Variational Inclusions for Fuzzy Mappings

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On Stability and Boundedness for Lipschitzian Differential Inclusions: The Converse of Lyapunov's Theorems

For Lipschitzian differential inclusions, we prove that the existence of suitable Lyapunov functions is necessary for uniform stability and uniform boundedness of solutions.     

双周期不等长刚性线Ⅲ型应力奇异因子的精确解

研究了含双周期刚性线夹杂复合材料的反平面剪切问题,其基本胞元含有四条不等长刚性线。运用复变函数方法,获得该问题严格的闭合解,得到了复合材料体内应力场的分布表达式,并在此基础上给出了刚性线尖端III型应力奇异因子的精确公式。数值算例显示了刚性线分布特征对材料细观应力场的影响,特别是短刚性线对主刚性线尖端应力场的屏蔽与放大作用。由本文解答的特殊情形,可以直接导出近年来其他学者获得的结果和一系列有意义的新结果。     

Inferring mechanism from time-series data: Delay-differential equations

When there is qualitative information about the underlying processes and structure of a dynamical system, it may be possible to infer very accurate quantitative information about these processes using only an output time series from the system. We illustrate how this can be accomplished for time series data from a delay-differential equation with a single fixed delay. Our approach exploits modern techniques for non-parametric function estimation, is robust to fairly high levels of dynamic noise and measurement error, and can be extended straightforwardly to more general delay-differential systems and multivariate systems.     

Stability analysis of numerical methods for systems of neutral delay-differential equations

Stability analysis of some representative numerical methods for systems of neutral delay-differential equations (NDDEs) is considered. After the establishment of a sufficient condition of asymptotic stability for linear NDDEs, the stability regions of linear multistep, explicit Runge-Kutta and implicitA-stable Runge-Kutta methods are discussed when they are applied to asymptotically stable linear NDDEs. Some mentioning about the extension of the results for the multiple delay case is given.     

Optimality Conditions and Synthesis for the Minimum Time Problem

We study the minimum time optimal control problem for a nonlinear system in R ⁿ with a general target. Necessary and sufficient optimality conditions are obtained. In particular, we describe a class of costates that are included in the superdifferential of the minimum time function, even in the case when this function is only lower semicontinuous. Two set-valued maps are constructed to provide time optimal synthesis.     

Formulating Measure Differential Inclusions in Infinite Dimensions

Measure differential inclusions were introduced by J. J. Moreau to study sweeping processes, and have since been used to study rigid body dynamics and impulsive control problems. The basic formulation of an MDI is d / d (t) K(t) where is a vector measure, an unsigned measure, and K() is a set-valued map with closed, convex values and is hemicontinuous. Note that need not be absolutely continuous with respect to . Stewart extended Moreau's original concept (which applied only to cone-valued K()) to general convex sets, and gave strong and weak formulations of d / d (t) K(t) where K(t) R ⁿ . Here the strong and weak formulations of Stewart are extended to infinite-dimensional problems where K(t) X where X is a separable reflexive Banach space; they are shown to be equivalent under mild assumptions on K().     

Banach空间中微分包含周期边值问题的唯一解和误差估计

旨在Banach空间中研究微分包含的周期边值问题(PBVP).假设F(t,u)仅满足弱Carathèodory条件,并不使用紧性条件,然而仍证明了该PBVP的唯一解能通过迭代序列的一致极限得到,并且还给出了解的误差估计.     

The Sweeping Processes without Convexity

We study the sweeping processes in a Hilbert space which are generated by a closed not necessarily convex moving set. A technique is developed, based on measurability properties of normal cones, in order to prove existence of solutions. Some existence results are proved, with or without hypothesis of compactness; moreover, under suitable assumptions, uniqueness and regularity properties are established. In particular, the well-known results of Moreau are extended to a class of not necessarily convex (called -convex) sets.     

Void growth and coalescence in ductile solids with stage III and stage IV strain hardening

State of the art ductile fracture models often rely on simple power laws to describe the strain hardening of the matrix material. Power laws do not distinguish between the two main stages of hardening observed in polycrystals, referred to as stage III and stage IV hardening, and which emerge from the evolution of the dislocation substructure. The aim of this study is to couple a physics based strain hardening law including these two stages to a micromechanics based ductile damage model. One of the main motivations is that, the stage IV constant hardening rate stage, occurring only at large strain, will be attained in most ductile failure problems if not at the overall level of deformation, at least locally around the growing voids. Furthermore, proper modelling of the stage III involving dislocation storage and recovery terms and the transition to stage IV provides a link with the underlying physical mechanisms of deformation and with the microstructure. First, in order to evaluate the effects of the stage III and stage IV hardening on void growth and coalescence, an extensive parametric study is performed on two-dimensional (2D) axisymmetric finite element (FE) unit cell calculations, using a Kocks-Mecking type hardening law. The cell calculations demonstrate that accounting for the stage IV hardening can have a profound effect on delaying void coalescence and increasing the ductility. The magnitude of the recovery term during stage III has also a significant effect on the void growth rate. Then, the Kocks-Mecking law is incorporated into the Gologanu-Leblond-Devaux (GLD) porous plasticity model supplemented by two different versions of the Thomason void coalescence criterion. The predictions of the damage model are in good agreement with the results of the FE calculations in terms of the stress-strain curves, the evolution of void shape and porosity, as well as the strain value at the onset of void coalescence.