三峡水电站充水保压蜗壳平面非线性分析

采用自编的三维钢筋混凝土非线性有限元程序，对三峡水电站充水保压蜗壳进行了平面非线性分析，分析了钢蜗壳及外围钢筋混凝土的应力变形特性。非线性计算分析表明，在蜗壳进口断面处，虽然外围混凝土较薄，但在设计内水压力、结构自重和设备重量这些荷载组合作用下，蜗壳进口断面混凝土可能不会开裂，因此钢材应力均比较低，结构具有较高的安全度。说明现有配筋方案钢筋用量可能偏多，没有充分发挥钢材的作用，在进一步设计时可以适当优化。     

Applications of Level 2 BLAS in the NAG library

We describe work done to improve the performance of NAG Library routines for nonlinear equations and nonlinear least squares problems on vector-processing machines. Calls to the Level 2 BLAS routines for matrix-vector operations were introduced wherever possible, so that further efforts to tune the code could be concentrated within the Level 2 BLAS, and advantage can be taken of optimized implementations of the Level 2 BLAS when they become available. Performance measurements from a CRAY-1S, an AMDAHL VP1100, and a CDC CYBER 205 are presented to illustrate the effectiveness of this strategy.     

非线性锥形梯度折射率透镜的光学特征

本文对非线性锥形梯度折射率透镜进行了分析,根据稳态自聚焦理论以及ABCD定律,导出了高斯光束通过这种透镜光斑尺寸及其位置的公式。讨论了几种特殊的情况,得到了一些重要的结果。     

参数强迫激励下非线性振子尖点型奇点的分叉

本文首先研究了不具有Z_2—对称性时的规范形理论和退化向量场的普适开折理论。然后利用这些理论研究了参数激励与强迫激励联合作用下非线性振动系统的尖点型奇点的余维2退化分叉。     

钢筋混凝土框架-剪力墙结构在强震作用下的非线性分析——Ⅱ、程序及算例

运用文献[1]所介绍的分析原理与方法,编制了强震作用下钢筋混凝土框架-剪力墙结构非线性地震反应时程分析的程序。本文介绍该程序的功能、框图,以及利用该程序计算所得到的几栋钢筋混凝土结构的非线性地震反应分析结果。算例表明,本程序计算结果可靠,能很好地用于解释震害和预测地震时结构可能发生的破坏。     

New approaches for error estimation and adaptivity for 2D potential boundary element methods

This work presents two new error estimation approaches for the BEM applied to 2D potential problems. The first approach involves a local error estimator based on a gradient recovery procedure in which the error function is generated from differences between smoothed and non‐smoothed rates of change of boundary variables in the local tangential direction. The second approach involves the external problem formulation and gives both local and global measures of error, depending on a choice of the external evaluation point. These approaches are post‐processing procedures. Both estimators show consistency with mesh refinement and give similar qualitative results. The error estimator using the gradient recovery approach is more general, as this formulation does not rely on an ‘optimal’ choice of an external parameter. This work presents also the use of a local error estimator in an adaptive mesh refinement procedure. This r‐refinement approach is based on the minimization of the standard deviation of the local error estimate. A non‐linear programming procedure using a feasible‐point method is employed using Lagrange multipliers and a set of active constraints. The optimization procedure produces finer meshes close to a singularity and results that are consistent with the problem physics. Copyright © 2002 John Wiley & Sons, Ltd.     

Multiplicative Operator Splittings in Nonlinear Diffusion: From Spatial Splitting to Multiple Timesteps

Operator splitting is a powerful concept used in many diversed fields of applied mathematics for the design of effective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an efficient nonlinear diffusion filtering on digital images, we analyze the possibility of using multiplicative operator splittings to process images from different perspectives.We start by examining the potential of using fractional step methods to design a multiplicative operator splitting as an alternative to AOS schemes. By means of a Strang splitting, we attempt to use numerical schemes that are known to be more accurate in linear diffusion processes and apply them on images. Initially we implement the Crank-Nicolson and DuFort-Frankel schemes to diffuse noisy signals in one dimension and devise a simple extrapolation that enables the Crank-Nicolson to be used with high accuracy on these signals. We then combine the Crank-Nicolson in 1D with various multiplicative operator splittings to process images. Based on these ideas we obtain some interesting results. However, from the practical standpoint, due to the computational expenses associated with these schemes and the questionable benefits in applying them to perform nonlinear diffusion filtering when using long timesteps, we conclude that AOS schemes are simple and efficient compared to these alternatives.We then examine the potential utility of using multiple timestep methods combined with AOS schemes, as means to expedite the diffusion process. These methods were developed for molecular dynamics applications and are used efficiently in biomolecular simulations. The idea is to split the forces exerted on atoms into different classes according to their behavior in time, and assign longer timesteps to nonlocal, slowly-varying forces such as the Coulomb and van der Waals interactions, whereas the local forces like bond and angle are treated with smaller timesteps. Multiple timestep integrators can be derived from the Trotter factorization, a decomposition that bears a strong resemblance to a Strang splitting. Both formulations decompose the time propagator into trilateral products to construct multiplicative operator splittings which are second order in time, with the possibility of extending the factorization to higher order expansions. While a Strang splitting is a decomposition across spatial dimensions, where each dimension is subsequently treated with a fractional step, the multiple timestep method is a decomposition across scales. Thus, multiple timestep methods are a realization of the multiplicative operator splitting idea. For certain nonlinear diffusion coefficients with favorable properties, we show that a simple multiple timestep method can improve the diffusion process.     

钻井井架力学性能分析

钻井井架作为钻机系统设备中的关键部分,其力学性能直接关系到整套钻机系统的安全生产。文章推导了常用于分析钻井井架力学性能的理论,即线性屈曲、几何非线性和双重非线性理论。提出同时用这三种理论对钻井井架进行综合比较分析,从而合理地预见井架力学性能的方法。以A形钻井井架为例,进行了详细的分析,得到了井架的失稳形式、极限承载、破坏特征及薄弱部位,为钻井井架的设计、优化与评定提供了参考。     

船舶操纵非线性系统的鲁棒变结构控制

本文采用伪线性化变换将船舶操纵非线性系统近似地化为线性可控正则型，并对线性化系统设计了一种连续的变结构以提高整个闭环系统的鲁棒性。该方案用于限制水域中船舶的航向航迹纠编控制中，取得了预期的结果。     

基于神经网络非线性系统辨识和控制的研究

本文提出了由静态的前馈网络和稳定的滤波器构成的非线性系统的辨识模型，在神经网络固有的逼近误差存在的情况下，从理论上讨论了神经网络应用于辨识控制过程中系统的稳定性问题，最后研究了在非线性系统的轨迹跟踪过程中增加滑动控制来偿神经网络的逼近误差，从而提高系统跟踪性能。