水-椭圆柱体相互作用分析的精确和简化模型

针对柔性椭圆柱体在水中的振动问题,提出一种代替水-结构动力相互作用的附加质量模型。基于椭圆柱体动水压力的计算公式建立了水中椭圆柱体的自由振动方程,进一步推导了水中椭圆柱体自振频率和振型的解析公式;基于振型叠加法推导了水中椭圆柱体地震动力反应的计算公式;通过附加质量代替水-结构相互作用,提出了水中椭圆柱体自振频率的计算公式;通过曲线拟合给出了附加质量的简化计算公式,该简化公式数学表达简单,适用于工程应用。     

任意光滑截面桥墩地震动水压力分析

对地震作用下任意光滑截面柱体上的动水压力,提出了一个解析的计算公式。基于辐射波浪理论,采用分离变量法推导了任意光滑截面柱体动水压力的精确计算公式,利用水层模态的正交性并将连续光滑函数展开为傅里叶级数确定计算公式的系数。通过对刚性椭圆形和圆端形截面柱体动水压力的计算表明,提出的动水压力解析公式具有很好的计算精度。     

行波效应对深水连续刚构桥地震响应的影响

跨海或库区的大跨度桥梁在地震作用下不仅需要考虑水体与桥墩的动力相互作用,同时由于各桥墩间跨度较大应考虑地震输入的行波效应。该文采用辐射波浪理论求解桥墩地震动水压力,建立了考虑地震动输入空间效应的深水桥梁地震响应分析方法,并考虑行波效应对深水连续刚构桥进行地震响应分析。研究表明:动水压力增大了桥梁结构的地震响应,其影响程度随着输入地震波和墩梁约束条件的不同而有所差异;考虑行波效应时地震动水压力对桥梁结构动力响应的影响较一致激励而言有所差别,同时地震动水压力对桥梁地震响应的影响随着视波速的不同而变化。由此得出结论,为合理评价地震动水压力对深水长大桥梁动力响应的影响应考虑地震动输入的行波效应。     

功率谱二次正交化法在随机地震动响应的应用

针对平稳激励下线性结构随机地震动响应方差和谱矩时频域法无解析解或时域法解析解复杂的问题,提出了结构响应功率谱的二次正交化法,并成功获得线性结构基于李鸿晶随机地震谱的系列响应（结构层位移和层间位移）的0～2阶谱矩和方差的简明封闭解。综合虚拟激励法和复模态方法,提出了线性结构频率响应特征值函数的二次正交法,即将频率响应特征值函数表示为振动复特征值和频域变量二次方和的线性组合;以李鸿晶随机地震动谱为例,基于留数定律获得该谱的二次正交式,进而获得结构地震动系列响应功率谱的二次正交式;获得了建筑结构随机地震动系列响应方差及0～2阶谱矩的统一简明封闭解。利用本文方法对一单自由度结构和一多自由度TMD耗能结构地震动响应进行分析,并与虚拟激励法进行了对比研究,结果表明本文所提方法为封闭解且可用于验证虚拟激励法谱矩分析时的精度。此外,本文方法可适用于各种线性结构基于各类平稳随机地震谱的随机响应封闭解的分析。     

椭圆柱三维简立方排列声子晶体的带隙结构

用平面波法研究了椭圆钢柱与环氧树脂组成的三维简立方晶格声子晶体的带隙结构.一般情况下,椭圆柱体的横截面形状对称性越高,带隙宽度极值和中心频率越大;带隙宽度随椭圆柱体绕其中心轴旋转角度的增大而增大,但带隙中心频率随旋转角度的增大而减小;无论柱体是否旋转,通过改变柱体横截面半径都比改变柱体高度更易获得宽带隙.     

两自由度椭圆柱体涡激振动的数值模拟

摘要：利用作者编制的基于松耦合方法求解气动弹性问题的程序,对高雷诺数条件下椭圆柱体的涡激振动进行了数值模拟。椭圆柱体的长短轴比接近2,来流和长轴垂直。数值结果表明：尽管椭圆柱体在横向和流向的动力参数不同,结构振动仍以横向振动为主;和圆柱以及方柱一样,两自由度椭圆柱体的涡激振动同样存在流向锁定和横向锁定,并且随着折减风速的增大,旋涡脱落模式从异相2S变化为同相2S。     

二维椭圆柱体正方列阵固态声子晶体的带隙结构研究

用平面波法计算了椭圆钢柱与环氧树脂组成的二维正方晶格声子晶体的带隙结构。结果表明：当椭圆柱体未旋转时,柱体的横截面形状对称性越高,带隙宽度越大;固定填充率而改变柱体截面半径时,填充率大,带隙宽度极值越大;若椭圆柱体绕其中心轴线旋转,带隙宽度将随之增大,其极值出现在椭圆柱体旋转44o或45o时,而且可以获得比圆柱体更宽的带隙;带隙中心频率随材料参数的变化也有明显的变化规律。     

椭圆柱三角晶格固态声子晶体的带隙结构

用平面波法研究了椭圆钢柱与环氧树脂组成的二维三角晶格声子晶体的带隙结构.结果表明,带隙的宽度和中心频率随填充率F或椭圆柱体横截面两半径之比T的变化表现出明显的变化规律;椭圆柱体横截面的对称性越高,带隙越宽;当F很小时,F对带隙中心频率的影响与T关系不大;椭圆柱体绕其中心轴旋转时,带隙的宽度呈现出与中心频率相反的变化规律,而且最小的带隙宽度及最高的中心频率均在柱体旋转60°左右出现.     

