用薄层法分析层状地基中条形基础的阻抗函数

薄层法是分析和模拟弹性波在层状介质中传播的一种半解析半数值方法,以往薄层法在柱坐标体系中建立求解方程,并通过直角坐标系和柱坐标系的转化关系而得到直角坐标系中的解答,本文从直角坐标直接推导了层状地基在无限长线荷载作用下的计算公式,求解了层状地基在垂直方向和水平方向上无限长线激振荷载作用下薄层法位移基本解.结合容积法得出了层状地基中基础-地基动力相互作用方程及条形基础阻抗函数的计算公式.本文计算了半无限弹性地基以及基岩上覆盖层在无限长简谐线荷载作用下的位移反应,计算了半无限弹性地基以及基岩上覆盖层地基中明置与埋置条形基础的地基阻抗函数.计算结果与已有的研究结果的比较表明两者吻合较好,验证了本文方法的适用性.     

用薄层法分析层状地基中各种基础的阻抗函数

薄层法是分析和模拟弹性波在层状介质中传播的一种半解析半数值方法.采用薄层单元和傍轴边界分别模拟层状地基和弹性半空间.利用薄层法位移基本解和容积法推导了层状地基中基础-地基动力相互作用方程及块式基础、桩基础和承台群桩基础阻抗函数的统一计算公式.通过计算半无限弹性地基中桩基础、块式基础和二层地基上基础的阻抗函数验证了方法的适用性.进而计算了某实际层状地基中承台群桩基础的阻抗函数,并与试验结果进行对比,两者吻合较好.本文方法可用于分析弹性层状地基中各种基础的阻抗函数.     

层状地基中的单桩沉降分析

本文利用薄层法得出层状地基在内、外部荷载作用下的位移格林函数,并由此结果求得层状地基的柔度矩阵。在此基础上,文中利用子结构法分析单桩的沉降问题,并与工程实测进行了比较,二者较为一致,说明了本文方法的有效性。     

用粘性边界有限元法分析弹性半无限地基中的动力问题

本文使用设置粘性边界单元的有限元方法，分析了简谐集中激振力产生的地表位移反应，刚性基础及桩基础的阻抗函数等半无限地基中的动力问题。计算结果与其他数值分析方法结果的比较表明，粘性边界单元的有限元方法适用于分析弹性半无限地基中的动力问题。本文还讨论了有限元网格尺寸及模型大小对计算结果的影响。     

用能量法分析层状材料弹性接触问题

利用能量法分析了层状材料（薄膜／基体）弹性接触问题，得到了具有一阶精度的闭合解，给出了求解薄膜弹性模量和泊松比的表达式，并与有限元的数值解进行了比较。二者比较结果表明：在工程材料范围内，理论解与数值解相差在6％以内；同时表明单相材料中剪切模量与弹性模量之间的关系也适用层状材料中的薄膜材料。在数值解的基础上，讨论了薄膜厚度与压头半径的比值对求解精度的影响，发现此比值对精度影响不大。通过对层状材料等效泊松比与等效弹性模量的定义，给出了用压痕实验测定薄膜泊松比与弹性模量的方法。     

层状地基中埋管地基阻抗函数的分析方法

本文首先利用波函数展开法推导了弹性半空间中埋管的地基轴向阻抗函数计算公式.然后采用层状地基中无限长线激振荷载薄层法基本位移解,结合容积法求解了层状地基中埋管的地基轴向、垂直及水平阻抗函数.分别用两种方法计算了弹性全空间、弹性半空间地基内埋管的地基轴向阻抗函数,两者的计算结果符合良好,验证了用薄层法求解的可行性.本文还利用薄层法分析了弹性半空间内埋管的埋深对地基水平、垂直及轴向阻抗函数的影响;计算了弹性半空间内埋管的轴向刚度系数并与我国及日本的相关规范对比分析;计算分析了上海典型层状地基内地铁隧道的地基阻抗函数.     

