弹性地基上受切向力作用梁稳定性研究

用广义微分求积法(GDQR)分析了弹性地基上复杂弹性支承条件下受切向力作用梁的稳定性问题。基于弹性支承梁的运动微分方程及边界条件,采用GDQR进行离散化,获得由动力方程组及边界条件合成的特征值矩阵方程。通过对相应特征值方程的具体分析,讨论了弹性地基模量、剪切系数、复杂边界条件对临界载荷的影响,研究了一端固定约束、另一端弹性约束梁弹性失稳区域随弹性地基模量和支承弹簧刚度变化的情况,得到了一些有益的结论。结果表明：GDQR能很好地解决此类系统的稳定性问题。     

多跨弹性支承连续矩形薄板屈曲分析

针对钢箱梁和混凝土薄壁箱梁受压翼缘的稳定问题,基于状态-空间向量法,提出了一种用于弹性支承连续矩形薄板弹性屈曲分析的计算方法。与有限条法结果对比,验证了该方法的可靠性。分析了跨间弹性支承刚度和布置以及荷载参数对屈曲的影响,结果表明:跨间弹性支承对连续矩形薄板屈曲影响明显,屈曲系数随着弹性支承刚度的增大呈非线性增长;等间距、等刚度布置弹性支承有利于板的稳定性,弹性支承的刚度或间距差别越大,对板的稳定性越不利;不同荷载工况下,弹性支承刚度-屈曲系数关系曲线的变化规律基本相同,弹性支承刚度较小时,荷载参数对屈曲系数影响显著,单向受压的屈曲系数可达双向等值受压的两倍。     

结构胶侧扭约束玻璃柱轴压承载力设计方法研究

玻璃柱在工程应用中的一种形式是采用结构胶将其与玻璃面板连接,结构胶对玻璃柱的约束效应能改善玻璃柱稳定性。考虑结构胶对玻璃柱的侧向弹簧约束及扭转弹簧约束作用,基于平衡方程推导了结构胶约束玻璃柱的轴压临界荷载公式,讨论了结构胶弹性模量及玻璃柱的柱高、截面高度、截面厚度对临界荷载的影响,发现结构胶弹性模量、玻璃截面厚度影响最为显著。基于等效刚度法将临界荷载公式推广至夹层玻璃柱。针对工程实践中常用的硅酮结构胶,提出了结构胶约束玻璃柱在轴压荷载作用下考虑玻璃开裂及结构胶破坏的承载力设计准则,并通过有限元模型计算验证了理论研究的合理性。     

Stability and vibration of a column model with load-dependent support stiffness

This paper considers the effects of supports whose flexural resistances change as they are loaded. A one-degree-of-freedom, rigid-bar model of a column is analysed. At the support, there is a rotational spring whose stiffness depends on the vertical load applied to the bar. The spring may harden, soften, or initially soften and then harden as the load is increased. Bifurcation loads, post-buckling behaviour, and vibration frequencies are determined. Parametric instability under harmonically-varying loads is also investigated. Some unusual behaviour is found, including cases with two or three bifurcation points. Sometimes there are no bifurcation points and the vertical equilibrium configuration of the model is stable under any load. It is seen that changes in the support stiffness due to compression may have a significant effect on the stability and vibration of a structure     

土-钢共同作用下大跨度波纹钢板管廊结构局部屈曲分析

对于采用深波和大波波形的大跨度波纹钢板综合管廊,其截面平直段在结构整体达到极限承载力之前可能发生局部屈曲。采用Rayleigh-Ritz法对大跨度综合管廊结构中波纹钢板平直段的局部屈曲进行分析。将波纹段考虑为平直段的弹性约束,土体作用考虑为只能承受压力的弹性基底,根据环压理论,得到了钢板平直段在环向均布压力作用下屈曲半波数分别为偶数和奇数时的屈曲荷载理论解。讨论了转动弹簧约束系数对临界屈曲系数的影响,得出非加载边波纹段对平直段的约束作用可视为简支或固支的转动约束系数值;得到了土体弹簧刚度与屈曲荷载间呈线性关系;讨论了板件纵横比与临界屈曲系数间的关系,得到了临界屈曲系数趋于定值时相应的板件纵横比,给出了简化公式。通过有限元值、简化公式值与理论值的对比,证实了简化公式的适用性。最后,根据屈服准则和等稳准则,提出相应的防止大跨径波纹钢板局部屈曲的宽厚比限值的计算公式,可为实际工程提供参考。     

Applicability of hierarchical fiber bundle materials to mechanical environments

Biomaterials use a hierarchical structure to optimize their self-healing behavior, for instance. However, the behavior may be constrained under different mechanical environments. In this paper, a system is suggested that the mechanical environment is modeled as a spring connected in series with the fiber bundle material. For the spring, the elastic behavior with stiffness is obeyed while, for the fiber bundle material, the nonlinear elastic constitutive relation is obeyed according to the Weibull distribution and the Daniels’ theory. Relying on the principle of total potential, the applicability condition is proposed for the system and the critical stiffness is thus derived for the spring. The applicability of hierarchical fiber bundle materials is finally investigated. The results show that the hierarchy can significantly change the critical stiffness, and hence demonstrates quite different applicability to a given mechanical environment.     

