Nonlinear analysis of laterally loaded rigid piles in cohesive soil

This article presents a method for the nonlinear analysis of laterally loaded rigid piles in cohesive soil. The method considers the force and the moment equilibrium to derive the system equations for a rigid pile under a lateral eccentric load. The system equations are then solved using an iteration scheme to obtain the response of the pile. The method considers the nonlinear variation of the ultimate lateral soil resistance with depth and uses a new closed‐form expression proposed in this article to determine the lateral bearing factor. The method also considers the horizontal shear resistance at the pile base, and a bilinear relationship between the shear resistance and the displacement is used. For simplicity, the modulus of horizontal subgrade reaction is assumed to be constant with depth, which is applicable to piles in overconsolidated clay. The nonlinearity of the modulus of horizontal subgrade reaction with pile displacement at ground surface is also considered. The validity of the developed method is demonstrated by comparing its results with those of 3D finite element analysis. The applications of the developed method to analyze five field test piles also show good agreement between the predictions and the experimental results. The developed method offers an alternative approach for simple and effective analysis of laterally loaded rigid piles in cohesive soil. Copyright © 2011 John Wiley & Sons, Ltd.     

An answer to an important controversy and the need for caution when using simple models to predict inelastic earthquake response of buildings with torsion

This paper presents evidence that the extension of conclusions based on the widely used simplified, one story, eccentric systems of the shear‐beam type, to actual, nonsymmetric buildings and consequent assessments of the pertinent code provisions, can be quite erroneous, unless special care is taken to match the basic properties of the simplified models to those of the real buildings. The evidence comes from comparisons of results obtained using three variants of simplified models, with results from the inelastic dynamic response of three‐ and five‐story eccentric buildings computed with detailed MDOF systems, where the members are idealized with the well‐known plastic hinge model. In addition, a convincing answer is provided on a pertinent hanging controversy: For frame‐type buildings, designed in accordance with the dynamic provisions of modern codes (such as EC8 or IBC2000), which allow reduced shears at the stiff edge due to torsion, the frames at the flexible sides are the critical elements in terms of ductility demands. Copyright © 2009 John Wiley & Sons, Ltd.     

A nonlinear stability analysis of convection in a generalized incompressible fluid

Abstract

We establish a nonlinear stability result for convection in a generalized incompressible fluid. Both numerical calculations and an asymptotic analysis are carried out. The linear and nonlinear results are shown to be very close in both cases, implying that the region of possible subcritical instabilities is very small.

During this work I was supported by a research studentship awarded by the Science and Engineering Council of the United Kingdom.     

Topographic instability and multiple equilibria on an f-plane

Abstract

The flow of a two-layer flow in a rotating channel on an f-plane over topography with sinusoidal variation of height in a direction parallel to the flow is investigated. When the two layers flow in opposite directions a resonance is found when the topographic scale matches the free mode of the system. We examine the stability of the forced mode in the vicinity of this resonance by means of a perturbation expansion of the topographic height. Both subresonant and super-resonant instabilities are found and their equilibration is examined. For small values of the dissipation multiple equilibria are found. The topographic drag releases potential energy even when the flow is baroclinically stable.     

On-line estimation of nonlinear physical systems

Recursive algorithms for estimating states of nonlinear physical systems are presented. Orthogonality properties are rediscovered and the associated polynomials are used to linearize state and observation models of the underlying random processes. This requires some key hypotheses regarding the structure of these processes, which may then take account of a wide range of applications. The latter include streamflow forecasting, flood estimation, environmental protection, earthquake engineering, and mine planning. The proposed estimation algorithm may be compared favorably to Taylor series-type filters, nonlinear filters which approximate the probability density by Edgeworth or Gram-Charlier series, as well as to conventional statistical linearization-type estimators. Moreover, the method has several advantages over nonrecursive estimators like disjunctive kriging. To link theory with practice, some numerical results for a simulated system are presented, in which responses from the proposed and extended Kalman algorithms are compared.     

滑坡灾害预报的非线性动力学方法

基于现代反演理论,建立了滑坡灾害预测的非线性动力学模型,给出了可预报时间尺度的确定方法及稳定性判断准则。通过实例分析表明,非线性动力学分析方法是行之有效的。     

用非线性模型研究环境温度场和涡度场对台风发生、发展的影响

本文采用二维板对称高截断谱模式研究了环境温度场和偶度场对台风发生、发展的影响，指出整层平均的环境温度场的水平梯度和涡度场是影响台风重要因子。较强的环境温度汤梯度的作用类似于水平方向不均匀加热场的作用，能造成暖区上升、冷区下沉的热力直接环流，并且温度场的梯度越大，环流越强。对于整层平均的绝对涡度场而言，只有弱的正的平均绝对涡度才有利于台风的维持。     

TROPICAL ATMOSPHERIC NONLINEAR STEADY RESPONSE SOLUTION UNDER EFFECTS OF PAIRED HEAT SOURCES OF CONTRASTING NATURE

Based on steady semi-geostrophic model equations,analysis is carried out of the linear and nonlinearmodification/response of the tropical atmosphere to the forcing of ideal paired heat sources of contrasting nature.Re-suits show that the linear part is dominant in the steady response but the nonlinear modification is quite noticable in theneighborhood of the heat source and between the paired sources,and the barotropic mode and second baroclinic modeplay a different role in the modification,with the barotropic(second baroclinic)mode modification depending largely onthe Rossby wave self-interaction(the magnitude due to the Kelvin-Rossby wave interaction)between the pairedsources.     

TROPICAL ATMOSPHERIC NONLINEAR STEADY RESPONSE SOLUTION UNDER EFFECTS OF PAIRED HEAT SOURCES OF CONTRASTING NATURE*

Based on steady semi-geostrophic model equations,analysis is carried out of the linear and nonlinear modification/response of the tropical atmosphere to the forcing of ideal paired heat sources of contrasting nature.Resuits show that the linear part is dominant in the steady response but the nonlinear modification is quite noticable in the neighborhood of the heat source and between the paired sources,and the barotropic mode and second baroclinic mode play a different role in the modification,with the barotropic(second baroclinic)mode modification depending largely on the Rossby wave self-interaction(the magnitude due to the Kelvin-Rossby wave interaction)between the paired sources.     

复杂性理论与滑坡动态预测研究新思路

概述了复杂性理论的发展及其对滑坡动态研究的影响；在概括滑坡预测研究现状的基础上，分析了滑坡动态预测的研究进展，最后是关于预测的几点思考，亦即滑坡动力学预测的研究方向。