On the use of the Trigonometric Ritz method for general vibration analysis of rectangular Kirchhoff plates

A comprehensive study on the use of a set of trigonometric functions, originally proposed by Beslin and Nicolas [Journal of Sound and Vibration 1997;202:633–55], as admissible solutions in the Ritz method for general vibration analysis of rectangular orthotropic Kirchhoff plates is presented. The approach is denoted here as Trigonometric Ritz method (TRM). Since its introduction, application of TRM was limited to a very few plate problems. The aim of this work is to extend the potential of the method on predicting natural flexural frequencies of plates with various complicating factors, including in-plane loads, elastically restrained edges, rigid/elastic concentrated masses, intermediate line and point supports or their combinations. Computational efficiency, stability, convergence and accuracy of the method are discussed and supported by extensive analysis. TRM-based solutions are compared with many reference cases available in the literature obtained with other methods or Ritz functions. Numerical results indicate that TRM exhibits good to excellent accuracy for all cases considered. New solutions are also presented for future comparison purpose.     

Large deflection elastoplastic analysis of thin shells

Results are presented and some modifications made to problems posed in an earlier paper by the authors on the extension of the semi-loof element to the analysis of shell structures involving instabilities, snap-through and material nonlinearities. In this paper, by adopting a more refined method for solving problems of plasticity, in conjunction with a subincremental technique, more accurate results are obtained. The second-order Runge-Kutta method employed in this study shows significant improvement in the accuracy of the streesses in the shell as compared to the case when only the simple point-slope method of Euler is used. The detailed computational procedure for elastoplastic analysis of shell problems is presented in a way that can readily be incorporated into standard computer packages. Results obtained for large deflection analysis of plastic shells of different geometries and boundary conditions are compared with the available solutions and show very good agreement.     

Response of pile embedded in stochastic ground media

This paper reports a study on the response variability of piles in ground media which is uncertain and is assumed to be one-dimensional stochastic field along the depth. For such problems, no general solutions can be obtained in an analytical form. Accordingly, approximations need to be introduced. In this study, a stochastic analysis based on the Galerkin method and the first-order approximation is proposed for estimating the response variability of a single pile embedded in stochastic ground media. The horizontal force is assumed to be applied from a superstructure in a deterministic manner. Numerical examples are presented to show the usefulness of this method with regard to the number of trial functions, and the spatial correlation property of the ground media. In addition, comparison is made using two different modelings, random variable modeling and stochastic field modeling for the stochastic ground media. Finally, the correlation-free upper bounds of response variation are proposed for the practical purpose.     

关于集中力作用线下的几个位移特解及评论

直接用应变积分的方法得到在集中力作用线下的几个弹性力学位移特解。定积分的一个端点离开集中力作用点有一微小的距离，说明当此距离趋近于0时这些位移解的渐近奇异性是合理的。对有关解答做了比较，说明了其之间的区别和联系。用应变积分求位移特解的解法容易将解推广到材料正交各向异性的情况。举出一个应用实例说明用应变积分求位移特解的方法，对解的物理意义有更直接更清楚的表示，从而指正一篇文献对集中力作用下岩石表面变形趋势的误解。     

基于位移控制边界单元法盾构隧道开挖引起分层土体变形分析

 考虑地基土体非均质性的影响,基于弹性层状半空间地基模型,提出分析多层地基中盾构隧道开挖引起周围土体不排水变形的位移控制边界单元法,改变了过去采用简化分析方法仅能在均质地基中进行求解的状况。针对盾构隧道开挖边界引入椭圆化非等量径向土体位移移动模式,建立层状地基中洞周边值问题的边界积分求解方程,并采用高阶等参单元代替低阶常分布单元得到边界离散方程,同时以弹性层状半空间地基模型的基本解代替常规均匀介质体的Kelvin或Mindlin基本解,最终求得隧道洞周给定位移条件下的土体位移场。算例分析表明：位移控制边界单元法在计算均质地基和非均质层状地基中都具有较好的精度;对于非均质层状地基,如果采用以往的将不同土体参数近似折算成平均值进而按照弹性均质地基进行求解会带来较大的计算误差。研究成果可为合理评估盾构隧道施工对周围环境的影响提供一定的理论依据。     

层状地基中的单桩沉降分析

对轴对称弹性力学方程进行Ｈａｎｋｅｌ变换，并利用传递矩阵方法得出层状地基在内部轴对称荷载作用下的位移解。利用此解析解建立了求解层状地基中单桩沉降的计算方法，并与Ｐｏｕｌｏｓ，Ｒａｎｄｏｌｐｈ和Ｗｒｏｔｈ，Ｒａｊａｐａｋｓｅ等人的经典解答进行了比较。     

Lateral buckling of beams analysed as elastically supported columns subject to a varying axial force

The stability problem for an elasticallu supported column subject to a varying axial force has been solved by means of a general numerical procedure based on Galerkin's method. Apart from the intrinsic value of the solution itself, its possible value modelling some complex stability problems in the area of restrained lateral-torsional stability problems is demonstrated and specific numerical solutions are applied to the case of lateral buckling of the free flange of a composite girder. The results obtained are discussed and suggestions for additional investigations are presented.     