横观各向同性层状场地中的单桩横向动力阻抗函数

本文采用横观各向同性层状弹性模型，模拟半空间上的层状场地，用阻尼器模拟透射边界代替半空间以吸收能量。利用薄层元素法和于结构法，并利用在这种边界下受水平简谐荷载作用下的格林函数，推导了这种场地中竖直单桩在水平—摇摆简谐荷载作用下的横向动力阻抗函数，并用实例计算了不同横观各向同性性质场地下的动力阻抗函数，并由此分析了场地的横观各向同性性质的强弱对单桩的横向动力阻抗函数所将产生的影响。计算表明：弱横观各向同性场地对阻抗函数的影响很小，以至可以忽略这种影响；而强横观各向同性场地对阻抗函数的影响较大，必须考虑其影响。另外，桩头约束的存在与否，对单桩的横向阻抗函数值也有较大的影响，桩头有约束的阻抗函数值要明显大于无约束的阻抗函数值。     

用无网格局部Petrov-Galerkin法分析非线性地基梁

利用无网格局部Petrov-Galerkin法求解了非线性地基梁。在Petrov-Galerkin方法中，采用移动最小二乘（MLS）近似函数作为场主量挠度的试函数并取移动最小二乘近似函数中的体验函数作为近似场函数的加权函数，采用罚因子法施加本质边界条件。文末给出了两个计算实例，算例的结果表明，Petrov-galerkin法不仅能成功地分析线性地基梁，而且也适用于解非线性地基梁，在分析非线性地基梁时具有收敛快，稳定性好的优点。     

矩形截面梁受二次分布力作用Airy应力函数的选取

1.前言矩形截面梁受二次分布力作用弯曲的多项式弹性力学解,文献[1]曾作过讨论,给出了Airy 应力函数的具体形式.但文献[1]只说“我们找到了一种多项式解答”,而没有公开这个应力函数的来源方法.     

确定岩土二次屈服函数中有关参数的一种方法

本文利用岩土单轴压缩和纯剪试验的强度指标,给出了岩土二次屈服函数中有关待定参数的一种确定方法及相应的计算公式.方法简单易行,可供理论分析和数值计算应用.     

若干综合应用递归二次规划法和边界元法的平面弹性结构形状优化问题

结构的边界表示为若干设计变量的函数,结构形状优化问题表示为数学规划问题。本文采用递归二次规划法求解数学规划问题,采用边界元法做结构分析,求解了受拉多边形板、受弯悬臂梁和空腹重力坝的形状优化问题。结果表明本文的求解方案非常有效。     

Consolidation Statistics Investigation via Thin Layer Method Analysis

In this paper, the Thin Layer Method (TLM) is adapted for solving one-dimensional primary consolidation problems. It is also combined with a stochastic formulation integrating Monte Carlo simulations to investigate primary consolidation of a random heterogeneous soil profile. This latter is modeled as a set of superposed layers extending horizontally to infinity, and having random properties. Spatial variability of soil properties is considered in the vertical direction only. Soil properties of interest are elastic modulus and soil permeability, modeled herein as spatially random fields. Lognormal distribution is chosen because it is suitable for strictly non-negative random variables, and enables analyzing the large variability of such properties. The statistics regarding final settlement and its corresponding time are investigated by performing a parametric study, which integrates the influence of variation coefficient of both elastic modulus and soil permeability, and vertical correlation length. Obtained results indicate that heterogeneity significantly influences primary consolidation of the soil profile, generating a quite different way of soil grain rearrangement and water pressure dissipation in comparison to the homogeneous case, and causing a delay in the consolidation process.     

弹塑性问题参数二次规划分析的隐式算法

传统的二次规划算法求解弹塑性问题时一般要经过对问题的线性化,如对屈服条件的一阶近似展开等,这在一定程度上会造成数值解的误差。为此,本文提出一种改进的策略,引入迭代与规划算法相结合的技术对问题进行处理,算法收敛平稳迅速,在大步长荷载增量下使算法的精度大大提高。由于本文的算法属于隐式算法,因而也就弥补了原二次规划算法求解弹塑性问题时只有显式算法的不足,从而达到了对原算法的进一步完善。     

Surface Forces Driven Wrinkling of an Elastic Half-Space Coated with a Thin Stiff Surface Layer

This paper studies surface instability of a coated semi-infinite linear elastic body interacting with another flat rigid body through surface van der Waals (vdW) forces under plane strain conditions. The emphasis is on the effect of the surface coating layer on the wavelength of surface wrinkling. It is shown that the surface of the coated elastic half-plane is always unstable even in the presence of a very stiff coating layer. However, the numerical results show that the stiff coating layer has a significant effect on the wavelength of the surface instability mode and can effectively prevent the surface from short-wavelength wrinkling. In particular, the surface tangential displacement associated with the surface instability vanishes when the elastic half-plane is incompressible. In this case, the in-plane rigidity of the coating layer has no effect on surface instability while the bending stiffness of the coating layer has an effect on the wave-length of the surface instability mode. Furthermore, the Poisson’s ratio of elastic half-plane has a significant role in the surface instability and the associated wave-length. C. Q. Ru is on leave from the University of Alberta, Edmonton, T6G. 2G8, Canada.     

