Theory of Flexural Shear, Bending and Torsion for a Thin-Walled Beam of Open Section

Aspects of the general Vlasov theory are examined separately as applied to a thin-walled channel section cantilever beam under free-end end loading. In particular, the flexural bending and shear that arise under transverse shear and axial torsional loading are each considered theoretically. These analyses involve the location of the shear centre at which transverse shear forces when applied do not produce torsion. This centre, when taken to be coincident with the centre of twist implies an equivalent reciprocal behaviour. That is, an axial torsion applied concentric with the shear centre will twist but not bend the beam. The respective bending and shear stress conversions are derived for each action applied to three aluminium alloy extruded channel sections mounted as cantilevers with a horizontal principal axis of symmetry. Bending and shear are considered more generally for other thin-walled sections when the transverse loading axes at the shear centre are not parallel to the section = s centroidal axes of principal second moments of area. The fixing at one end of the cantilever modifies the St Venant free angular twist and the free warping displacement. It is shown from the Wagner-Kappus torsion theory how the end constrained warping generates an axial stress distribution that varies with the length and across the cross-section for an axial torsion applied to the shear centre. It should be mentioned here for wider applications and validation of the Vlasov theory that attendant papers are to consider in detail bending and torsional loadings applied to other axes through each of the centroid and the web centre. Therein, both bending and twisting arise from transverse shear and axial torsion applied to each position being displaced from the shear centre. Here, the influence of the axis position upon the net axial and shear stress distributions is to be established. That is, the net axial stress from axial torsional loading is identified with the sum of axial stress due to bending and axial stress arising from constrained warping displacements at the fixing. The net shear stress distribution overlays the distributions from axial torsion and that from flexural shear under transverse loading. Both arise when transverse forces are displaced from the shear centre.

A new higher-order shear deformation theory and refined beam element of composite laminates

A new higher-order shear deformation theory based on global-local superposition technique is developed. The theory satisfies the free surface conditions and the geometric and stress continuity conditions at interfaces. The global displacement components are of the Reddy theory and local components are of the internal first to third-order terms in each layer. A two-node beam element based on this theory is proposed. The solutions are compared with 3D-elasticity solutions. Numerical results show that present beam element has higher computational efficiency and higher accuracy.

Layerwise third-order shear deformation theory with transverse shear stress continuity for piezolaminated plates

Regarding laminated structures,an electromechanically coupled Finite Element(FE)model based on Layerwise Third-Order Shear Deformation(LW-TOSD)theory is proposed for sta-tic and dynamic analysis.LW-TOSD ensures the continuity of in-plane displacements and trans-verse shear stresses.The current LW-TOSD can be applied to arbitrary multi-layer laminated structures with only seven Degrees of Freedom(DOFs)for each element node and eliminates the use of the shear correction factors.Moreover,a shear penalty stiffness matrix is constructed to sat-isfy artificial constraints to optimize the structural shear strain.A dynamic finite element model is obtained based on LW-TOSD using the Hamilton's principle.First,the accuracy of the current model is validated by comparing with literature and ABAQUS results.Then,this study carries out numerical investigations of piezolaminated structures for different width-to-thickness ratios,length-to-width ratios,penalty stiffness matrix,boundary conditions,electric fields and dynamics.

On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams

Due to the conflict between equilibrium and constitutive requirements,Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest.As an alternative,the stress-driven model has been recently developed.In this paper,for higher-order shear deformation beams,the ill-posed issue(i.e.,excessive mandatory boundary conditions(BCs)cannot be met simultaneously)exists not only in strain-driven nonlocal models but also in stress-driven ones.The well-posedness of both the strain-and stress-driven two-phase nonlocal(TPN-Strain D and TPN-Stress D)models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded(FG)materials.The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions.By using the generalized differential quadrature method(GDQM),the coupling governing equations are solved numerically.The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.

BENDING THEORIES FOR BEAMS AND PLATES WITH SINGLE GENERALIZED DISPLACEMENT

Classical bending theories for beams and plates can not be used for short, stubby beams and thick plates since transverse shearing effect is excluded, and ordinary theories with multiple generalized displacements can not be used for long, slender beams and thin plates since the innate relation between rotation angle and deflection is ignored. These two types of theories are not consistent due to the contradiction of dependence and independence of the rotation angle. Based on several basic assumptions, a new type of theories which not only include the transverse shearing effect is presented, but also the relation between potation angle and deflection is obtained. Analytical solutions of several simple beams are given. It has been testified by numerical examples that the new theories can be used for either long, slender beams and thin plates or short, stubby beams and thick plates.

