仿紧集上新型抽象广义双拟变分不等式

笔者在本文应用文献[1]中得到的极大极小不等式研究了仿紧集上新型抽象广义双拟变分不等式解的存在性问题.     

基于统一解的盾构隧道施工引起地下管线竖向位移计算

盾构隧道施工会对周围土体产生扰动,当土体沉降和变形过大时,会对邻近地下管线产生危害。采用统一土体移动模型解计算盾构隧道施工引起的土体自由位移场,通过能量方法建立变分控制方程,得到盾构隧道施工引起地下管线竖向位移的计算方法,将计算结果与刘晓强方法计算结果及实测数据进行对比,并分析土质条件、管线轴线埋深、管线材质等因素对管线竖向位移的影响。结果表明:与刘晓强方法相比,基于统一解的能量变分法计算结果与实测值更加吻合;双线盾构隧道施工引起的管线竖向位移在两隧道中轴线两侧呈不对称分布;不同土质条件对管线的竖向位移和沉降槽宽度有较大影响,而不同管线埋深、材质的影响较小。     

矩形桩竖向受荷三维弹性变分解

矩形桩作为一种典型的横截面非圆形桩，通常采用等效圆形桩的近似方法来分析，未能从理论上考虑桩-土相互作用。针对该问题，结合复变函数保角变换技术提出一种适用于竖向受荷矩形桩的三维弹性变分方法。基于最小势能原理和变分法获得桩位移函数和土竖向位移传递函数的控制微分方程，为克服土体位移传递函数求解域边界形状复杂的困难，应用保角变换将桩-土接触面的复杂边界形状转化为简单边界，并获得了桩位移函数的解析解及土体竖向位移函数的半解析解。使用MATLAB软件编制相应的分析程序，并将分析得到的结果与有限元分析及现有解答进行对比。最后，对影响桩沉降的主要因素进行参数分析。研究结果表明：所得解与有限元分析结果吻合得更好，证明了所提分析方法的正确性；摩擦桩量纲一化的桩顶刚度随桩-土模量比的增加逐渐减小，当桩的长细比增加到某数值时，其对桩顶刚度的影响可忽略不计，即摩擦桩存在有效桩长；相对于摩擦桩，当桩-土模量比较大时，其对端承桩的桩顶刚度影响较小，当端承桩长细比足够大时，可转化为摩擦桩；桩顶刚度随土体泊松比先减小后增加，间接表明其不仅受土体抗剪强度的影响，而且受土体压缩性能的影响；在相同混凝土用量下，当桩-土模量比较小时，与等横截面面积圆桩相比，矩形桩的桩顶刚度明显大于圆桩，当桩-土模量比超过某数值时，二者桩顶刚度逐渐趋于一致；当桩-土模量比较小时，等横截面面积矩形桩随横截面长宽比的增加，桩顶刚度增加。     

Optimal competitive freight network design as hierarchical variational inequalities programming problems

Freight networks are a case of systems that multiple participants are composing interrelations along the complete supply chain. Their interrelations correspond to alternative behavior, namely, cooperation, non-cooperation and competition, while they are large-scale spatially distributed systems combining multiple means of transportation and the infrastructure and equipment typically utilized for servicing demand, results to a complex system integration. In this paper, the case of the optimal design of freight networks is investigated, aiming to highlight the particularities emerging in this case of transportation facilities strategic and/or operational planning and the multiple game-theoretic and equilibrium problems that are structured in cascade and in hierarchies. The application that is investigated here focuses in the design of a significant ‘player’ of the freight supply chain, namely container terminals, while the proposed framework will aim on analyzing investment strategies built on integrated demand–supply models and the optimal network design format. The approach will build on the multilevel Mathematical Programming with Equilibrium Constraints (MPECs) formulation, but is further extended to cope with the properties introduced by the ‘designers’ (infrastructure authorities), shippers and carriers competition in all levels of MPECs. Since container terminals are typically competing each other, the nomenclature used here for formulating appropriate MPECs problems are based on hierarchies of Variational Inequalities (VI) problems, able to capture the alternative relationships emerging in realistic freight supply chains. The proposed formulations of the competitive network design case is addressed by a novel approach of co-evolutionary agents, which can be regarded as new in equilibrium estimation. Finally, the results are compared with alternative network design cases, namely the centralized cooperative and exchanging design. Under this analysis it is able to highlight the differences among alternative design cases, but moreover an estimation of the ‘price of anarchy’ in transportation systems design is offered, an element of both theoretical as well as practical relevance.     

