板料冲压数值模拟中网格自适应算法插入新结点的新方法

介绍了板料冲压数值模拟中的网格自适应加减密技术,针对加密中插入新结点通常采用的边平分法,提出了新的方法。首先,引入了扩展单元,通过比较其与普通单元的形函数说明了扩展单元的性质。其次,给出了自适应加减密的过程,通过比较单元边上两结点的结点向量夹角之差来决定是否加减密,在形成所有的加减密单元边后,根据几种情况进行相关单元的加减密处理。在提出的插入新结点的新方法中,充分利用结点向量的信息,使新结点的位置更逼近于实际边界。试验结果显示该算法正确,稳定。

Post-earthquake Rainfall-triggered Slope Stability Analysis in the Lushan Area

The ＂4.20＂ Lushan earthquake in Sichuan province, China has induced a large amount of geological hazards and produced abundant loose materials which are prone to post-earthquake rainfall- triggered landslides. A detailed landslide inventory was acquired through post-earthquake emergent field investigation and high resolution remote sensing interpretation. The rainfall analysis was conducted using historical rainfall records during the period from 1951 to 2010. Results indicate that the average annual rainfall distribution is heterogeneous and the largest average annual rainfall occurs in Yucheng district. The Stability Index MAPping （SINMAP） model was adopted to assess and analyze the post- earthquake slope stability under different rainfall scenarios （light rainfall, moderate rainfall, heavy rainfall, and rainstorm）. The model parameters were calibrated to reflect the significant influence of strong earthquakes on geological settings. The slope stability maps triggered by different rainfall scenarios were produced at a regional scale. The effect of different rainfall conditions on the slope stability is discussed. The expanding trend of the unstable area was quantitatively assessed with the different critical rainfall intensity. They provide a new insight into the spatial distribution and characteristics of post- earthquake rainfall-triggered landslides in the Lushan seismic area. An increase of rainfall intensity results in a significant increase heterogeneous distribution strongly correlated with of unstable area. The of slope instability is the distribution of earthquake intensity in spite of different rainfall conditions. The results suggest that the both seismic intensity and rainfall are two crucial factors for post- earthquake slope stability. This study provides important references for landslide prevention and mitigation in the Lushan area after earthquake.

Free Surface Flow Generated by Submerged Twin-cylinders in Forward Motion Using a Fully Nonlinear Method

The free surface flow generated by twin-cylinders in forced motion submerged beneath the free surface is studied based on the boundary element method. Two relative locations, namely, horizontal and vertical, are examined for the twin cylinders. In both cases, the twin cylinders are starting from rest and ultimately moving with the same constant speed through an accelerating process. Assuming that the fluid is inviscid and incompressible and the flow to be irrotational, the integral Laplace equation can be discretized based on the boundary element method. Fully-nonlinear boundary conditions are satisfied on the unknown free surface and the moving body surface. The free surface is traced by a Lagrangian technique. Regriding and remeshing are applied, which is crucial to quality of the numerical results. Single circular cylinder and elliptical cylinder are calculated by linear method and fully nonlinear method for accuracy checking and then fully nonlinear method is conducted on the twin cylinder cases, respectively. The generated wave elevation and the resultant force are analysed to discuss the influence of the gap between the two cylinders as well as the water depth. It is found that no matter the kind of distribution, when the moving cylinders are close to each other, they suffer hydrodynamic force with large absolute value in the direction of motion. The trend of force varying with the increase of gap can be clearly seen from numerical analysis. The vertically distributed twin cylinders seem to attract with each other while the horizontally distributed twin cylinders are opposite when they are close to each other.

Limit equilibrium method for slope stability based on assumed stress on slip surface

