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.     

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.     

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。     

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.     

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 -     

Failure in two-cycle fatigue

In proof grading, a method of grading structural timber based on proof testing, it is possible for proof tested timber to have a strength less than the proof load used. Such timber, termed “rogues”, can occur because of damage due to the proof test, i.e. it is possible to have fatigue due to a single load cycle. Laboratory and mill studies were undertaken to examine and quantify the statistical characteristics of the strength of these rogues.     

考虑状态模糊性时广义失效概率计算的鞍点逼近方法

针对状态具有模糊性的广义可靠性分析问题,提出了一种广义失效概率计算的鞍点逼近方法.所提方法首先将广义失效概率的积分区域依据功能函数的取值离散化,在离散的积分区域中,功能函数对模糊失效域的隶属函数近似保持为常数,从而将模糊可靠性问题转化为随机可靠性问题,进而利用近似的鞍点逼近方法求得广义失效概率.该文给出了所提方法的实现步骤和原理,并用算例验证了所提方法的合理性和可行性.由于基于鞍点逼近的考虑状态模糊性时广义失效概率的计算方法具有较高的效率和精度,因而所提方法具有一定的工程意义.     

Impact Failure of Planetary Materials:

The dynamic fragmentation of a fine grained granitoid material has been examined. Target thicknesses ranged from 7 to 40 mm and impact energies from 12 to 2,500 J. Combined particle image velocimetry and image enhancement techniques are introduced and have been used to measure the size and velocity of material ejected laterally from the rear of the target during impact testing. Non-dimensional groups were formed and fitted with coefficients to predict median values of the distribution of mass and kinetic energy among radial distance, R, from the impact centre, ejecta velocities, v, and ejecta lengths, L. The statistics are well correlated with increasing non-dimensional impact energy (positive correlation for radial distance and velocity, and negative correlation for ejecta length). Median values were used to collapse cumulative distributions and non-centred Gaussian fits were used to describe these curves. Approximately 85 % of the total mass and kinetic energy is captured between R/R_{50 %} = 0.3 to 2, v/v_{50 %} = 0.3 to 2, and L/L_{50 %} = 0.2 and 3. This data facilitates a better comparison among a wide range of test conditions, especially when attempting to extrapolate principal features of impacts into brittle materials at higher velocities. The ejecta tracking techniques and methodologies can be used to improve current impact testing experiments and computer modelling validation.     

Reliability Index and Failure Probability

Abstract

Numerical algorithms for the solution of nonlinear algebraic equation systems are discussed. Special application to the mechanism and multibody system kinematic analysis, as well as to the problems of constraint stabilization during dynamics simulation is regarded. Special attention is paid to the approaches of a separate solution of the differential equations and constraint stabilization. Numerical procedures that are effective additions to the well-known algorithms based on the Newton-Raphson method are presented. The problems of loss of precision and achievement of large unreal increments of the varying parameters are discussed. The traditional Newton-Raphson method is modified by applying a step reduction procedure that is developed numerically for the symbolic form of kinematic and dynamic equations. An optimization method for stabilization of constraints using the mass matrix of dynamic equations is suggested. According to the objective function defined the stabilization procedure provides minimal deviations of the parameters and their velocities with respect to the solution of the differential equations. No generalized coordinate partitioning is required either for solution of the dynamic equations or for stabilization of the constraints. Several examples of kinematic analysis of single and four contour plane mechanisms and constraint stabilization are solved, and the results are compared. The advantages of the algorithms developed are tested with a high-degree of initial deviation from the real solution. It is also shown that the step correction algorithm could provide admissible solution even when, in many cases, the classical approaches are not reliable. An example of the direct and inverse kinematic problem solutions of the four-degrees-of-freedom spatial platform is presented.     

现场复制光栅技术研究混杂复合材料层板裂纹扩展机理

本文运用现场复制变形光栅技术研究了混杂复合材料GLALL层板中铝合金层Ⅰ型裂纹疲劳扩展,得到了不同工况,不同裂纹尺寸下裂纹场的U、V等位移线条纹图,并分析了特征点及裂尖区应变变化规律.本文为进一步研究和使用混杂复合材料提供了可靠的力学依据,并证明了现场复制变形光栅技术可以被有效地应用于现场工况下诸多复杂的实际问题中去.     

Failure probability assessment of parallel redundant structures

Considered in the analysis are complex systems with parallel redundancy. The failure probability of such a system is assessed by the strength probabilistic properties of the structural elements. There is a finite number of parallel structural elements that provides the maximum possible reliability of the system. Parallel systems may fail by instantaneous growth of failed elements. The tendency to catastrophic failure depends on the element strength probability and overload. Calculated is the critical stress corresponding to the beginning of catastrophic failure of the parallel system. Weibull probability distribution is used for describing the structural element strength. The critical stress ranges from 50% to 95% of the mean single element strength; depends on the overload and probability distribution.