数字图像相关方法中匹配及过匹配形函数的误差分析

基于图像子区的数字图像相关方法需采用合适的形函数来近似目标图像子区的真实变形。由于实际测量时目标子区的局部变形往往是未知的,实际采用的不同阶次(零阶、一阶和二阶)的形函数不可避免地产生误匹配(欠匹配和过匹配)问题,从而引入位移测量的系统或随机误差。尽管由欠匹配形函数引起的系统误差已被充分认识,由过匹配形函数引起的位移误差仍缺少理论解释。本文首先推导出采用一阶和二阶形函数的数字图像相关方法的随机误差理论公式,随后采用一系列数值实验验证了理论公式的准确性。结果显示:过匹配形函数不会引入额外的系统误差,但会增加随机误差,且二阶形函数的随机误差是一阶形函数的二倍。考虑到由欠匹配一阶形函数引入的系统误差往往远大于过匹配二阶形函数的随机误差,因此在未能确知变形的情况下,推荐使用二阶形函数。     

矩形薄板弯曲问题的二维广义有限积分变换法

运用二维广义有限积分变换解法,本文推导出不同边界条件下矩形薄板弯曲问题的解析解．在推导过程中,选取满足边界条件的梁振型函数为广义积分变换的积分核,由此构造出广义有限积分变换对,通过对薄板弯曲问题的控制方程进行二维广义积分变换,可以将控制方程转换为易于求解的线性代数方程组．该方法无需预先选取位移函数,无需进行繁琐的叠加过程,求解过程思路清晰,说明该方法更加正确合理．最后通过计算实例对比,验证了该方法的合理性及所推导公式的正确性．     

Finite Difference Method for the Acoustic Radiation of an Elastic Plate Excited by a Turbulent Boundary Layer: A Spectral Domain Solution

A finite difference method is developed to study, on a two-dimensional model, the acoustic pressure radiated when a thin elastic plate, clamped at its boundaries, is excited by a turbulent boundary layer. Consider a homogeneous thin elastic plate clamped at its boundaries and extended to infinity by a plane, perfectly rigid, baffle. This plate closes a rectangular cavity. Both the cavity and the outside domain contain a perfect fluid. The fluid in the cavity is at rest. The fluid in the outside domain moves in the direction parallel to the system plate/baffle with a constant speed. A turbulent boundary layer develops at the interface baffle/plate. The wall pressure fluctuations in this boundary layer generates a vibration of the plate and an acoustic radiation in the two fluid domains. Modeling the wall pressure fluctuations spectrum in a turbulent boundary layer developed over a vibrating surface is a very complex and unresolved task. Ducan and Sirkis [1] proposed a model for the two-way interactions between a membrane and a turbulent flow of fluid. The excitation of the membrane is modeled by a potential flow randomly perturbed. This potential flow is modified by the displacement of the membrane. Howe [2] proposed a model for the turbulent wall pressure fluctuations power spectrum over an elastomeric material. The model presented in this article is based on a hypothesis of one-way interaction between the flow and the structure: the flow generates wall pressure fluctuations which are at the origin of the vibration of the plate, but the vibration of the plate does not modify the characteristics of the flow. A finite difference scheme that incorporates the vibration of the plate and the acoustic pressure inside the fluid cavity has been developed and coupled with a boundary element method that ensures the outside domain coupling. In this paper, we focus on the resolution of the coupled vibration/interior acoustic problem. We compare the results obtained with three numerical methods: (a) a finite difference representation for both the plate displacement and the acoustic pressure inside the cavity; (b) a coupled method involving a finite difference representation for the displacement of the plate and a boundary element method for the interior acoustic pressure; (c) a boundary element method for both the vibration of the plate and the interior acoustic pressure. A comparison of the numerical results obtained with two models of turbulent wall pressure fluctuations spectrums - the Corcos model [3] and the Chase model [4] - is proposed. A difference of 20 dB is found in the vibro-acoustic response of the structure. In [3], this difference is explained by calculating a wavenumber transfer function of the plate. In [6], coupled beam-cavity modes for similar geometry are calculated by the finite difference method. This revised version was published online in July 2006 with corrections to the Cover Date.