In the limit equilibrium framework, two- and three-dimensional slope stabilities can be solved according to the overall force and moment equilibrium conditions of a sliding body. In this work, based on Mohr-Coulomb(M-C) strength criterion and the initial normal stress without considering the inter-slice(or inter-column) forces, the normal and shear stresses on the slip surface are assumed using some dimensionless variables, and these variables have the same numbers with the force and moment equilibrium equations of a sliding body to establish easily the linear equation groups for solving them. After these variables are determined, the normal stresses, shear stresses, and slope safety factor are also obtained using the stresses assumptions and M-C strength criterion. In the case of a three-dimensional slope stability analysis, three calculation methods, namely, a non-strict method, quasi-strict method, and strict method, can be obtained by satisfying different force and moment equilibrium conditions. Results of the comparison in the classic two- and three-dimensional slope examples show that the slope safety factors calculated using the current method and the other limit equilibrium methods are approximately equal to each other, indicating the feasibility of the current method; further, the following conclusions are obtained: 1) The current method better amends the initial normal and shear stresses acting on the slip surface, and has the identical results with using simplified Bishop method, Spencer method, and Morgenstern-Price(M-P) method; however, the stress curve of the current method is smoother than that obtained using the three abovementioned methods. 2) The current method is suitable for analyzing the two- and three-dimensional slope stability. 3) In the three-dimensional asymmetric sliding body, the non-strict method yields safer solutions, and the results of the quasi-strict method are relatively reasonable and close to those of the strict method, indicating that the quasi-strict method can be used to obtain a reliable slope safety factor.

Effect of non-uniform stress characteristics on stress measurement in specimen

There is a remarkable difference in stress distribution between a specimen and a plate removed from the specimen.The plate presents a uniform stress distribution whereas the specimen presents a non-uniform stress distribution.Firstly,the real stress distributions in plates with thickness of 30,40 and 50 mm and then in the specimens were obtained through simulation and X-ray surface stress measurement.Secondly,in order to study the impact of specimens shapes and processing ways on the results accuracy,two irregular shapes (parallelogram and trapezoid) and two processing ways (saw and electron discharge machining (EDM)) were compared and analyzed by simulation and experiment using layer removal method,then the specimen effects on measurement results were evaluated.The results show that:1) the non-uniform stress distribution characteristics of the specimen near the surface of the cut is significant,the range of non-uniform stress distribution is approximately one-thickness distance away from the cut,and it decreases gradually along the depth;2) In order to ensure the stability in the results,it is suitable to take the specimen plane size 2-3 times of its thickness;3) Conventional processing methods have little effect on experimental results and the average deviation is less than 5%.

Singular Perturbations for a Class of Fourth-order Nonlinear Boundary Value Problem

This paper is devoted to study the following the singularly perturbed fourth-order ordinary differential equation ∈y（4） =f（t,y＇,y＇＇,y＇＇＇）,0t1,0ε1 with the nonlinear boundary conditions y（0）=y＇（1）=0,p（y＇＇（0）,y＇＇＇（0））=0,q（y＇＇（1）,y＇＇＇（1））=0 where f：[0,1]×R3→R is continuous,p,q：R2→R are continuous.Under certain conditions,by introducing an appropriate stretching transformation and constructing boundary layer corrective terms,an asymptotic expansion for the solution of the problem is obtained.And then the uniformly validity of solution is proved by using the differential inequalities.

Three-dimensional analysis of natural convection in nanofluid-filled parallelogrammic enclosure opened from top and heated with square heater

A numerical study based on the finite volume method has been performed to study the three-dimension natural convection in a parallelogrammic top side opened cavity filled nanofluid with partially heated square at the bottom side.Results are obtained for different governing parameters such as nanoparticle concentration (φ) from 0 to 0.05,inclination angle of the back and front walls (α) from 5° to 75°,Rayleigh number from 10^3 to 10^5,and length of heater changer from 0.1 to 1.The main finding from the obtained result showed that the inclination angle and nanoparticle volume fraction affect the flow structure and enhance the heat transfer.

On p-mean Curvature Operator with Critical Exponent

This paper is concerned with the existence of positive solutions of the followingDirichlet problem for p-mean curvature operator with critical exponent： -div（（1 ＋｜↓△u｜^2 ）p-2/2 ↓△u） = λup-1＋μ u=q-1,u 〉 0,x x∈Ω,u=0,x∈ δΩ,where u ∈ W01,P is a bounded domain in R^N（N 〉 p 〉 1） with smooth boundary δΩ, 2≤p ≤q〈p,p=Np/N-p,λ,μ〉0. It reaches the conclusions that this problem has at least one positive solution in the different cases. It is discussed the existences of positivesolutions of the Dirichlet problem for the p-mean curvature operator with critical exponentby using Nehari-type duality property firstly. As p = 2, q = p, the result is correspond tothat of Laplace operator.

