Structural interfaces in linear elasticity. Part II: Effective properties and neutrality

The model of structural interfaces developed in Part I of this paper allows us to analytically attack and solve different problems of stress concentration and composites. In particular, (i) new formulae are given for effective properties of composite materials containing dilute suspensions of (randomly oriented) reinforced elliptical voids or inclusions; (ii) a new definition is proposed for inclusion neutrality (to account for the fact that the matrix is always ‘overstressed’, and thus non-neutral in a classical sense, at the contacts with the interfacial structure), which is shown to provide interesting stress optimality conditions. More generally, it is shown that the incorporation of an interfacial structure at the contact between two elastic solids exhibits properties that cannot be obtained using the more conventional approach of the zero-thickness, linear interface. For instance: contrary to the zero-thickness interface, both bulk and shear effective moduli can be optimized for a structural interface; effective properties higher that those possible with a perfect interface can be attained with a structural interface; and neutrality holds with a structural interface for a substantially broader range of parameters than for a zero-thickness interface.     

Structural interfaces in linear elasticity. Part I: Nonlocality and gradient approximations

Many biological and optimal materials, at multiple scales, consist of what can be idealized as continuous bodies joined by structural interfaces. Mechanical characterization of the microstructure defining the interface can nowadays be accurately done; however, such interfaces are usually analyzed employing models where those properties are overly simplified. To introduce into the analysis the microstructure properties, a new model of structural interfaces is proposed and developed: a true structure is introduced in the transition zone, joining continuous bodies, with geometrical and material properties directly obtained from those of the interfacial microstructure. First, the case of an elliptical inclusion connected by a structural interface to an infinite matrix is solved analytically, showing that nonlocal effects follow directly from the introduction of the structure, related to the inclination of the connecting elements. Second, starting from a discrete structure, a continuous model of a structural interface is derived. The usual zero-thickness linear interface model is shown to be a special case of this more general continuous structural interface model. Then, a gradient approximation of the interface constitutive law is rigorously derived: it is the first example of the analytical derivation of a nonlocal interface model from the microstructure properties. The effects introduced in the mechanical behavior by both the continuous model and its gradient approximation are illustrated by solving, for the first time, the problem of a circular inclusion connected to an infinite matrix by a structural interface and subject to remote uniform stress.     

基于时间序列分析的结构损伤特征提取与预警方法

基于在线监测数据的损伤诊断是结构健康监测的核心课题之一.本文基于时间序列分析ARMA模型探讨了结构损伤特征提取和损伤预警的实现方法.首先对监测数据建立ARMA模型,并基于模型中自回归部分参数,采用主成分分析的方法提出了新的结构损伤特征指标.然后采用t-检验考察该指标在损伤前后是否存在显著性的变化,从而可以有效地实现结构损伤预警.三跨连续梁数值算例表明,本文提出的损伤特征指标对结构的微小损伤具有敏感性,具备结构在线实时损伤预警的应用价值.     

Elastico-viscous squeeze films: Part 2. superimposed rotation

The first part of this paper contains a reconsideration of the conventional squeeze-film situation. It is shown that the Part 1 concentration on the half-time t_{$\text{1}\text{2}$} sometimes hides interesting elastico-viscous effects, since these are most pronounced at short times after the load is applied.The bulk of the paper is concerned with the more general situation in which a rotational flow is superimposed on the basic squeezing flow. This is brought about by rotating the bottom plate. An approximate theoretical analysis is shown to lead to a satisfactory prediction of observed behaviour under conditions of light loading.The experiments show substantial transient stress-overshoot effects under some conditions and there is also a possible indication of long-range memory effects in some of the experiments.     

On optimization of many-revolution low-thrust orbit transfers: Part 2

Quasioptimal and numerical solutions of the exact equations of optimal low-thrust motion in a Newtonian central gravity field are compared. The main properties of the optimal solutions are confirmed. It is established that the characteristic velocity is independent of the spacecraft or constant-thrust engine parameters Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 115–122, September 2008.     

