陡坡地基上高填路堤极限承载力研究

结合山区高速公路建设的实践,采用大型室内模型试验,找出了荷载作用下陡坡地基上高填方路堤滑动破坏面出现的位置及形态。通过对路堤边坡稳定性计算的极限分析上限法进行研究,根据折线形滑动面形式建立机动容许速度场,推导计算斜坡地基上高填方路堤稳定性及极限承载力的计算公式。运用此方法对斜坡地基上不同斜坡坡度、不同填土高度、不同路堤宽度以及不同路堤边坡坡度的填方路堤极限承载力进行计算,得出各个因素对其极限承载力的影响。研究结果表明:路堤填筑高度和顶面宽度对其极限承载力的影响最大,其次为斜坡坡度的影响,而路堤边坡坡度对其影响并不显著。建议在斜坡地基上填方路堤的设计与施工过程中综合考虑斜坡坡度、填土高度、路堤宽度、路堤边坡坡度、极限承载力等各种因素的影响,以确保山区高速公路安全畅通。     

可交换随机序列和的中心极限定理的收敛速度

讨论了一类重要的相依随机变量序列－可交换随机变量序列部分和的中心极限问题。在与独立同分布随机变量序列部分和的中心极限问题相同的条件下，利用可交换随机变量的结构定理和Ｂｅｒｒｙ－Ｅｓｓｅｅｎ方法，获得了可交换随机变量序列部分和收敛于标准正态分布的最优收敛速度。     

集中荷载作用下不同边界条件的直梁简谐受迫振动的稳态解

应用功的互等定理求解不同边界条件下直梁简谐受迫振动的稳态解,给出了相应的一系列具有实际价值的稳态解。     

二维黑洞的熵与能斯特定理

利用砖墙模型，直接计算1＋1维（时-空）黑洞背景下标量场的自由能和玻色子熵．结果表明，黑洞的熵与内外视界有关．如果计及内视界贡献，当辐射温度趋于零时，二维黑洞熵趋于零，满足能斯特定理，可看成Plank绝对熵．当不考虑内视界贡献时，黑洞熵具有对数发散项，与已有结论一致．     

达布定理的一个应用

应用达布定理,纠正了不定积分计算中的一个错误。     

Robust hierarchical controller with conditional integrator based on small gain theorem for reference trajectory tracking of autonomous vehicles

ABSTRACT

A robust trajectory tracking controller is designed for autonomous vehicles based on a hierarchical architecture to make the autonomous vehicle track a given reference trajectory. The controller consists of two sub controllers: kinematic controller and dynamic controller. Based on the kinematics of tracking reference trajectory, a desired yaw rate is calculated by kinematic controller to make the lateral deviation global asymptotic stable. Then, steering wheel angle is calculated by a vehicle dynamic controller to make the vehicle yaw rate converge to the desired value and make the vehicle dynamic stable. Conditional integration method is used in the sub controllers. This method guarantees global asymptotic stability of tracking reference values and considers the uncertainty of parameters and constraints of desired yaw rate and actuators. Then based on small-gain theorem, the condition of the finite-gain L stability is given to the hierarchical controller to ensure the interconnected sub systems stable and prevent the amplification of system disturbance. Finally, the effectiveness and robustness of the controller are validated by real vehicle experiments.     

Development of a systematic and practical methodology for the design of vehicles semi-active suspension control system

In this paper, a novel systematic and practical methodology is presented for design of vehicle semi-active suspension systems. Typically, the semi-active control strategies developed to improve vehicle ride comfort and stability have a switching nature. This makes the design of the controlled suspension systems difficult and highly dependent on an extensive trial-and-error process. The proposed methodology maps the discontinuous control system model to a continuous linear region, where all the time and frequency design techniques, established in the conventional control system theory, can be applied. If the semi-active control system is designed to satisfy some ride and stability requirements, an inverse mapping offers the ultimate control law. At the end, the entire design procedure is summarised in six steps. The effectiveness of the proposed methodology in the design of a semi-active suspension system for a Cadillac SRX 2005 is demonstrated with road tests results. Real-time experiments confirm that the use of the newly developed systematic design method reduces the required time and effort in real industrial problems.     

一类奇异泛函微分方程边值问题的正解

利用锥拉伸与锥压缩不动点理论讨论了一类具有限时滞二阶奇异泛函微分方程三点边值问题正解的存在性,建立了一类奇异泛函微分方程边值问题至少存在一个正解的充分性条件并推广和改进了已有的结果.     

一类含有时滞的脉冲微分方程的正周期解

研究了一类含有时滞的脉冲微分方程,在系数变号的情形下,利用锥上的不动点定理获得了其正ω-周期解的存在性结果.     

管棚预支护条件下水下隧道开挖面三维稳定性分析

基于塑性极限分析理论,建立了考虑渗流力的管棚预支护条件下隧道开挖面三维稳定性分析模型,由此确定开挖面的极限支护压力。结合深圳地铁实际工程,采用该方法计算得到的开挖面极限支护压力与流固耦合数值计算结果吻合较好,验证了该方法的合理性,进而研究了管棚预支护对隧道开挖面渗流力的影响,分析了地下水位和管棚剩余长度与开挖面渗流力的关系。分析结果表明:渗流力对隧道开挖面稳定性有显著的影响,而且渗流力与地下水位呈线性关系,当隧道在富水地层施工时,必须考虑渗流力对隧道开挖面稳定性的影响;采用管棚预支护可以显著地减小隧道开挖面处的渗流力,但当开挖面前方管棚剩余长度超过2倍洞径时,再增加管棚长度对减小开挖面渗流力的效果不明显。