Ⅳ级围岩地铁暗挖车站开挖工法探讨

该文依托重庆地铁金山寺车站工程,提出了设计的双侧壁导坑法在Ⅲ~Ⅳ级围岩施工存在的问题,在车站开挖工法初步增选了三台阶法、保留核心土法,对车站开挖三种工法建立弹塑性有限元进行模拟分析,得到了三种开挖工法的围岩位移分析结果,再经过工法比选,提出了一种安全合理的工法,即保留核心土法,从而指导车站的开挖施工,解决了双侧壁导坑法在Ⅲ~Ⅳ级围岩施工存在的问题,可为类似工程提供参考。     

A benchmark study on importance sampling techniques in structural reliability

Several widely used importance sampling methods for the estimation of failure probabilities are compared. The methods are briefly reviewed, and a set of evaluation criteria for the comparison of the methods is chosen. In order to perform a fair comparison the developers of the schemes were asked to solve a number of problems selected in view of the evaluation criteria. Their solutions are presented and discussed. Conclusions about the performances of the schemes under different circumstances are given.     

Developing an element free method for higher order shear deformation analysis of plates

A procedure is presented to eliminate transverse shear locking in analysis of laminated composite plates using Element Free Galerkin (EFG) method based on higher-order transverse shear deformation theory (HSDT). In the procedure, derivatives of the transverse displacement are introduced as independent variables. Thus, a formulation requiring C⁰ continuity shape functions for approximation is proposed for higher-order transverse shear deformation analysis of plates. Shear locking is avoided considering reduced integration for shear stiffness matrix; a method which is implemented in FEM. Moving Least Squares (MLS) method is utilized for shape functions and the penalty method is implemented to impose approximate boundary conditions. The present solutions are verified with other higher-order shear deformable studies. Moreover, a comparison between the present solutions with those obtained by EFG procedure based on First-order transverse Shear Deformation Theory (FSDT) is performed.     

层状土中污染物的一维扩散解析解

扩散是污染物在填埋场细颗粒土质衬里中迁移的主要方式,同时土质衬里存在着成层的情形。在建立了污染物在层状土中的一维扩散模型的基础上,通过分离变量法得到了解析解。基于该解析解,编制了相应的计算程序。通过与有限差分法对比,证明了该解析解的正确性及有效性。算例分析了不同衬里的放置顺序对污染物扩散的影响,虽然两种情况下土层的浓度剖面不同,但两者的击穿曲线是一致的。该解析解可用于对试验数据的拟合、对复杂数值模型的检验以及为垃圾填埋场衬里系统的初步设计提供参考。     

Integral solutions for transient fluid flow through a porous medium with pressure-dependent permeability

This paper presents an integral method for analyzing transient fluid flow through a porous medium, which has pressure-dependent permeability. Approximate analytical solutions have been obtained for one-dimensional linear and radial flow by an integral-solution technique, in which the density of the fluid, and the porosity and permeability of the formation, are treated as arbitrary functions of pressure. The integral solutions have been checked by comparison with exact solutions for constant-permeability cases and with numerical simulation results for general non-linear flow problems, and good agreement has been obtained for both cases.In the study of transient flow of fluids through porous media, intrinsic or absolute permeability of the formation has often been treated as a constant in order to avoid solving a non-linear problem. The present work shows that the assumption of a pressure-independent permeability may introduce significant errors for flow in certain pressure sensitive media. Application of the integral solutions to slightly compressible fluid flow in a horizontal fracture set is illustrated. The calculations show that neglect of changes in fracture permeability leads to large errors under the condition of high injection pressure.     

Refined second-order reliability analysis

A refined second-order method is presented for structural reliability analysis. Exact and approximate reliability solutions are obtained for a circular shaft subject to random bending moments and a random torque. The comparison of the approximate results with exact ones shows that the first-order approximation is only applicable to the case where the failure surface is “far” from the origin, while the suggested second-order approximation yields quite accurate results even if the failure surface is “close” to the origin.     

