A Simple Criterion for the Existence of Rank-One Connections between Martensitic Wells

We show that for the two wells SO(3) U and SO(3) V to be rank-one connected, where the 3 × 3 symmetric positive definite U and V have the same eigenvalues, it is necessary and sufficient that det(U − V) = 0, a result that does not hold in higher dimensions. Using this criterion and a result of Gurtin, formulae for the twinning plane and the shearing vector are obtained, which yield an extremely simple condition for the occurrence of so-called compound twins. As an illustration, we apply our results to the cubic-to-monoclinic transition. This revised version was published online in August 2006 with corrections to the Cover Date.     

Equivalence between Rank-One Convexity and Polyconvexity for Some Classes of Elastic Materials

Let W(F) = φ(λ ₁ ^s + λ ₂ ^s + λ ₃ ^s ) + ψ(λ ₁ ^r λ ₂ ^r + λ ₁ ^r λ ₃ ^r + λ ₂ ^r λ ₃ ^r ) + f(λ ₁ λ ₂ λ ₃) be a stored energy function. We prove that, for this function, rank-one convexity is equivalent to polyconvexity.under suitable assumptions on φ, ψ and f.     

The Random Nature of Column Failure

ABSTRACT

An approximate quasi-static theory is developed to predict large plastic deformation and perforation of spherical shells subjected to impact by blunt-ended projectiles at normal incidence. Based on experimental observations for quasi-static load-displacement characteristics, the problem of a spherical shell under normal impact by a flat-ended missile may be analyzed through the solutions to that of an equivalent circular plate struck transversely by the same missile. It is shown that the approximate theoretical predictions with a = 30 (here a is an empirical constant) are in good agreement with experimental data, in terms of maximum permanent transverse displacements and dimple radii. Furthermore, a theoretical formula for ballistic limits of spherical shells under missile impact is presented and the range of applicability of the theory is discussed.     

螺栓连接件微动疲劳特性分析

工程中钢结构构件经常采用螺栓连接,被连接部位多处于复杂受力状态,单轴疲劳理论已无法满足该形式下构件的寿命评估需求.针对现有理论不足,本文建立了螺栓连接件有限元模型,研究了不同工况下被连接件微动疲劳裂纹萌生位置,并基于临界平面的多轴疲劳理论,比较了四种常用模型的适用性以及预测了连接件的疲劳寿命.结果表明:(1)裂纹萌生位置位于受拉端螺栓孔附近的滑移粘着区,在相同螺栓预紧力下,该位置与施加的疲劳载荷大小无关;(2)基于临界平面方法的四种模型均可以较好判断裂纹萌生位置,其中SWT(Smith-Watson-Topper)模型对不同载荷水平下的螺栓连接件微动疲劳寿命预测效果较好,大部分预测结果位于±2倍分散带之内,预测结果优于其他三种模型;(3)在规范规定的螺栓预紧力范围内,被连接件裂纹萌生区域距孔边的距离与预紧力大小无关,可能是由于预紧力变化范围内的粘着滑移区未发生明显变化所致,并且随着预紧力减小,被连接件的寿命预测值反而增大.     

半刚性连接钢框架的拟动力实验研究

在钢框架结构的设计中, 通常将梁柱节点处理为完全刚接或理想的铰接.但是在实际框架中, 梁柱节点表现出半刚性.目前的实验研究基本都基于结构和构件的静力分析.本文对半刚性连接钢框架结构进行了拟动力实验研究,得出了在地震波激励作用下,半刚性节点初始刚度对钢框架的楼层刚度、基底剪力、楼层位移和楼层加速度的影响.对实验结果进行对比分析可以看出,在结构侧向位移满足的前提下半刚性连接刚度的减弱会引起结构作用效应的降低.实验总结出的节点半刚性对结构动力性能影响的一些结论,将为高层钢结构设计规范的修改提供实验基础.     

高速瓦楞辊的磨损失效分析

本文对进口的高速瓦楞辊的磨损失效形式进行了分析，认为其主要磨损形式是磨粒磨损，即齿侧为滑动磨粒磨损，齿底为应变疲劳磨粒磨损，而齿预则包括了这两种磨损形式；齿顶和齿根两侧都是磨损最严重的部位；磨粒主要是纸中夹带的ＳｉＯ２砂粒。文章最后还明确指出，瓦楞辊的返修期应当定在其出现非均匀磨损之前，但是由于楞齿承受曲应力而诱发疲劳裂纹，故此返修次数是有限的。     

Non-persistence of Homoclinic Connections for Perturbed Integrable Reversible Systems