结合贝叶斯-MCMC更新的RC梁抗剪承载力概率模型的可靠度分析

为分析钢筋混凝土(RC)梁抗剪承载力,首先,基于国内外100组RC梁抗剪承载力试验数据作为先验信息,结合我国GB 50010-2010规范的抗剪承载力,综合考虑混凝土与箍筋的材料强度、截面尺寸、剪跨比、配箍率等因素的影响,通过贝叶斯-马尔科夫链蒙特卡洛(MCMC)方法对我国规范模型进行更新与修正;随后,结合Monte Carlo模拟,对所建立的RC梁概率抗剪承载力模型进行可靠度分析,验证了该模型具有较好的计算精度与可靠性。结果表明:概率模型均值与试验值比值K的均值与标准差分别为1.013与0.171,试验值落在概率模型的95%置信区间范围内,且可靠指标分布在4.0左右,说明建立的概率模型具有较好的预测效果与可靠性。

基于固有频率的错断式坠落危岩体稳定系数计算模型

错断式坠落危岩体的安全稳定程度受后缘裂缝深度控制,基于静力学的稳定系数计算可得到后缘裂隙深度临界值,但静力学计算方法无法得到裂隙深度的实时变化。基于修正Timoshenko梁建立岩梁动力学方程,结合动力基础半空间理论对岩梁的约束刚度及边界条件做深入分析,得到不同裂缝深度条件下危岩体固有频率理论解析。基于数值计算验证固有频率算法的正确性,并得出结论:随裂隙深度增大,固有频率不断降低,固有频率对危岩体后缘裂隙深度变化较为敏感,根据危岩体的固有频率值可反算危岩体后缘裂隙深度。基于固有频率与危岩体后缘裂隙深度之间的关系建立错断式坠落危岩体稳定系数计算模型,并采用室内试验进行验证,得出结论:危岩体固有频率与其后缘裂隙深度近似为负线性相关。基于固有频率的错断式坠落危岩体稳定系数计算模型可为危岩体自动化监测提供有益借鉴。

基于MCFT理论的PC空心板梁抗剪强度分析

为研究预应力混凝土空心板梁的抗剪强度,基于6次预应力混凝土空心板梁抗剪强度试验,对板梁斜裂缝扩展、极限抗剪强度开展分析,基于修正斜压场理论(MCFT),建立了板梁理论计算模型,研究了预应力混凝土空心板梁箍筋间距的等效间距法确定原则,对比试验数据,验证了其有效性并分析弯剪组合效应对抗剪强度的影响,针对预应力、配筋率、钢筋和混凝土强度等不同参数开展分析。结果表明:加载点位置抗剪强度计算值与试验抗剪强度的比值为0.71,剪跨中点位置抗剪强度计算值与试验抗剪强度的比值为0.99,支座位置纯剪状态下抗剪强度计算值与试验抗剪强度的比值为1.11,考虑弯矩后,板梁抗剪强度削弱,剪跨中点位置计算值与试验值更为接近;预应力混凝土空心板梁在弯剪组合状态下,全黏结预应力钢筋数量由2根提高到10根,抗剪强度提高21.7%;随预应力筋数量的增多,有效预应力大小对抗剪强度的影响更为显著,当弯矩为100 kN·m时,有效预应力由186 MPa增加到1395 MPa的过程中,2根预应力筋抗剪强度提高10.2%,6根预应力筋抗剪强度提高15.3%,10根预应力筋抗剪强度提高20.3%。

基于n阶剪切变形理论的表面梯度脱碳汽车前轴弯曲分析

汽车前轴在热锻和热处理过程中,材料的表面会发生一定深度的脱碳,脱碳层的力学性能随脱碳深度呈梯度变化,影响了前轴在载荷下的弯曲性能。利用分段函数构建两侧表面功能梯度变化、内部性能均匀的简支夹芯梁,根据n阶剪切变形理论研究梁在两点载荷作用下的弯曲行为。利用虚功原理推导出位移场控制方程,采用Navier解析方法得到简支边界条件下梁的弯曲行为,并与相关文献中的实例进行比较。结果表明:n阶剪切变形理论具有良好的精度与可靠性;梁的挠度与转角随脱碳指数k的增大而增大,并于k≈10处达到准稳态;脱碳深度大于5 mm时,脱碳层厚度对梁弯曲时产生应力的影响比梁的高度变化带来的影响更大;两侧脱碳深度不对称时,物理中性面发生迁移;梁的弯曲挠度与转角随梁的厚度、宽度的增大而减小,但梁的厚度变化的影响更大。

