基于敏度阈值拓扑优化方法在飞机加强框设计中的应用

为了能够有效地降低飞机结构承力件的重量，针对飞机骨架，以加强框的概念设计为研究内容，通过对“敏度阈值”概念的分析，指出其不足，提出了“改进的敏度阈值”概念，并与“约束补偿”策略结合而形成新的拓扑优化算法，用于加强框的材料布局设计．多个算例中的拓扑优化结果均显示其结构型式十分新颖，值得深入地探讨．     

L p-Perturbations of Invariant Subbundles for Linear Systems

We use Riccati's equations and the ordinary and exponential dichotomies to get simple recurrent formulae for the asymptotic integration of linear systems subjected to L _p -perturbations with arbitrary p 1. Moreover, we establish conditions which are necessary and sufficient for the persistence of one-dimensional invariant subbundles for the linear system under L _p -perturbations. In this way, we prove the sharp nature of the well known Levinson and Hartman–Wintner asymptotic theorems.     

含裂纹三点弯曲梁起始扩展的动态分析

本文利用高速摄影捕捉含裂纹三点弯曲梁在冲击下裂纹扩展过程，借助动态焦散线对裂纹尖端初始曲线范围内的应力第二不变量分布进行了试验研究，并通过Ｄｅｔ．－准则对动载下裂纹起始扩展的条件和方向进行了分析。结果表明：裂纹扩展的实际方向与理论预测相一致；Ｄｅｔ．－准则与焦散线相结合在动态断裂力学研究中具有广泛的使用价值     

一种复合材料梁架结构的强度可靠性分析

为解决分析复合材料框架式结构的强度可靠性问题 ,应用最小势能原理 ,设计推导了一种具有复杂剖面形状 ,考虑横向剪切 ,承受横向集中及分布载荷作用的层合梁单元。根据一具体水平梁架的实际情况 ,结合有限元处理程序中组装总体刚度矩阵的特点 ,较好地实现了层合梁之间的不完全简支连接。分析系统强度可靠性时 ,通过可调控的运行方式 ,有效解决了挑选失效模式与离散单元数目之间的关系 ,使系统可靠性的计算更合理     

Properties of Chaotic and Regular Boundary Crisis in Dissipative Driven Nonlinear Oscillators

The phenomenon of the chaotic boundary crisis and the related concept of the chaotic destroyer saddle has become recently a new problem in the studies of the destruction of chaotic attractors in nonlinear oscillators. As it is known, in the case of regular boundary crisis, the homoclinic bifurcation of the destroyer saddle defines the parameters of the annihilation of the chaotic attractor. In contrast, at the chaotic boundary crisis, the outset of the destroyer saddle which branches away from the chaotic attractor is tangled prior to the crisis. In our paper, the main point of interest is the problem of a relation, if any, between the homoclinic tangling of the destroyer saddle and the other properties of the system which may accompany the chaotic as well as the regular boundary crisis. In particular, the question if the phenomena of fractal basin boundary, indeterminate outcome, and a period of the destroyer saddle, are directly implied by the structure of the destroyer saddle invariant manifolds, is examined for some examples of the boundary crisis that occur in the mathematical models of the twin-well and the single-well potential nonlinear oscillators.     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

The controllability for switched linear system with time-delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time-delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis. Contributed by YE Qing-kai Foundation items: the National Natural Science Foundation of China (69925307, 60274001); the National Key Basic Reasearch and Development Program (2002CB312200); the Postdoctoral Program Foundation of China Biography: XIE Guang-ming (1972∼), Doctor (E-mail: xiegming@mech.pku.edu.cn)     

三维复合型断裂的试验方法探讨

探讨了一种能够揭示三维复合型断裂现象并能记录这些现象的三维复合型断裂研究的实验方法，用此方法完成了LC4－CS航空结构铝合金不同厚度紧凑拉伸试样的I＋Ⅱ复合型断裂试验。结果表明：此方法能够简便地确定出复合型裂纹的起裂载荷、破坏载荷、裂尖张开位移、滑移位移和起裂角，基本解决三维复合型断裂研究所需实验数据问题。同时发现此种材料试样的承载能力和超裂方向的确具有明显的厚度效应。     

A Multibody Loop Constraints Approach for Modelling Cam/Follower Devices

This paper proposes a formulation for modelling mechanisms witha cam/follower type of contact using a multibody approach in relativecoordinates. The proposed approach is inspired from the wheel/railcontact model developed by Fisette and Samin but, in the present case,possible intermittent contact between the cam and the follower isconsidered, for generality purposes.Loop kinematicconstraints are introduced to satisfy tangent and punctual contact aslong as the bodies lean against each other. The effective presence (ornot) of the contact is governed by the sign of the normal constraintforce which can be computed thanks to the Lagrange multiplierstechnique.The above-mentioned option to kinematicallyconstraint the bodies in their contact phase unavoidably leads to ashift from one model to another when a contact disappears (or,conversely, reappears). Indeed, this increases (or decreases) the numberof degrees of freedom of the current system. The control of the variablepartitioning is thus absolutely necessary and is all the more complex sothat practical applications can contain several pairs of bodies inintermittent contact.Illustrative examples are proposed: acomparison with another multibody formalism, an experimental validationand the modelling of universal wheels of mobile robots which representsa quite original application of the proposed formulation.     

About the basic integral variants of holonomic nonconservative dynamical systems

In this paper, we prove that for holonomic nonconservative dynamical system the Poincaré and Poincaré-Cartan integral invariants do not exist. Instead of them, we introduce the integral variants of Poincaré-Cartan's type and of Poincare's type for holonomic nonconservative dynamical systems, and use these variants to solve the problem of nonlinear vibration. We also prove that the integral invariants introduced in references [1] and [2] are merely the basic integral variants given by this paper. Project supported by National Natural Science Foundation of China     

Geometric Singular Perturbations for Multiple Turning Points: Invariant Manifolds and Exchange Lemmas

In this paper, we consider singularly perturbed systems with multiple sets of turning points. Two types of related results contributing to geometric singular perturbation theory are obtained. The first result establishes a new class of invariant manifolds. The second result consists of several exchange lemmas that characterize the evolution of an invariant manifold passing through the vicinity of the slow manifold.Partially supported by NSF Grants DMS-0071931 and DMS-0406998.