Dynamic and disequilibrium analysis of interdependent infrastructure systems

There is a growing awareness in recent years that the interdependencies among the civil infrastructure systems have significant economic, security and engineering implications that may influence their resiliency, efficiency and effectiveness. To capture the various types of infrastructure interdependencies and incorporate them into decision-making processes in various application domains, Zhang and Peeta (2011) propose a generalized modeling framework that combines a multilayer infrastructure network (MIN) concept and a market-based economic approach using computable general equilibrium (CGE) theory and its spatial extension (SCGE) to formulate a static equilibrium infrastructure interdependencies problem. This paper extends the framework to address the dynamic and disequilibrium aspects of the infrastructure interdependencies problems. It briefly reviews the static model, and proposes an alternative formulation for it using the variational inequality (VI) technique. Based on this equivalent VI formulation, a within-period equilibrium-tending dynamic model is proposed to illustrate how these systems evolve towards an equilibrium state within a short duration after a perturbation. To address a longer time scale, a multi-period dynamic model is proposed. This model explicitly considers the evolution of infrastructure interdependencies over time and the temporal interactions among the various systems through dynamic parameters that link the different time periods. Using this model, numerical experiments are conducted for a special case with a single region to analyze the sensitivity of the model to the various parameters, and demonstrate the ability of the modeling framework to formulate and solve practical problems such as cascading failures, disaster recovery, and budget allocation in a dynamic setting.     

Efficiency Loss of the Multiclass Stochastic Traffic Equilibrium Assignment with Fixed Demand

There exists efficiency loss when introducing a user equilibrium traffic assignment in comparison with the system optimization assignment. Seeking the upper bound of the efficiency loss has attracted many scholars' attentions. The existing researches mainly focus on single user class and deterministic traffic assignment, few on stochastic user equilibrium (SUE) assignment with multiple user classes. In this paper, the authors investigate the upper bound of this SUE's inefficiency. Two decision-making criteria are used in the SUE, namely, time-based and monetary-based. It is shown that the upper bound of efficiency loss caused by the time-based SUE depends on the type of link travel time function, the network complexity, the travel demand, and the degree of users' perception error to travel cost. The upper bound of efficiency loss caused by the monetary-based SUE depends on the value of time of user classes besides the aforementioned factors.     

Precision analysis and dynamic stability in the numerical solution of the two-dimensional wheel/rail tangential contact problem

ABSTRACT

In this paper the two-dimensional contact problem is analysed through different mesh topologies and strategies for approaching equations, namely; the collocation method, Galerkin, and the polynomial approach. The two-dimensional asymptotic problem (linear theory) associated with very small creepage (or infinite friction coefficient) is taken as a reference in order to analyse the numerical methods, and its solution is tackled in three different ways, namely steady-state problem, dynamic stability problem, and non-steady state problem in the frequency domain. In addition, two elastic displacements derivatives calculation methods are explored: analytic and finite differences. The results of this work establish the calculation conditions that are necessary to guarantee dynamic stability and the absence of numerical singularities, as well as the parameters for using the method that allows for maximum precision at the minimum computational cost to be reached.     

Hilbert空间广义变分不等式的迭代方法

应用辅助原则技术,在部分相关强单调和非空有界闭子集条件下,提出了一个解广义变分不等式问题的预测校正算法.作为应用,给出了许多解不同类型变分不等式的新的结果.     

Fixed Points and Asymptotic Properties of Neutral Stochastic Delay Differential Equations

This paper discusses a linear neutral stochastic differential equation with variable delays. By using fixed point theory, the necessary and sufficient conditions are given to ensure that the trivial solution to such an equation is pth moment asymptotically stable. These conditions do not require the boundedness of delays, nor derivation of delays. An example was also given for illustration.