Limit equilibrium analysis for rock slope stability using basic Hoek–Brown strength criterion

Hoek–Brown(HB)strength criterion can reflect rock’s inherent failure nature,so it is more suitable for analyzing the stability of rock slopes.However,the traditional limit equilibrium methods are at present only suitable for analyzing the rock slope stability using the linear equivalent Mohr–Coulomb(EMC)strength parameters instead of the nonlinear HB strength criterion.Therefore,a new method derived to analyze directly the rock slope stability using the nonlinear HB strength criterion for arbitrary curve slip surface was described in the limit equilibrium framework.The current method was established based on certain assumptions concerning the stresses on the slip surface through amending the initial normal stressσ0 obtained without considering the effect of inter-slice forces,and it can satisfy all static equilibrium conditions of the sliding body,so the current method can obtain the reasonable and strict factor of safety(FOS)solutions.Compared with the results of other methods in some examples,the feasibility of the current method was verified.Meanwhile,the parametric analysis shows that the slope angleβhas an important influence on the difference of the results obtained using the nonlinear HB strength criterion and its linear EMC strength parameters.Forβ≤45°,both of the results are similar,showing the traditional limit equilibrium methods using the linear EMC strength parameters and the current method are all suitable to analyze rock slope stability,but forβ>60°,the differences of both the results are obvious,showing the actual slope stability state can not be reflected in the traditional limit equilibrium methods,and then the current method should be used.

Dynamic limit equilibrium analysis of sliding block for rock slope based on nonlinear FEM

Traditional rigid body limit equilibrium method （RBLEM） was adopted for the stability evaluation and analysis of rock slope under earthquake scenario. It is not able to provide the real stress distribution of the structure, while the strength reduction method relies on the arbitrary decision on the failure criteria. The dynamic limit equilibrium solution was proposed for the stability analysis of sliding block based on 3-D multi-grid method, by incorporating implicit stepping integration FEM. There are two independent meshes created in the analysis： One original 3-D FEM mesh is for the simulation of target structure and provides the stress time-history, while the other surface grid is for the simulation of sliding surface and could be selected and designed freely. As long as the stress time-history of the geotechnical structure under earthquake scenario is obtained based on 3-D nonlinear dynamic FEM analysis, the time-history of the force on sliding surface could be derived by projecting the stress time-history from 3-D FEM mesh to surface grid. After that, the safety factor time-history of the sliding block will be determined through applying limit equilibrium method. With those information in place, the structure＇s aseismatic stability ean be further studied. The above theory and method were also applied to the aseismatic stability analysis of Dagangshan arch dam＇s right bank high slope and compared with the the result generated by Quasi-static method. The comparative analysis reveals that the method not only raises the FEM＇s capability in accurate simulation of complicated geologic structure, but also increases the flexibility and comprehensiveness of limit equilibrium method. This method is reliable and recommended for further application in other real geotechnical engineering.

Parametric Analysis of the Stability of Degraded Railroad Platforms

The current study is developed based on one of the types of subgrade rupture risk suggested by Selig and Waters （1994）. It aims to evaluate subgrade stability railroad, which consists of the slope stability analysis of a railway yard embankment subjected to a wagon load type gondola parked on this track. This proposed analysis was taken into consideration because there are Brazilian railroads in high deterioration level. In some of these lines the tracks are submitted to increasing amount of load every year. The adopted model slope stability to the studied railroad embankments considers the rupture on circular line. It was applied the Geoslope-Slope/W software, version 6, to the evaluation of the platform-slope system. Several situations are adopted to reach the minimum safety slope, permitting to analyze the platform stability to keep railroad traffic under adequate safety level.

Mechanical response of bridge piles in high-steep slopes and sensitivity study

The bridge piles located in high-steep slopes not only endure the loads from superstructure, but also the residual sliding force as well as the resistance from the slope. By introducing the Winkler foundation theory, the mechanical model of piles-soils-slopes system was established, and the equilibrium differential equations of pile were derived. Moreover, an analytic solution for identifying the model parameters was provided by means of power series method. A project with field measurement was compared with the proposed method. It is indicated that the lateral loads have great influences on the pile, the steep slope effect is indispensable, and reasonable diameter of the pile could enhance the bending ability. The internal force and displacements of pile are largely based upon the horizontal loads applied on pile, especially in upper part.