输液管线中的地震动水压力及其影响因素

强烈地震作用可使地上输液管线中的液体产生较大的动水压力。基于模态叠加原理及地震反应谱理论，考虑流体可压缩性及管弹性，建立了输液管线地震动水压力的计算模型。根据流体所处边界条件的不同，给出两种典型工况下，管流地震动水压力的计算公式，并与依据附加质量模型计算所得的结果进行了比较。比较结果表明：管线长度对管流地震动水压力有显著的影响，对长管道而言，以附加质量模型求得的的地震动水压力高于考虑流体可压缩性时求得的地震动水压力，而对于短管道，情况刚好相反。另外，场地类型及管流所处工况对管流地震动水压力也有显著的影响，软土场地上的管理道。其内部流体地震动水压力明显高于硬土场地上的动水压力。     

考虑水底柔性反射边界的深水桥墩地震动水压力分析

在深水桥墩地震动水压力分析中一般假定水底为完全反射边界,而忽略水底柔性介质对动水压力波的吸收作用。该文考虑水底柔性反射边界,基于辐射波浪理论,建立了深水桥墩地震动水压力的计算公式,深入分析了水底柔性反射边界对动水压力的影响。研究表明:水底柔性反射边界会在特定的荷载激励频率范围内对深水桥墩动水压力产生影响,且动水压力随水底反射系数的减小而减小,深水桥墩地震动水压力分析可以忽略水底柔性边界的影响。从而为长大桥梁地震灾变过程精细化模拟提供了理论依据。     

外压作用下椭圆截面柱壳的弹性屈曲

基于能量法推导了外压作用下椭圆截面柱壳弹性屈曲临界荷载的理论解,推导中考虑了椭圆截面连续变化的曲率,引入带有衰减系数的位移函数以反映外压作用下椭圆柱壳的变形特点,并利用里兹法求解外压椭圆柱壳的能量方程。由椭圆柱壳理论解退化求得的圆柱壳外压屈曲荷载与已有文献的经典解吻合良好,与有限元分析结果的比较进一步验证了该文理论解的准确性。基于理论解的参数分析表明:在外压作用下,椭圆柱壳具备比圆柱壳更优越的力学性能;椭圆柱壳的外压屈曲荷载随椭圆截面比的增大而增大,随壳体名义径厚比的减小而增大;椭圆柱壳的外压屈曲荷载随壳体长度的增大而降低,但当名义长径比大于1左右后,屈曲荷载基本保持不变。     

Interactions between inclusions and various types of cracks

The problems of a crack inside, outside, penetrating or lying along the interface of an anisotropic elliptical inclusion are considered in this paper. Because the crack may be represented by a distribution of dislocation, integrating the analytical solutions of dislocation problems along the crack and applying the technique of numerical solution on the singular integral equation, we can obtain the general solutions to the problems of interactions between cracks and anisotropic elliptical inclusions. Since there are no analytical solutions existing for the general cases of interactions between cracks and inclusions, the comparison is made with the numerical results obtained by other methods or with the analytical results for the special cases which can be reduced from the present problems. These results show that our solutions are correct and universal     

Free-surface flow of a fluid body with an inner circular cylinder in impulsive motion

An analytical theory and numerical computations are developed for the two-dimensional free-surface flow of an initially circular layer of inviscid fluid surrounding a rigid circular cylinder. The two cylinders are initially concentric. The fluid packet is released from rest and the flow suddenly starts forced by gravity and by the simultaneous impulsive motion of the inner body. A small-time expansion of the fully nonlinear free-surface problem is developed and a closed-form solution is found up to third order for an arbitrary radius of the rigid cylinder. For the gravitational flow around the body at rest, the solution is extended up to fourth order. Free-surface profiles and hydrodynamic forces on the cylinder are calculated and discussed against numerical solutions of the exact unsteady nonlinear problem. Some basic features, such as the formation of an almost uniform layer surrounding the upstream side of the body, are captured by the theory quite well and only later on in time significant quantitative differences appear. Similarly, the behaviour of hydrodynamic loads is rather well predicted during initial stages preceding larger fluctuations observed on a longer time-scale.     

深水矩形空心桥墩在地震作用下附加动水压力分析

基于辐射波浪理论建立了矩形空心桥墩流体控制方程,以自由表面波动条件、水底水质点运动边界条件、结构与水的速度连续条件为边界条件,采用分离变量法推导了矩形空心桥墩内、外域水体速度势一般解,进而导出了矩形空心墩内、外域水体的附加动水压力的解析式,对某桥墩自振特性的计算表明,该附加动水压力解析式具有较高的计算精度.     