Buckling analysis of embedded nanotubes using gradient continuum theory

The buckling of nanotubes embedded in an elastic matrix is modeled within the framework of Timoshenko beams. Both a stress gradient and a strain gradient approach are considered. The energy variational approach is adopted to obtain the critical buckling loads. The dependences of the buckling load on the nonlocal parameter, the stiffness of the surrounding elastic matrix, and the transverse shear stiffness of the nanotubes are obtained. The results show a significant dependence of critical buckling load on the nonlocal parameter and the stiffness of the surround matrix. The Euler beam model, which neglects the shear stiffness of the nanotubes, over-predicts the critical buckling load. It is also found that the strain gradient model provides the lower bound and the stress gradient model provides the upper bound for the critical buckling load of nanotubes. In addition to mechanical buckling, thermally induced buckling of the nanotubes embedded in an elastic matrix is also studied. All results are expressed in closed-form and therefore are easy to use by materials scientists and engineers for the design of nanotubes and their composites.     

基于矩阵位移法的桩锚结构分析方法

采用将桩锚结构视为荷载作用-侧向弹簧支承的连续梁模型,支护桩为直立的弹性地基梁,主动土体转换为土压力,锚杆简化成为可逐步施加的弹簧支承,而被动土体则用侧向支承的土体弹簧替代.土体弹簧的刚度K是通过半无限大弹性空间内部水平荷载作用下的Mindlin 解来确定,这种方法降低了因深度加深而带来弹簧刚度的增长率,更加符合实际情况.针对这种弹性地基梁模型,提出了以矩阵分析为手段的计算方法,该法优点在于将桩锚视为桩-锚-土三者协同作用的支护结构,同时在计算过程中充分考虑了基坑分步开挖的施工过程对支护桩、锚杆以及被动土体的变形影响.通过实例分析表明:矩阵位移法为桩锚结构设计提供了一种合理、有效的计算方法.     

Asymmetric buckling of shell-stiffened annular plates

The present study is devoted to some stability problems of annular plates with shell-stiffening. The plate is simply supported, or clamped, or elastic restrains are applied on the boundaries of the plate. Though the load is axisymmetric we shall assume that the deformations are not necessarily axisymmetric. The displacement fields in the plate and the shell are expanded into Fourier series. For the shell all physical quantities are derived from an appropriately chosen Galerkin function. The main goal is to clarify the effect of a stiffening shell on the buckling load. Hence the field equations together with the boundary- and continuity conditions are clarified. These provide the eigenvalue problem from which the critical load can be calculated. In order to solve the eigenvalue problem we have established, appropriate numerical methods are used.     

Size-dependent fracture and higher order J-integral for solids characterized by strain gradient elasticity

Elastic fracture is governed by the material's strain energy released rate and depends on the applied loads and the stiffness of the structure. The effect of stiffness on fracture as a function of structural size is typically modeled using strain-based elastic fracture mechanics, but recent experimental evidence indicated that when the size of the structure is on the order of the higher order material length scale parameters, elastic strain gradients would stiffen the structure. In this paper, the higher order J-integral and energy-released rate for the analysis of fracture of strain gradient stiffened structures are developed. The effects of beam size on the fracture behaviors of strain gradient stiffened cantilevers on a substrate were analyzed using the higher order J-integral and the energy-released rate. Analyses revealed that the fracture load is elevated to more than 1.4 times of the un-stiffened case when the bending stiffness is doubled by strain gradient stiffening. Elastic fracture is shown to have an added dependence on the size of the structure when strain gradient stiffening is non-negligible.     