基于哈密顿理论的薄壁结构双向弯曲分析

从能量变分原理出发,由勒让德变换引入对偶变量,导出了薄壁结构双向弯曲问题的哈密顿对偶求解体系,将薄壁结构的控制微分方程转化为哈密顿对偶方程,其系统矩阵具有辛矩阵的特性,可用精细积分法求该体系的高精度数值解。算例计算结果表明,本方法具有较高的精度和适用性,并可方便地用于变截面薄壁结构的计算。     

基于极限平衡法与极限分析法等效性的地基承载力系数N_γ的上限解

针对地基承载力系数Nγ真实解答尚未获得的现状,提出一种计算Nγ上限解的数值计算方法。在论证极限平衡法与极限分析法等效性的基础上,采用一组三角条块逼近满足机动许可的潜在破坏机构,通过极限平衡法建立条间力的递推公式,依据推力最大原理优化条块底线的倾角,得到最危险破坏机构及对应的地基承载力系数Nγ的上限数值解,进而分析地表倾斜情况下的Nγ及其修正方法;最后,为了便于工程应用,给出Nγ及地表倾斜修正系数ξγ的近似表达式。通过与已有研究成果的比较,验证该方法的合理性。研究表明:该方法计算过程简单易于编程实现,能够得到相对小的上限解。研究成果可用于地基承载力的理论分析,为深入研究地基承载力系数Nγ提供参考。     

论设计中的比较方法

一些复杂结构,当缺少适当的计算方法,或基础资料不足,不能进行精确分析时,设计中的比较方法便成为一个重要课题。土力学地基问题存在不定因素尤多,地区性强,需要依赖丰富经验进行判断。其中粉砂震动液化问题特别复杂,当前国内外都仅能按统计法则给出经验公式。其间很难找出共同规律,这就给如何制订抗液化的合理措施带来困难。本文的比较方法就是为检验措施的安全系数而提出的。设计中采用比较方法将会带来巨大经济效益。     

Nichtlineare Querschnittsanalyse als Optimierungsproblem

Nonlinear analysis of cross‐sections as an optimisation problem. Strains and stresses in cross‐sections of beams can not be calculated by elementary strength of materials when the relations between strains and stresses are nonlinear. Numerical solutions are very often obtained by the finite‐element‐method or similar and by solving systems of nonlinear equations. In this paper an alternative formulation of the mechanical model is proposed. This approach is based on the principle of minimum of total potential energy. Numerical solutions are found by nonlinear optimisation. The strain energy is directly included as a variable in the mathematical model. Thus the specifics of material behaviour can be taken into account without basic modification of the algorithm. The possibility to use generally available standard software for the numerical solution of nonlinear optimisation problems is an important advantage of the presented method.     

Estimation of floor acceleration demands in high‐rise buildings during earthquakes

A simplified method to estimate lateral acceleration demands in high‐rise buildings subjected to earthquakes is presented. In the proposed method acceleration demands are obtained by approximating the dynamic characteristics of the building with those of a continuous model consisting of a combination of a flexural cantilever beam and a shear cantilever beam. Closed‐form solutions for mode shapes, period ratios and modal participation factors for the first six modes of vibration are presented. The method is evaluated by comparing peak floor acceleration demands and acceleration time histories computed with the proposed method to those recorded during earthquakes in six instrumented high‐rise buildings. A comparison of floor spectra computed with the approximate method and spectra computed with recorded motions is also presented. Results indicate that the proposed method produces relatively good results with a very small computational effort and requires only a small amount of information about the building. Variations of accelerations demands along the height are closely examined in each building for each component. It is shown that the variation of acceleration demands along the height of high‐rise buildings can differ significantly from that currently recommended in US seismic provisions for anchoring building nonstructural components. Copyright © 2005 John Wiley & Sons, Ltd.     

Torsional collapse of thin-walled prismatic columns

Torsional collapse of thin-walled prismatic columns is studied analytically and numerically. Simple torsional collapse models are developed to predict the collapse behavior of square columns under large plastic rotation using energy method. By considering the combined effect of geometry and material, the onset of the sectional plastic buckling is predicted and the critical twisting rotation for sectional buckling is obtained. Next, an analytical expression is derived for the moment-rotation relation valid for rotation up to 180°. The analytical solution is shown to compare well with the numerical results. The solutions are then extended for rectangular and hexagonal thin-walled columns. Numerical simulations for rectangular and hexagonal columns are also carried out and the results are presented in this paper for the purpose of comparison.     

Comparative evaluation of methods to determine the earth pressure distribution on cylindrical shafts: A review

Various methods used for calculating and measuring the earth pressure distribution on cylindrical shafts constructed in sand are evaluated. Emphasis is placed on a comparison between the calculated earth pressure using different methods for given sand and wall conditions. The effects of the assumptions made in developing these solutions on the pressure distribution are discussed. Physical modeling techniques used to simulate the interaction between vertical shafts and the surrounding soil are presented. The earth pressure measured and the wall movements required to establish active condition are assessed. Depending on the adopted method of analysis, the calculated earth pressure distribution on a vertical shaft lining may vary considerably. For shallow shafts, the theoretical solutions discussed in this study provide consistent estimates of the active earth pressure. As the shaft depth exceeds its diameter, the solutions become more sensitive to the ratio between the vertical and horizontal arching and only a range of earth pressure values can be obtained. No agreement has been reached among researchers as to the magnitude of wall movement required to establish active conditions around shafts and further investigations are therefore needed.