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   

Gravitational collapse and equilibrium conditions of a toroidal vortex with thermal pressure     

K. Yu. Bliokh  V. M. Kontorovich 《Astronomy Letters》2003,29(11):724-730

We found the equilibrium conditions for a self-gravitating toroidal vortex by taking thermal pressure into account. These conditions are shown to significantly differ from those for a disk or a sphere. The evolution of a thin vortex turns it into a compact vortex that loses mechanical stability for low masses at a polytropic index γ<4/3 but retains stability for sufficiently high masses and densities determined by the velocity circulation in the vortex.  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   

Geobarometry for Peridotites: Experiments in Simple and Natural Systems from 6 to 10 GPa   总被引：3，自引：0，他引：3  

Brey  Gerhard P.; Bulatov  Vadim K.; Girnis  Andrei V. 《Journal of Petrology》2008,49(1):3-24

Experiments with peridotite minerals in simple (MgO–Al₂O₃–SiO₂,CaO–MgO–SiO₂ and CaO–MgO–Al₂O₃–SiO₂)and natural systems were conducted at 1300–1500°Cand 6–10 GPa using a multi-anvil apparatus. The experimentsin simple systems demonstrated consistency with previous lowerpressure experiments in belt and piston–cylinder set-ups.The analysis of spatial variations in pyroxene compositionswithin experimental samples was used to demonstrate that pressureand temperature variations within the samples were less than0·4 GPa and 50°C. Olivine capsules were used in natural-systemexperiments with two mineral mixtures: SC1 (olivine + high-Alorthopyroxene + high-Al clinopyroxene + spinel) and J4 (olivine+ low-Al orthopyroxene + low-Al clinopyroxene + garnet). Theexperiments produced olivine + orthopyroxene + garnet ±clinopyroxene assemblages, occasionally with magnesite and carbonate-richmelt. Equilibrium compositions were derived by the analysisof grain rims and evaluation of mineral zoning. They were comparedwith our previous experiments with the same starting mixturesat 2·8–6·0 GPa and the results from simplesystems. The compositions of minerals from experiments withnatural mixtures show smooth pressure and temperature dependencesup to a pressure of 8 GPa. The experiments at 9 and 10 GPa producedandradite-rich garnets and pyroxene compositions deviating fromthe trends defined by the lower pressure experiments (e.g. higherAl in orthopyroxene and Ca in clinopyroxene). This discrepancyis attributed to a higher degree of oxidation in the high-pressureexperiments and an orthopyroxene–high-P clinopyroxenephase transition at 9 GPa. Based on new and previous resultsin simple and natural systems, a new version of the Al-in-orthopyroxenebarometer is presented. The new barometer adequately reproducesexperimental pressures up to 8 GPa. KEY WORDS: garnet; mineral equilibrium; multi-anvil apparatus; orthopyroxene; geobarometry  相似文献   

On the Assessment of Failure in Slope Stability Analysis by the Finite Element Method   总被引：3，自引：0，他引：3  

H. Zheng  D. F. Liu  C. G. Li 《Rock Mechanics and Rock Engineering》2008,41(4):629-639

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Formation of Equilibrium Beach Profile of the Abandoned Yellow River Delta Coast in North Jiangsu     

XU  Min 《中国海洋工程》2001,(1):139-146

The abandoned Yellow River Delta coast is a typical erodible silty and muddy coast in China. The paper analyses the marine dynamic characteristics and the mechanism of beach erosion of this area. Analysis and calculation show that in this sea area wave and tidal current action should be considered. Based on the above analysis, an equilibrium beach profile calculation model is developed, in which the wave-current interaction is considered while sediment supply and sediment re-deposition are neglected. The model consists of four parts: (1) calculation of wave parameters, (2) calculation of velocity due to wave-current interaction at different water depth, (3) calculation of friction velocity and shear stress at different water depths, and (4) calculation of the amount of sediment erosion, erosion intensity and variation of beach profile. Calculated results are in good agreement with observed data. Finally, the evolution tendency is discussed and the equilibrium beach profile of this coast is calculated. B  相似文献   

波浪作用下岸坡和海底平衡条件的研究     

沈剑平  范德江 《中国海洋大学学报(自然科学版)》1993,(4)

提出波浪作用下岸坡和海底动态和静态平衡条件的数学模型。在已建立的推移质泥沙体积输沙率基本关系式的基础上,根据连续方程,计算出底坡、泥沙、波浪三要素在动态和静态平衡情况下的关系式,得出反映这种关系的底坡平衡函数曲线图。用实际资料对这一函数曲线进行了验证,并对实际资料相对模型的某些差异作出解释。  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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