Fully coupled elastoplastic hydro-mechanical analysis of unsaturated porous media using a meshfree method

This paper presents the first application of an advanced meshfree method, ie, the edge-based smoothed point interpolation method (ESPIM), in simulation of the coupled hydro-mechanical behaviour of unsaturated porous media. In the proposed technique, the problem domain is spatially discretised using a triangular background mesh, and the polynomial point interpolation method combined with a simple node selection scheme is adopted for creating nodal shape functions. Smoothing domains are formed on top of the background mesh, and a constant smoothed strain, created by applying the smoothing operation over the smoothing domains, is assigned to each smoothing domain. The deformation and flow models are developed based on the equilibrium equation of the mixture, and linear momentum and mass balance equations of the fluid phases, respectively. The effective stress approach is followed to account for the coupling between the flow and deformation models. Further coupling among the phases is captured through a hysteretic soil water retention model that evolves with changes in void ratio. An advanced elastoplastic constitutive model within the context of the bounding surface plasticity theory is employed for predicting the nonlinear behaviour of soil skeleton. Time discretisation is performed by adopting a three-point discretisation method with growing time steps to avoid temporal instabilities. A modified Newton-Raphson framework is designed for dealing with nonlinearities of the discretised system of equations. The performance of the numerical model is examined through a number of numerical examples. The state-of-the-art computational scheme developed is useful for simulation of geotechnical engineering problems involving unsaturated soils.     

On a global expansion of the disturbing function in the planar elliptic restricted three-body problem

Starting with a simple Taylor-based expansion of the inverse of the distance between two bodies, we are able to obtain a series expansion of the disturbing function of the three-body problem (planar elliptic case) which is valid for all points of the phase space outside the immediate vicinity of the collision points. In particular, the expansion is valid for very high values of the eccentricity of the perturbed body. Furthermore, in the case of an interior mean-motion resonant configuration, the above-mentioned expression is easily averaged with respect to the synodic period, yielding once again a global expansion of (R) valid for very high eccentricities.Comparisons between these results and the numerically computed exact function are presented for various resonances and values of the eccentricity. Maximum errors are determined in each case and their origin is established. Lastly, we discuss the applicability of the present expansion to practical problems.     

On the stability of particular solutions of the singly averaged Hill problem

We consider the particular solutions of the evolutionary system of equations in elements that correspond to planar and spatial circular orbits of the singly averaged Hill problem. We analyze the stability of planar and spatial circular orbits to inclination and eccentricity, respectively. We construct the instability regions of both particular solutions in the plane of parameters of the problem.     

济宁市嘉祥县石灰岩矿山地质环境评价与治理

在对嘉祥县石灰岩矿进行地质灾害危险性评估、矿山环境地质问题评价的基础上,建立了一套评价体系,其中地质灾害危险性评估分为2个评价指标,矿山环境地质问题评价分为2种要素3个指标,同时将矿山恢复治理难易程度也作为一个评价因子。评价过程中对各指标危害性大、中、小程度均单独赋值,然后将各指标的分值进行叠加,确定出矿山环境地质问题的等级,将概划出的13个评价单元分为极差、差、一般3个区。提出了强化矿山管理、植树造林、科学避让、修建拦水坝等保护与治理措施及建议。     

有关边界层问题中一类奇异积分方程新的存在性结果

对边界层理论新结果中出现的一类奇异积分方程w（t）=∫1 t（1-s）（λ＋λs＋s）/w（s）ds＋（1-t）∫t 0s/w（s）ds,t∈（0,1）进行讨论，并得出了上述方程在λ∈（-1/2,0）上正解存在性的新结果。     

On The Concept Of Periapsis In Hill’s Problem

The concept of closest approach is analyzed in Hill’s problem, resulting in a partitioning of the position space. The different behavior between the direct and retrograde motion is explained analytically, resulting in a simple estimate of the variation of Hill’s periodic and quasi-circular orbits as a function of the Jacobi constant. The local behavior of the orbits on the zero velocity surfaces and an analytical definition of local escape and capture in Hill’s problem are also given.     

Tidal effects on temperature front in the Yellow Sea

Temperature front (TF) is one of the important features in the Yellow Sea, which forms in spring, thrives in summer, and fades in autumn as thermocline declines. TF intensity ⋎S _T ⋎ is defined to describe the distribution of TF. Based on the MASNUM wave-tide-circulation coupled model, temperature distribution in the Yellow Sea was simulated with and without tidal effects. Along 36°N, distribution of TF from the simulated results are compared with the observations, and a quantitative analysis is introduced to evaluate the tidal effects on the forming and maintaining processes of the TF. Tidal mixing and the circulation structure adapting to it are the main causes of the TF. Supported by the National Basic Research Program of China (No. G1999043809) and the National Science Foundation of China (No. 49736190).     

Boundary curves for families of planar orbits

For monoparametric familiesf(x,y)=c of planar orbits, created by a planar potentialV(x,y), we introduce the notion of the family boundary curves (FBC). All members of the familyf(x,y)=c are traced in an allowable region of thexy plane, defined by the corresponding FBC, with total energyE=E(c) varying along the family. Family boundary curves are also found for two-parametric familiesf(x,y,b)=c. The relation of equilibrium points and asymptotic orbits, possibly possessed by the potentialV(x,y), to be FBC is studied.     

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

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.     

Robe's restricted three-body problem revisited

Robe's restricted three-body problem is reanalyzed with a view to incorporate a new assumption, namely that the configuration of the fluid body is that described by an hydrostatic equilibrium figure (Roche's ellipsoid). In the concomitant gravitational field a full treatment of the buoyancy force is given. The pertinent equations of motion are derived, the linear stability of the equilibrium solution is studied and the connection between the effect of the buoyancy forces and a perturbation of the Coriolis force is pointed out.