Analytical Treatment of Some Extended Problems in Structural Optimization,Part I

ABSTRACT

Optimization problems involving supports of unspecified location as well as variable external actions and reactions of nonzero cost are discussed in the context of both plastic and elastic beams and frames, of non-preassigned, partially preassigned, and preassigned cost distribution, and of strength or deflection constraints.

The static-kinematic optimality criteria for various classes of problems are illustrated with simple examples and the results are checked by an independent method, i.e., by differentiation of the total cost with respect to the unknown variables. It is shown that for certain classes of problems the conditions introduced reduce to existing criteria by Prager and Masur.     

Analytical Treatment of Some Extended Problems in Structural Optimization,Part II

ABSTRACT

The Prager-Shield theory of optimal plastic design is applied to systems of preassigned topography (configuration) subject to either a single or several alternate load conditions. For the particular case of pin-jointed frames and a single load system, the criteria derived are shown to reduce to a condition obtained recently by Prager. The method is extended to cover joints of nonzero cost and it is illustrated with examples of trusses and grillages.

Finally, the optimization of discrete grillages having movable beams in preassigned directions is considered.     

结构模态参数的时序分析(ARMAV模型)识别法

本文简述了用时间序列分析(ARMAV 模型)识别结构模态参数的原理,对建模方法进行了分析,并对建模分析中至关重要的初值选择问题进行了讨论,提出了一种有效的初值的选取方法;在模拟计算部分中,用 Wilson-θ积分法模拟了一个三个自由度的振动和低信噪比、大阻尼振动和密集模态等复杂情形,对用时序方法(ARMAV 模型)识别模态参数的能力进行了检验;最后通过对实验数据进行有效的预处理后,用时序方法(ARMAV 模型)识别出一个真实结构(圆盘)的第一、二阶模态参数,并得到结构的完整振型.     

Elastic recovery of immiscible blends Part 2: Transient flow histories

Immiscible polymer blends are known to display an unusual elastic recovery after stress release. Recoil after steady-state shearing is well understood and obeys specific scaling relations. Releasing the stress before the steady-state morphology has been reached results in a more complex elastic recovery, including very large final values. This behaviour is investigated systematically. Model blends are used, consisting of nearly inelastic components; hence the measured recoil can be attributed totally to contributions from the interface. The instantaneous structure at the onset of the recoil can vary greatly in transient experiments, ranging from slightly deformed droplets to highly elongated filaments. The effects of this initial structure on the ultimate recoil and time scale of the recovery are studied. The morphological changes during recovery are considered as well. It is demonstrated that they can be computed from the normal stresses during stress relaxation with comparable initial morphologies. This indicates that the same morphological changes occur during stress relaxation and constrained recoil. A scaling relation for the recoil curves has been derived from the Doi-Ohta theory, which is confirmed by the experiments. Received: 9 December 1998 Accepted: 5 April 1999     

A review of turbomachinery tip gap effects: Part 2: Rotating machinery

This two part review covers experiments examining the effects of blade tip gaps encountered in turbomachines and the methods by which the synthesised data are currentl used in turbomachine design and analysis. Data gained since the 1930's are subdivided for convenience into cascade (Part 1) and rotating machinery (Part 2) data, with a further subdivision into diffusing, or compressor type flows and accelerating, or turbine type flows. The overall trend is that an increasing tip gap, whose effect can reach over most or all of the blade height, reduces turbomachine performance. There is some evidence among the compressor and compressor cascade data that an optimum gap exists when the opposing effects of secondary flows and tip leakage with rotor/wall relative movement tend to balance. Turbine data are, in general, more regular than the body of compressor data, possibly because of the enhanced effect of, usually, undefined boundary layers in diffusing flow in the latter. Comment is made in Part 2 on the predictive and design models reported in the liturature     

Explosive instability of geostrophic vortices. Part 2: parametric instability

In a two-layer quasi-geostrophic model, a baroclinic vortex is submitted to a periodic forcing of its mean baroclinic azimuthal velocity. It is shown that parametric effects could stabilize a vortex which is baroclinically unstable in the absence of forcing. Conversely, parametric resonance can destabilize a baroclinically stable vortex, under conditions on the vortex parameters, on the ratio of layer thicknesses or on the forcing frequency.