Elastic solutions for stresses in a transversely isotropic half‐space subjected to three‐dimensional buried parabolic rectangular loads     

Cheng‐Der Wang  Jyh‐Jong Liao 《国际地质力学数值与分析法杂志》2002,26(14):1449-1476

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

Stability of the periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions     

Abdul Ahmad 《Celestial Mechanics and Dynamical Astronomy》1995,61(2):181-196

The periodic solutions of the restricted three-body problem representing analytic continuations of Keplerian rectilinear periodic motions are well known (Kurcheeva, 1973). Here the stability of these solutions are examined by applying Poncaré's characteristic equation for periodic solutions. It is found that the isoperiodic solutions are stable and all other solutions are unstable.  相似文献   

Restricted Three-Body Problem: An Approximation of its General Solution – Part One – the Manifold of Symmetric Periodic Solutions     

Kostantinos Papadakis  Constantine Goudas 《Astrophysics and Space Science》2006,305(2):99-124

This paper gives the results of a programme attempting to exploit ‘la seule bréche’ (Poincaré, 1892, p. 82) of non-integrable systems, namely to develop an approximate general solution for the three out of its four component-solutions of the planar restricted three-body problem. This is accomplished by computing a large number of families of ‘solutions précieuses’ (periodic solutions) covering densely the space of initial conditions of this problem. More specifically, we calculated numerically and only for μ = 0.4, all families of symmetric periodic solutions (1st component of the general solution) existing in the domain D:(x ₀ ∊ [−2,2],C ∊ [−2,5]) of the (x ₀, C) space and consisting of symmetric solutions re-entering after 1 up to 50 revolutions (see graph in Fig. 4). Then we tested the parts of the domain D that is void of such families and established that they belong to the category of escape motions (2nd component of the general solution). The approximation of the 3rd component (asymmetric solutions) we shall present in a future publication. The 4th component of the general solution of the problem, namely the one consisting of the bounded non-periodic solutions, is considered as approximated by those of the 1st or the 2nd component on account of the `Last Geometric Theorem of Poincaré' (Birkhoff, 1913). The results obtained provoked interest to repeat the same work inside the larger closed domain D:(x ₀ ∊ [−6,2], C ∊ [−5,5]) and the results are presented in Fig. 15. A test run of the programme developed led to reproduction of the results presented by Hénon (1965) with better accuracy and many additional families not included in the sited paper. Pointer directions construed from the main body of results led to the definition of useful concepts of the basic family of order n, n = 1, 2,… and the completeness criterion of the solution inside a compact sub-domain of the (x ₀, C) space. The same results inspired the ‘partition theorem’, which conjectures the possibility of partitioning an initial conditions domain D into a finite set of sub-domains D i that fulfill the completeness criterion and allow complete approximation of the general solution of this problem by computing a relatively small number of family curves. The numerical results of this project include a large number of families that were computed in detail covering their natural termination, the morphology, and stability of their member solutions. Zooming into sub-domains of D permitted clear presentation of the families of symmetric solutions contained in them. Such zooming was made for various values of the parameter N, which defines the re-entrance revolutions number, which was selected to be from 50 to 500. The areas generating escape solutions have being investigated. In Appendix A we present families of symmetric solutions terminating at asymptotic solutions, and in Appendix B the morphology of large period symmetric solutions though examples of orbits that re-enter after from 8 to 500 revolutions. The paper concludes that approximations of the general solution of the planar restricted problem is possible and presents such approximations, only for some sub-domains that fulfill the completeness criterion, on the basis of sufficiently large number of families.  相似文献   

Non-Existence of New Meromorphic First Integrals in the Planar Three-Body Problem     

Alexei V. Tsygvintsev 《Celestial Mechanics and Dynamical Astronomy》2003,86(3):237-247

We consider the planar three-body problem and prove that, apart from some exceptional cases, there is no additional first integral meromorphic with respect to positions, mutual distances and momenta.  相似文献   

用层次分析法决策地下水库回灌方案的排序问题     

李云峰  王文科  李志刚  王希宁 《地球科学与环境学报》1992,(2)