Effective spring stiffness for a planar periodic array of collinear cracks at an interface between two dissimilar isotropic materials

Explicit analytical expressions are obtained for the longitudinal and transverse effective spring stiffnesses of a planar periodic array of collinear cracks at the interface between two dissimilar isotropic materials; they are shown to be identical in a general case of elastic dissimilarity (the well-known open interface crack model is employed for the solution). Since the interfacial spring stiffness can be experimentally determined from ultrasound reflection and transmission analysis, the proposed expressions can be useful in estimating the percentage of disbond area between two dissimilar materials, which is directly related to the residual strength of the interface. The effects of elastic dissimilarity, crack density and crack interaction on the effective spring stiffness are clearly represented in the solution. It is shown that in general the crack interaction weakly depends on material dissimilarity and, for most practical cases, the crack interaction is nearly the same as that for crack arrays between identical solids. This allows approximate factorization of the effective spring stiffness for an array of cracks between dissimilar materials in terms of an elastic dissimilarity factor and two factors obtained for cracks in a homogeneous material: the effective spring stiffness for non-interacting (independent) cracks and the crack interaction factor. In order to avoid the effect of the crack surface interpenetration zones on the effective spring stiffness, the range of the tensile to transverse load ratios is obtained under the assumption of small-scale contact conditions. Since real cracks are often slightly open (due to prior loading history and plastic deformation), it is demonstrated that for ultrasound applications the results obtained are valid for most practical cases of small interfacial cracks as long as the mid-crack opening normalized by the crack length is at least in the order of 10⁻⁵.     

基于二阶理论的弹性约束变截面悬臂梁刚度与稳定性分析

从计入二阶效应的挠曲微分方程出发,对惯性矩沿轴向二次变化的变截面Bernoulli-Euler梁在弹性约束下的刚度和稳定性进行了分析,推导了在弹性约束下变截面悬臂梁在复合载荷作用下的挠度和稳定性的精确表达式,给出轴向压力引起的挠度影响系数。在极端情况下,该文公式可相应退化为根部固支的变截面梁及等截面梁之刚度与稳定表达式。将该文的计算结果与用ANSYS软件密分单元的计算结果进行分析比较,分析比较结果验证了该文推导的刚度和稳定性表达式的正确性,该文方法可广泛应用于弹性约束下变截面悬臂梁的刚度和稳定性分析。     

具有形状记忆合金弹簧支承的转子系统的动力稳定性研究

提出一个具有形状记忆合金（SMA）弹簧支承的旋转轴转子系统的自由振动分析模型。基于Euler-Bernoulli梁理论建立旋转轴的连续分布弹性振动方程, 并且考虑旋转轴材料内阻的影响。采用Brinson模型分析SMA螺旋弹簧的受限回复刚度特性。在振型假设的基础上利用虚功原理得到转子系统的特征方程。通过数值计算分析了SMA弹簧的激励温度和初始应变对转子系统的临界转速和失稳阈的影响规律。研究表明, 利用SMA弹簧的受限回复特性调节支承刚度可以提高转子系统的临界转速和失稳阈,从而增强转子系统的动力学稳定性。     

土工合成材料加筋土挡墙筋材内力分析

土工合成材料加筋土挡墙是一种新型的挡土结构,它具有经济性好、性能优越、适应性强等优点。而筋材内力计算是该类结构设计的一个关键步骤,因此该类结构的推广应用需要一种合理易用的内力分析方法。该文讨论了几种土工合成材料加筋土挡墙的筋材内力分析方法,并对这些方法的优缺点进行评述。这些方法包括基于主动土压力系数的方法、基于经验的K刚度法、基于极限平衡的加筋边坡稳定分析方法、基于非线性弹性与变形协调的理论方法、以及基于增量非线性及填土剪胀性的筋材内力分析方法等。通过比较分析发现,如忽略面板作用且填土强度得到完全发挥,基于主动土压力系数以及极限平衡边坡分析的方法适用于分析加筋土挡墙在强度极限状态时的筋材内力,但填土强度的发挥水平决定于筋材的长期刚度。另一方面,如能合理考虑筋材的长期刚度以及面板的约束作用,基于筋土变形协调的理论分析方法适用于分析加筋土挡墙在正常工作荷载作用下的筋材内力。     

Dynamic stability behavior of damped laminated beam subjected to uniformly distributed subtangential forces

The dynamic stability behavior of damped laminated beam with various boundary conditions subjected to the uniformly distributed subtangential forces is investigated using the finite element formulation. The formal engineering approach of the mechanics for the thin-walled laminated beam based on kinematic assumptions consistent with Vlasov beam theory is used. An extended Hamilton’s principle is employed to obtain the mass-, damping-, elastic stiffness-, geometric stiffness matrices, and the load correction stiffness matrix due to the subtangential forces, respectively. The method for the evaluation of critical values for divergence and flutter of the nonconservative systems is briefly introduced in case of considering and neglecting damping effects. Throughout numerical examples, the influence of various parameters on the dynamic stability behavior of the nonconservative laminated beam is newly investigated: (1) the variation of the divergence and flutter loads due to the nonconservativeness with respect to the fiber orientation, (2) the effect of boundary condition on the instability region of the divergence-flutter system, and (3) the influence of external and internal damping on the flutter load.     