预应力超高性能混凝土工字形梁抗剪性能试验

为了研究预应力超高性能混凝土(ultra-high performance concrete,UHPC)工字形梁的抗剪性能和抗剪承载力计算方法,设计并完成了3片预应力UHPC工字形梁的单点加载试验,获得了试验梁的荷载-位移曲线、破坏模式和裂缝分布特征等关键结果;基于试验结果,结合法国UHPC规范、瑞士UHPC规范、中国公路桥梁规范及公路桥涵超高性能混凝土应用规范意见稿计算了试验梁的抗剪承载力,分析了各个规范的适用性。此外,基于修正压力场理论(modified compression filed theory,MCFT),分别采用Mohr-Coulomb准则和Rankine准则,计算了试验梁的抗剪承载力,并进行了分析讨论。研究表明:预应力UHPC工字梁的抗剪承载力随着剪跨比的增加而减小,箍筋对于抗剪承载力影响较大;各国规范对UHPC梁的抗剪承载能力的计算较为保守。采用Mohr-Coulomb准则的计算结果较Rankine准则的计算结果与试验值更为接近;特别是小剪跨比的试验梁,处于弯剪复合状态,Mohr-Coulomb准则考虑了受压区UHPC法向和切向应力的影响,更为接近实际状况。

双参数弹性基功能梯度圆柱管自由振动的高阶梁理论解

基于高阶剪切变形梁理论,推导了Winkler-Pasternak弹性基径向功能梯度空心圆柱管自由振动行为的控制方程。该方法无须引入剪切修正系数,自动满足空心圆柱管内外表面剪应力自由边界条件。通过引入辅助函数,将关于挠度和转角的耦合控制方程化为单一高阶微分控制方程。给出了典型边界条件下功能梯度空心圆柱管的频率和振型。将计算结果与已有文献结果对比,验证了所提理论的精度。可以为工程中常见的Winkler-Pasternak弹性基梁结构提供更高精度的一维弹性理论解,研究结果表明,功能梯度材料的梯度参数和弹性地基刚度系数对固有频率值影响显著。与高阶固有频率相比,刚度系数对低阶固有频率的影响更加明显。

高阶剪切变形理论下Pasternak地基上FG-CNTRC梁自由振动及屈曲分析

功能梯度碳纳米管增强复合材料(functionally graded carbon nanotube-reinforced composite,FG-CNTRC)作为新一代先进复合材料,因其优越的力学性能而被研究者们广泛关注。该研究以Pasternak地基上FG-CNTRC梁为研究对象,基于不同高阶剪切变形理论,将一种具有插值特性的无网格法——稳定移动克里金插值(stabilized moving Kriging interpolation,SMKI)应用于求解Pasternak地基上FG-CNTRC梁的自由振动及屈曲问题。基于稳定移动克里金插值和不同高阶剪切变形理论给出FG-CNTRC梁的位移场,利用Hamilton原理和最小势能原理分别推导了Pasternak地基上FG-CNTRC梁的自由振动和屈曲控制方程。采用MATLAB软件编制了相关程序,将该研究解与解析解或文献解对比,证明了该方法在计算Pasternak地基上FG-CNTRC梁自由振动与屈曲的有效性及准确性。最后,还讨论了不同高阶剪切变形理论、地基系数、碳纳米管体积分数等对其自振频率和屈曲临界荷载的影响。

剪切梁结构扭矩传感器的应变解析

为实现对机器人在复杂情况下的灵活控制,需要在机器人关节处增加扭矩传感器,扭矩传感器是获取机器人关节运行状态的重要检测部件。考虑机器人自身尺寸限制及工作场景等因素,扭矩传感器采用轮辐式结构。本文介绍了扭矩传感器的结构和工作原理,分析了传感器弹性横梁在扭矩载荷作用下的变形协调条件,基于变形协调条件和铁木辛柯梁理论推导了剪切梁的应变计算公式,并建立了简化力学解析模型。通过有限元分析对力学模型的准确性和对弹性体结构参数的敏感性进行了验证。算例结果表明,该简化力学模型得出的结果和有限元结果数值相对误差在8.9%以内,表明了该简化力学解析模型的准确性。

重大改建船的原船重量重心分布推算

文章以“海州湾之星”改建船为例,演算了如何在没有初始重量重心分布的情况下,利用静力学原理推算原船重量重心分布的方法,并利用该方法得到原船空船重量重心分布,核算了改建后船舶的总纵强度,并取得船级社的认可,可为同行提供借鉴。

Size-dependent sinusoidal beam model for dynamic instability of single-walled carbon nanotubes

In this study, a model for dynamic instability of embedded single-walled car- bon nanotubes （SWCNTs） is presented. SWCNTs are modeled by the sinusoidal shear deformation beam theory （SSDBT）. The modified couple stress theory （MCST） is con- sidered in order to capture the size effects. The surrounding elastic medium is described by a visco-Pasternak foundation model, which accounts for normal, transverse shear, and damping loads. The motion equations are derived based on Hamilton＇s principle. The differential quadrature method （DQM） in conjunction with the Bolotin method is used in order to calculate the dynamic instability region （DIR） of SWCNTs. The effects of differ- ent parameters, such as nonlocal parameter, visco-Pasternak foundation, mode numbers, and geometrical parameters, are shown on the dynamic instability of SWCNTs. The re- sults depict that increasing the nonlocal parameter shifts the DIR to right. The results presented in this paper would be helpful in design and manufacturing of nano-electromechanical system （NEMS） and micro-electro-mechanical system （MEMS）.