The dynamics of an analytic reversible vector field (X,) is studied in with one real parameter close to 0; X=0 is a fixed point. The differential D_x (0,0) generates an oscillatory dynamics with a frequency of order 1—due to two simple, opposite eigenvalues lying on the imaginary axis—and it also generates a slow dynamics which changes from a hyperbolic type—eigenvalues are —to an elliptic type—eigenvalues are —as passes trough 0. The existence of reversible homoclinic connections to periodic orbits is known for such vector fields. In this paper we study a particular subclass of such vector fields, obtained by small reversible perturbations of the normal form. We give an explicit condition on the perturbation, generically satisfied, which prevents the existence of a homoclinic connections to 0 for the perturbed system. The normal form system of any order admits a reversible homoclinic connection to 0, which then does not survive under perturbation of higher order. It will be seen that normal form essentially decouples the hyperbolic and elliptic part of the linearization to any chosen algebraic order. However, this decoupling does not persist arbitrary reversible perturbation, which finally causes the appearance of small amplitude oscillations.     

Fluid Dynamics at Connections in Paediatric Cardiac Surgery*

The modified Blalock-Taussig shunt is a connection created between the systemic and pulmonary arterial circulations to improve pulmonary perfusion in children with congenital heart diseases. Survival of these patients is critically dependent on blood flow distribution between the pulmonary and systemic circulations, that in turn depends upon the fluid dynamic behaviour of the shunt. Computational fluid dynamics, structural analyses as well as in vitro experiments were carried out to derive a quantitative relationship between the shunt flow and the corresponding pressure drop. While computational fluid dynamics simulations were based on the assumption of rigid wall for the shunt and the arteries, proper distensible conduits were used in the in vitro study and the structural analysis of the anastomosis deformation. The results indicated that the internal pressure combined with wall distensibility modifies the cross-sectional area of the distal anastomosis (between the shunt and the pulmonary artery). This fact affects the pressure drop across the shunt, especially at low pressures. Based on the results from the computational analyses and the in vitro experiments, a relationship between pressure drop and flow in the shunt was obtained, which matches data from clinical measurements.     

Statically Admissible Stress Fields for Plastic Design of Connections of Steel Structures

ABSTRACT

The technique of statically admissible plastic stress fields is used in the plastic design of complex connections -of steel structures. An appropriate stress field gives a safe estimate of the shape of the connection design. Complex three-dimensional stress fields are composed of elementary subfields. Thus the procedure of plastic design consists in appropriate arrangement of subfields into a complex system of stresses.     

Exact Connections of Warping Fields and Torsional Rigidities of Symmetric Composite Bars

Saint-Venant's torsion of symmetric cylindrical bars consisting of two or four homogeneous phases is studied. A symmetric section is meant that the cross section of the cylindrical bar possesses reflectional symmetry with respect to one or more axes. Each constituent region may have different shear modulus. The idea of the analysis is to superimpose suitably reflected potentials to obtain the torsion solution of the same composite section but with different moduli. For two-phase sections, we show that, if the warping fields for a given symmetric section with phase shear moduli μ₁ and μ₂ are known a priori, then the warping fields for the same configuration but with a different set of constituent moduli μ₁ ^′ and μ₂ ^′ are readily found through simple linear superpositions. Further, suppose that the torsional rigidities T(μ₁,μ₂) and T(μ₁ ^′,μ₂ ^′) for any two sets of phase moduli can be measured by some experimental tests or evaluated through numerical procedures, then the torsional rigidity for any other combinations of constituent moduli T(μ₁ ^′′,μ₂ ^′′) can be exactly determined without any recourse to the field solutions of governing differential equations. Similar procedures can be applied to a 4-phase symmetric section. But the coefficients of superposition are only found for a few branches. Specifically, we find that depending on the conditions of μ and μ^′, admissible solutions can be divided into three categories. When the correspondence between the warping field is known to exist, a link between the torsional rigidities can be established as well. This revised version was published online in June 2006 with corrections to the Cover Date.     