GDQR求解弹性地基上输流管道的稳定性

用广义微分求积法（GDQR）研究了弹性地基上输流管道的稳定性问题。基于输流管道运动微分方程及边界条件,采用GDQR进行离散化,获得由动力方程组及边界条件合成的特征值矩阵方程。通过对相应特征值方程的具体分析,计算了左端固定、右端弹性支承下输流管道的发散失稳流速和颤振失稳流速,研究了临界失稳流速和稳定区域随两端支撑弹簧刚度、扭转弹簧刚度的变化情况,分析了质量比、双参数模型地基反力系数和剪切模量对输流管道稳定区域图的影响,得到了一些有益的结论。研究结论对于工程实践有一定的指导意义。     

刚度特性对八连杆隔离器隔振、隔冲性能的影响分析

为提高惯导设备隔离器的防护能力,设计了一种能够大幅度卸载任意方向冲击载荷的多杆并联隔离器,并选择能以小变形承受大载荷的碟簧作为弹性元件。同时,为分析隔离器的刚度特性及其对隔离器隔振、隔冲性能的影响,进行了准静态压缩实验、振动试验和冲击试验。研究发现,随着隔冲杆中碟簧数量增加,预紧力增大,弹性元件的准零刚度特性渐强,垂向及水平向隔振能力产生不同程度的削弱。在隔冲性能上,当准零刚度特性较为明显时,试验和仿真计算得到的加速度响应峰值更大,但随冲击载荷增加,隔离率趋于稳定。最后得出,当弹性元件具有较弱的准零刚度特性时,有利于保证隔离器在复杂冲击环境下,保持较好隔振、隔冲能力,为多杆并联隔离器的优化设计提供了参考。     

考虑剪切变形影响的框架柱弹性稳定

该文研究了考虑剪切变形影响的压杆弹性稳定,着重分析了压杆自身的剪切变形对其稳定临界荷载的影响。该文提出了考虑剪切变形影响的杆件单元一阶、二阶转角位移方程。提出了考虑剪切变形影响,计算两端任意转动约束轴压杆有侧移失稳及无侧移失稳的近似公式,通过与精确解对比,近似法具有很好的精度。讨论了压杆有侧移失稳临界荷载与压杆抗侧刚度之间的内在联系,根据这一规律,提出了近似计算两端转动约束轴压杆,具有侧向不完全支撑时的临界荷载。     

Elastica buckling analysis of a simple frame

Summary A nonlinear stability analysis based on an analytical approach of elastic type is performed for the first time on a simple two-bar frame. In order to obtain an exact determination of its buckling and postbuckling behavior the effect of compressibility of the bar centroidal axis is taken into account. This effect implies very slight increase in the buckling load which can be safely ignored. Moreover, it is found that even in the most extreme cases of geometry and stiffness, the critical buckling displacements are of negligibly small magnitude contrary to existing results obtained by the nonlinear kinematic stability analysis. The two foregoing findings enable us to replace the limit point by a bifurcation point. Such a simplification, being correct in an asymptotic sense, allows the application of a stability analysis of frames by considering their bars as incompressible.A variety of numerical results shows the degree of accuracy and the range of applicability of the aforementioned nonlinear kinematic stability analysis by comparing it with the exact method of stability analysis proposed herein.With 2 Figures     

Influence of the prebuckling stress-field on the critical loads of inhomogeneous composite laminates

The paper studies the uniaxial buckling behavior of composite laminates in which preselected variations of fiber spacing in the constituent laminae are adopted. Such laminates are referred to as inhomogeneous laminates because of the variable elastic stiffness along the coordinate axes. A non-uniform prebuckling stress state observed even under constant uniaxial compression has a pronounced influence on the buckling behaviour of an inhomogeneous laminate. A procedure is summarized for computing the critical load of a laminate using the Ritz method which exploits an analogy between the bending and stretching formulations and utilizes Gram-Schmidt orthogonal polynomials. The paper illustrates that the variation in fiber spacing is an innovative way of increasing the critical load for a prescribed amount of fiber and highlights its remarkable sensitivity to the nature of fiber spacing, in-plane and out-of-plane boundary conditions, fiber type and the aspect ratio of the laminate.