Thermo-mechanical Behaviors of Functionally Graded Shape Memory Alloy Timoshenko Composite Beams

This paper focuses on the thermo-mechanical behaviors of functionally graded(FG)shape memory alloy(SMA)composite beams based on Timoshenko beam theory.The volume fraction of SMA fiber is graded in the thickness of beam according to a power-law function and the equivalent parameters are formulated.The governing differential equations,which can be solved by direct integration,are established by employing the composite laminated plate theory.The influences of FG parameter,ambient temperature and SMA fiber laying angle on the thermo-mechanical behaviors are numerically simulated and discussed under different boundary conditions.Results indicate that the neutral plane does not coincide with the middle plane of the composite beam and the distribution of martensite is asymmetric along the thickness.Both the increments of the functionally graded parameter and ambient temperature make the composite beam become stiffer.However,the influence of the SMA fiber laying angle can be negligent.This work can provide the theoretical basis for the design and application of FG SMA structures.

General analytical solution to bending of composite laminated beams with delaminations

Based on the first-order shear deformable beam theory, a refined model for composite beams containing a through-the-width delamination is presented, and the deformation at the delamination front is considered. Different from the ordinary delami- nated beam theory, each of the perfectly bonded portions of the new model is constructed as two separated beams along the interface without assuming a plane section at the de- lamination front. The governing equations of the delaminated portions and bonded ones are established, combined with continuity conditions of displacements and internal forces. Solutions of delaminated composite beams with different boundary conditions, delamina- tion locations and sizes axe shown in excellent agreement with the finite element results, showing efficiency and applicability of the present model.

Vibration and Instability of Third⁃Order Shear Deformable FGM Sandwich Cylindrical Shells Conveying Fluid

The vibration and instability of functionally graded material(FGM)sandwich cylindrical shells conveying fluid are investigated.The Navier-Stokes relation is used to describe the fluid pressure acting on the FGM sandwich shells.Based on the third-order shear deformation shell theory,the governing equations of the system are derived by using the Hamilton’s principle.To check the validity of the present analysis,the results are compared with those in previous studies for the special cases.Results manifest that the natural frequency of the fluid-conveying FGM sandwich shells increases with the rise of the core-to-thickness ratio and power-law exponent,while decreases with the rise of fluid density,radius-to-thickness ratio and length-to-radius ratio.The fluid-conveying FGM sandwich shells lose stability when the non-dimensional flow velocity falls in 2.1-2.5,which should be avoided in engineering application.

跨走滑断层隧道失稳演化过程及稳定性分析

研究目的:为评判跨走滑断层隧道的稳定性,首先视跨断层隧道为一含剪切带的“围岩-断层-围岩”复合岩体系统,揭示其失稳演化机制;其次基于含断层带复合剪切梁理论,推导跨走滑断层隧道失稳临界损伤长度、临界损伤荷载和极限位移计算表达式;最后对影响隧道稳定性的主要参数进行敏感性分析。研究结论:(1)跨走滑断层隧道失稳演化过程主要经历3个典型阶段,即含剪切带的“围岩-断层-围岩”系统变形协调促使强度降低、断层剪切带两侧围岩受拉而呈现拉裂损伤区、“围岩-复合剪切带-围岩”系统达到新的平衡状态;(2)当断层宽度、动摩擦系数、峰值剪应力、剪切梁剪切模量越小,隧道埋深、剪切梁宽度、塑性软化剪切模量越大,跨走滑断层隧道稳定性越差;(3)跨走滑断层隧道稳定性影响因素的敏感性为:断层宽度t>剪切梁剪切模量G>隧道埋深H>滑动摩擦系数μf>断层塑性软化剪切模量Gfs>断层峰值剪应力τfc;(4)本研究结论可为跨走滑断层隧道设计提供一定的理论依据。

Determination of Shear Center of Arbitrary Cross-Section

In structural analysis, it is often necessary to determine the geometrical properties of cross section. The location of the shear center is greater importance for an arbitrary cross section. In this study, the problems of coupled shearing and torsional were analyzed by using the finite element method. Namely, the simultaneous equations with respect to the warping, shear deflection, angle of torsion and Lagrange’s multipliers are derived by finite element approximation. Solving them numerically, the matrix of the shearing rigidity and torsional rigidity is obtained. This matrix indicates the coupled shearing and torsional deflection. The shear center can be obtained determining the coordinate axes so as to eliminate the non-diagonal terms. Several numerical examples are performed and show that the present method gives excellent results for an arbitrary cross section.