Connections and geodesic characteristic of equations of motion for constrained mechanical systems

I.IntroductionSinceEinsteinestablishedgeneralrelativityatthebiginningofthiscentury,differentialgeometry,especiallythemodernditTerentialgeometry,hasbeenextellsivelyappliedtomanyfieldsofphysics.Thestudyofregularholonomicmechanicalsystemsinthemodernsettingofdifferentialgeometryhasahistoryofmorethanthirtyyears.Andtheresearchtendstoperfectgraduallyt'~'l.Sinceearlyin1980'sthegeometrizationaboutconstrainedmechanicalsystemsandsingularmechanicalsystemshasbeenattachedimportanceextensivelyandsomeresult…     

钢结构框架中组合梁等效刚度的确定方法

刚接或半刚性连接的组合梁在荷载作用下,在梁的长度范围内既有正弯矩作用段,又有负弯矩作用段,由于组合梁截面在正弯矩作用和负弯矩作用下截面抗弯刚度不一致,因而在弯矩为零的点处梁的截面抗弯刚度发生突变,而组合梁框架分析的关键是确定组合梁刚度突变分界点的位置及确定在整体分析中所采用的等效梁的刚度。本文根据应变能相等的原理对钢结构框架中组合梁的等效抗弯刚度进行了研究,推导了其等效刚度的表达式,并给出不同荷载作用形式下刚接框架组合梁等效刚度简化计算公式,为组合梁钢框架的整体分析提供了便利。最后分析了水平荷载以及梁柱连接特性对组合梁等效刚度的影响,分析结果表明,采用本文提出的组合梁等效刚度进行半刚性连接框架整体分析偏于安全。     

一种固体推进剂破坏的细观实验研究

固体推进剂是一种颗粒填充高能聚合物,其破坏时所表现出的一些行为和金属的破坏相比,有明显不同之处。本文利用扫描电镜,给出了受载情况下固体推进剂试件的损伤发展以及裂纹扩展过程。结果表明,损伤的发展过程也就是微裂纹区扩展及微裂纹密度加大的过程,而裂纹扩展过程中的慢速扩展和亚临界扩展的最大区别则是其裂尖损伤区范围不同,同时也表明,裂纹尖端和边缘的微裂纹损伤区尺寸已不容忽略。     

典型密封元件的失效分析与失效过程研究

飞机整体油箱结构的密封性对飞机安全性和续航能力有很大影响,所以密封胶失效分析和失效过程研究就显得相当重要．为了研究密封胶的失效,根据密封胶的受力特点,本文设计了典型元件的密封试验（平板型和T型）,通过试验得到了这两种结构的失效载荷和最大载荷．同时,利用有限元模拟软件ABAQUS对试验进行了模拟计算,使用cohesive模块实现对密封胶层的模拟．通过观察胶层失效过程,得到了胶层失效后的破坏路径,找到了容易发生泄漏的位置,并给出了失效载荷与最大载荷的关系．通过对比试验结果和模拟计算结果,验证了有限元模拟分析的可靠性,并对结果进行了讨论．     

Connections between different models describing imperfect interfaces in periodic fiber-reinforced composites

The paper addresses the problem of modeling of fiber reinforced composites with imperfect bonding between the matrix and the inhomogeneities. The imperfections of different kinds are usually modeled as either layered inhomogeneities or by springs of certain stiffnesses distributed along the matrix/fiber interfaces. We compare the two approaches for the case of incompressible layer between the phases and calculate effective properties of fiber reinforced composites with periodic square arrays of fibers possessing imperfect contact with the surrounding material. We identify the interval of thickness at which the interphase does not influence the effective properties and show how the imperfection effects described by different models can be expressed in terms of each other.     

谐波齿轮传动减速器的固体润滑失效机理

在同型号的谐波轮传动减速器和相同的试验条件下，考察了不同固体润滑薄膜体系的润滑性能和磨损特性；结合试验后柔轮和刚轮的工作表面形貌和磨粒的分析，初步探讨了固体薄膜润滑下谐波减速器的磨损机理及其润滑失效机理，结果表明，谐波减速器齿轮磨擦副的润滑膜配伍是影响谐波减速器润滑状态和运行寿命的重要因素。在分析研究的基础上，提出了改进谐波减速器齿轮副固体润滑的设想，并且研制出在给定条件下适用的固体润滑薄膜体系。     

杆系结构系统失效模式识别的几何法及其应用

在结构可靠性分析中,由于外载、材料性能参数等的随机性,在所有可能的失效模式中,必有少数几个失效模式其出现概率比其他失效模式要大得多,因此求取这为数不多的临界失效模式就是结构系统可靠性分析中一个主要课题.本文提出了求取杆系结构系统失效模式(即机构)的几何法.它是从几何方程出发,求得一机构,然后在此机构的基础上经过简单的矩阵相加.相乘就可得到其他机构.同时采用比例加载乘子λ这一物理意义明潦的参数来作为判别是否为临界机构的准则,效果很好.算例表明了此法的可行性,有效性.     

Failure of solids under strain

Journal of Applied Mechanics and Technical Physics -