistance to either bending, torsion, or combined bending and torsion for given dimensions, face sheet thicknesses and core relative density. It is found that the relative contributions of the honeycomb core to torsion and bending resistances are sensitive to the configuration of cell walls and the optimal properties significantly exceed those of stochastic metallic foams as sandwich beam core materials for this configuration.     

Saint-Venant’s Problem for Compound Piezoelectric Beams

The solution of the Saint-Venant’s Problem for a slender compound piezoelectric beam presented in this paper generalizes the recent solution by the authors and E. Harash (J. Appl. Mech. 11:1–10, 2007) for a homogeneous piezoelectric beam and the solution for a compound elastic beam developed by O. Rand and the first author (Analytical Methods in Anisotropic Elasticity with Symbolic Computational Tools, Birkhauser, Boston, 2005). Justification for this approximation emerges from the St. Venant’s Principle. The stress, strain and (electrical) displacement components (“solution hypothesis”) are presented as a set of initially assumed expressions involving twelve tip loading parameters, six unknown weight coefficients, and three pairs of torsion/bending functions of two variables. Each pair of functions satisfies the so-called coupled non-homogeneous Neumann problem (CNNP) in the cross-sectional domain. The work develops concepts of the torsion/bending functions, the torsional rigidity and piezoelectric shear center, the tip coupling matrix, for a compound piezoelectric beam. Examples of exact and approximate solutions for rectangular laminated beams made of transtropic materials are presented.      

有初应力钢筋混凝土压弯扭构件非线性有限元分析

钢管初应力是钢管混凝土在大跨度桥梁,高层超高层建筑应用中广大工程技术人员关心的问题,本文在钢材随动强化模型和混凝土边界模型的基础上编制了计算有初应力的钢管钢混凝压弯扭构件全过程曲线的非线性有元程序。     

On the truth of nanoscale for nanobeams based on nonlocal elastic stress field theory： equilibrium, governing equation and static deflection

This paper has successfully addressed three critical but overlooked issues in nonlocal elastic stress field theory for nanobeams： （i） why does the presence of increasing nonlocal effects induce reduced nanostructural stiffness in many, but not consistently for all, cases of study, i.e., increasing static deflection, decreasing natural frequency and decreasing buckling load, although physical intuition according to the nonlocal elasticity field theory first established by Eringen tells otherwise？ （ii） the intriguing conclusion that nanoscale effects are missing in the solutions in many exemplary cases of study, e.g., bending deflection of a cantilever nanobeam with a point load at its tip; and （iii） the non-existence of additional higher-order boundary conditions for a higher-order governing differential equation. Applying the nonlocal elasticity field theory in nanomechanics and an exact variational principal approach, we derive the new equilibrium conditions, do- main governing differential equation and boundary conditions for bending of nanobeams. These equations and conditions involve essential higher-order differential terms which are opposite in sign with respect to the previously studies in the statics and dynamics of nonlocal nano-structures. The difference in higher-order terms results in reverse trends of nanoscale effects with respect to the conclusion of this paper. Effectively, this paper reports new equilibrium conditions, governing differential equation and boundary condi- tions and the true basic static responses for bending of nanobeams. It is also concluded that the widely accepted equilibrium conditions of nonlocal nanostructures are in fact not in equilibrium, but they can be made perfect should the nonlocal bending moment be replaced by an effective nonlocal bending moment. These conclusions are substantiated, in a general sense, by other approaches in nanostructural models such as strain gradient theory, modified couple stress models and experiments.     

Scaling of dislocation-based strain-gradient plasticity

By taking into account the dislocations that are geometrically necessary for producing a curvature or twist of the atomic lattice in crystals, Gao et al. recently developed a theory of strain-gradient plasticity on the micrometer scale and showed that it agrees relatively well with the tests of hardness, torsion and bending of copper on the micrometer scale. This paper subjects this theory to an asymptotic scaling analysis. It is shown that the small-size asymptotic limit of this theory exhibits (1) an unusually strong size effect in which the corresponding nominal stresses in geometrically similar structures of different sizes D vary as D^−5/2, and (2) an asymptotic approach to a load-deflection diagram whose tangent stiffness gradually increases, starting with an infinitely small initial stiffness at infinitely small stress. Although this peculiar small-size asymptotic behavior might not be attainable within the practical applicability range of a continuum theory, it renders questionable any efforts to construct approximations of an asymptotic matching character, with a two-sided asymptotic support, which have previously been proven effective for quasibrittle materials such as concrete, rock, ice and fiber composites. A possible simple modification of the existing theory with respect to the small-size asymptotic properties is suggested. However, the questions of experimental justification of such a modification and its compatibility with the dislocation theory will require further study. The small-size asymptotic properties of other strain gradient theories of plasticity have not been analyzed, except for those of the previous Fleck-Hutchinson theory, which have been found reasonable.