Green's function method for axisymmetric flows: analysis of the Taylor-Couette flow

A numerical method for the solution of the Navier-Stokes equations in rotationally symmetric flow problems is presented. The numerical procedure is based on a boundary integral equation formulation with the fundamental solution of the Stokes' equation accounting for the rotational symmetry. The proposed methodology has been applied to the study of the Taylor-Couette flow between two concentric rotating cylinders of infinite axial length. A comparison with the available theoretical, experimental or numerical findings is performed to evaluate the accuracy of the present results. As predicted by the analytical theory and confirmed by the experiments, multiple solutions that are found for Reynolds numbers higher than the critical value, indicate the proposed methodology as a useful tool to get physical insight on the instabilities occurring in the solution of the Navier-Stokes equations.     

Analytical elastic solutions for pressurized hollow cylinders with internal functionally graded coatings

The main objective of this work is to obtain analytical solutions for thick-walled cylinders subjected to internal and external pressure in which the entire wall is made of functionally graded material or of only a thin functionally graded coating present on the internal homogeneous wall. We assume that the materials are isotropic with constant Poisson’s ratio; as far as the Young modulus is concerned, we consider a power and an exponential. The proposed analytical solutions show the effects of the different profiles describing the graded properties of the materials on the stress and displacement fields; in addition, comparisons between graded coating and conventional homogeneous coating highlight the advantage of the graded material on the interface stress reduction. Furthermore, we show how even a thin graded coating can be useful to satisfy the requirements of a specific application without having to make an entire wall with graded properties. This investigation permits us to optimize the elastic response of cylinders under pressure by tailoring the thickness variation of the elastic properties and to reduce manufacturing costs given by the technological limitations that occur to produce entire functionally graded walls.     

Linear finite elements with orthogonal discontinuous basis functions for explicit earthquake ground motion modeling

The dynamic explicit finite element method is commonly used in earthquake ground motion modeling. In this method, the element mass matrix is approximately lumped, which may lead to numerical dispersion. On the other hand, the orthogonal finite element method, based on orthogonal polynomial basis functions, naturally derives a lumped diagonal mass matrix and can be applied to dynamic explicit finite element analysis. In this paper, we propose finite elements based on orthogonal discontinuous basis functions, the element mass matrices of which are lumped without approximation. Orthogonal discontinuous basis functions are used to improve the accuracy and reduce the numerical dispersion in earthquake ground motion modeling. We present a detailed formulation of the 4‐node tetrahedral and 8‐node hexahedral elements. The relationship between the proposed finite elements and conventional finite elements is investigated, and the solutions obtained from the conventional explicit finite element method are compared with analytical solutions to verify the numerical dispersion caused by the lumping approximation. Comparison of solutions obtained with the proposed finite elements to analytical solutions demonstrates the usefulness of the technique. Examples are also presented to illustrate the effectiveness of the proposed method in earthquake ground motion modeling in the actual three‐dimensional crust structure. Copyright © 2010 John Wiley & Sons, Ltd.     

二维非均质材料应力场的数值化计算方法

等效夹杂方法是求解含杂质材料弹性应力场的一种有效方法,但是其解析求解只适用于椭球/椭圆类杂质问题。本文提出一种基于等效夹杂方法的数值化计算方法,介绍了其基本理论,并引入共轭梯度法求解该方法的一致性条件线性方程组。该方法通过计算区域的数值离散,能够实现对二维任意形状杂质弹性场的求解。将该方法得到的结果与解析解进行比较,验证了该方法的有效性。讨论了数值化等效夹杂方法在效率以及收敛性上的表现。通过对比证明,利用共轭梯度法实现该方法,能在保持精度的同时,相较于高斯消元法具有较大的效率优势。最后通过半椭圆杂质和氧化锆/氧化铝共挤复合材料算例验证了该方法处理任意形状杂质的能力。     

堆载-电渗联合作用下的一维非线性大变形固结理论

堆载-电渗联合作用下的软土地基加固属于大变形固结问题。该文在Esrig电渗固结理论的基础上,建立了拉格朗日坐标下以超静孔压作为变量的一维非线性大变形固结理论方程,推导出相应的超静孔压、沉降、平均固结度和孔隙比的解析公式,且通过了模型试验的验证。之后,采用该解分析了土体在堆载-电渗联合作用下的地基大变形固结特性,且与Esrig小变形固结解析解进行对比。结果表明:堆载-电渗联合作用下,考虑大变形的计算结果更符合工程实际,且此解可用于对大变形固结问题数值解法的验证。     

Finite element analyses of three-dimensional crack problems in piezoelectric structures

In this paper, electromechanical fracture mechanics and finite element techniques for crack analyses are extended to three-dimensional crack configurations. Penny-shaped cracks and elliptical cracks are analyzed, subjected to combined mechanical tension and electric fields. For the penny-shaped crack, exact solutions originating from different resources are compared with numerical results. Some errors in the literature concerning the analytical solution for the elliptical crack are corrected. Numerical results of the stress-intensity factors and energy release rates for these crack configurations are presented.