本文引用了一种新的系统分析方法(层次分析法)对地下水库人工回灌的复杂系统进行了择优排序研究,取得了满意的结果。实践证明,层次分析法对于地下水库人工回灌方案的择优是一种简捷实用的决策方法。  相似文献   

Usefulness of geological,mineralogical, chemical and chemometric analytical techniques in exploitation and profitability studies of iron mines and their associated elements     

M. Dolores Petit-Dominguez  M. Isabel Rucandio  Almudena Galan-Saulnier  Rosario Garcia-Gimenez 《Journal of Geochemical Exploration》2008

Due to the high number of variables involved in mine profitability studies, it is often very difficult to establish connections among them in order to provide a blend of market saleable quality products. In this sense, analytical chemistry together with chemometry are essential and indispensable disciplines to tackle these studies. The aim of this work was to demonstrate the utility of these disciplines to carry out optimization studies of iron mines. For this purpose, one of the most important iron mines of the Iberian Peninsula was chosen, sited in the mountain range of Sierra Menera, near the location of Ojos Negros (Teruel, Spain). Geological, mineralogical and chemical composition of 148 samples was analyzed, corresponding to different depths of three drill holes (named TE1, TE2 and TE3). In particular, aspects concerning to chemical composition are very important, since the mean contents of certain elements, such as phosphorus, sodium and potassium, should be restricted to the established limits to prevent that companies can drive back the raw material if they do not fulfil the necessary requirements. On the other hand, the large number of analysed samples drove us to use a statistical processing of the data. Among other aspects, it provides a way to find possible connections among a high number of variables and classify samples into compositional groups sharing similar composition, in order to limit the mineralised area and to obtain enough information about the amount of those chemical elements associated to iron ores. Data obtained from all these analytical techniques were in good agreement and provide a methodology that can be of wide interest applied to different geological studies.  相似文献   

Second order wave diffraction forces and runup by finite—infinite element method     

B.Y. Li  S.L. Lau  C.O. Ng 《Applied Ocean Research》1991,13(6):270-286

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On the radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas   总被引：1，自引：0，他引：1  

Y.H. Zheng  P.F. Liu  Y.M. Shen  B.J. Wu  S.W. Sheng 《Ocean Engineering》2007,34(3-4):436-450

The radiation and diffraction of linear water waves by an infinitely long rectangular structure submerged in oblique seas of finite depth is investigated. The analytical expressions for the radiated and diffracted potentials are derived as infinite series by use of the method of separation of variables. The unknown coefficients in the series are determined by the eigenfunction expansion matching method. The expressions for wave forces, hydrodynamic coefficients and reflection and transmission coefficients are given and verified by the boundary element method. Using the present analytical solution, the hydrodynamic influences of the angle of incidence, the submergence, the width and the thickness of the structure on the wave forces, hydrodynamic coefficients, and reflection and transmission coefficients are discussed in detail.  相似文献   

分离入射波与反射波的解析方法   总被引：5，自引：0，他引：5  

王永学  彭静萍等 《海洋工程》2003,21(1):42-46,52

提出了一种新的分离入射波和反射波的解析方法（AM）。利用两点处的 波高信息，运用Hilbert变换得到波浪信号在复域内的解析表达式，不需要计算合成波高和相位差即可实现信号的分离。根据分离结果，可以精确地估计入射波与反射波的幅值以及反射系数等参数，能够获得入射波与反射波之间的相位信息，并且可方便地用于不规则波的分离。文中通过数值模拟与物理模型实验对AM法进行了检验，所得的结果与实际值非常吻合。  相似文献   

论氢化物的形成及其在分析测试领域的应用          下载免费PDF全文

郑大中  王惠萍  郑若锋 《江苏地质》2008,32(1):5-11

论述了氢化物形成的普遍性、氢化物的物理化学性质、元素周期系各类元素的氢化物类型。认为一些金属离子、非金属离子在酸性介质中与硼氢化钾（钠）作用及金属锌等强还原剂作用生成氢化物。综述了氢化物的形成在分析测试领域的应用：试样分解、分离富集、容量分析、光度分析、原子光谱分析、质谱分析。  相似文献