Application of cusp catastrophe theory to reliability analysis of slopes in open-pit mines

A method of slope reliability analysis was developed by imposing a state equation on the limit equilibrium theory, given the basis of a fixed safety factor technique. Among the many problems of reliability analysis, the most important problem is to find a performance function. We have created a new method of building a limit state equation for planar slip surfaces by applying the mathematical cusp catastrophe theory. This new technique overcomes the defects in the traditional rigid limit equilibrium theory and offers a new way for studying the reliability problem of planar slip surfaces. Consequently, we applied the technique to a case of an open-pit mine and compared our results with that of the traditional approach. From the results we conclude that both methods are essentially consistent, but the reliability index calculated by the traditional model is lower than that from the catastrophic model. The catastrophe model takes into consideration two possible situations of a slope being in the limit equilibrium condition, i.e., it may or may not slip. In the traditional method, however, a slope is definitely considered as slipping when it meets the condition of a limit equilibrium. We conclude that the catastrophe model has more actual and instructive importance compared to the traditional model.

Evolutions of texture and grain boundary plane distributions in a ferritic stainless steel

The grain size, textures and grain boundary plane distributions in a cold-rolled and annealed ferritic stainless steel were investigated by means of EBSD techniques. The results show that, following cold rolling with the thickness reduction of 85%, relatively low temperature （780℃） annealing brings an extremely sluggish grain growth and no grain texture develops when the annealing time varies from 5 min to 480 min. The free energy reduction of the system is mainly caused by the grain boundary plane re-orientation in addition to minor grain growth because the distributions of grain boundary planes are moderately preferred on { 100} according to the five parameter analyses （FPA） concerning the grain boundary plane characteristics. However, in the case of high-temperature （1 000 ℃） annealing, the average grain size does not increase until annealing time is prolonged to 90 min, after which extensive grain growth occurs and strong {100}（hkl） texture emerges whereas nearly random grain boundary plane distributions are observed. The free energy reduction of the system is most likely attributed to the selective growth.

Multi-domain Boundary Element Method with Dissipation

The wave diffraction and radiation around a floating body is considered within the framework of the linear potential theory in a fairly perfect fluid. The fluid domain extended infinitely in the horizontal directions but is limited by the sea bed, the body hull, and the part of the free surface excluding the body waterplane, and is subdivided into two subdomains according to the body geometry. The two subdomains are connected by a control surface in fluid. In each subdomain, the velocity potential is described by using the usual boundary integral representation involving Green functions. The boundary integral equations are then established by satisfying the boundary conditions and the continuous condition of the potential and the normal derivation across the control surface. This multi-domain boundary element method （MDBEM） is particularly interesting for bodies with a hull form including moonpools to which the usual BEM presents singularities and slow convergence of numerical results. The application of the MDBEM to study the resonant motion of a water column in moonpools shows that the MDBEM provides an efficient and reliable prediction method.

CO2 Marginal Abatement Cost and Determinants——An Empirical Analysis of Sample Cities in China

This paper investigates the marginal abatement cost （MAC） of CO： emissions across 104 Chinese cities between 2001 and 2008. Based on parametric directional distance function, this paper discovers that the mean marginal abatement cost of CO2 emissions for sample cities was 967 yuan/ton. In terms of region, CO： marginal abatement cost is significantly higher in China＇s eastern region than in central and western regions; in terms of provincial-level region, it is the highest in Shanghai and the lowest in Shaanxi in terms of city, it is the highest in Shanghai and the lowest in Zhangjiajie with the ratio between their medians being at 48：1; in terms of time, marginal abatement cost has been always on the rise with significant intercity disparities. There is a U-shaped curve relationship between marginal abatement cost of cities and CO2 emissions per unit of GDP, which is negatively correlated with the share of secondary industry and positively correlated with the level of urbanization.

Fracture Analysis for Torsion Problems of a Gravity Platform Column with Cracks Under Wind Load

Ocean platforms are subjected to a variety of environment loads, such as those from winds, waves, currents, etc. In this study, the torsion problems of a gravity platform column with cracks under wind load were investigated. The colmnn was assumed to be a composite cylinder. Therefore the torsion fracture problem of a composite cylinder was considered, and new boundary integral equations for the Saint-Venant torsion problem of a composite cylinder with curvilinear cracks were derived. The problem was re- duced to solving the boundary integral equations on every boundary. By using the new boundary element method, the torsion prob- lem of the gravity platform colunm with a straight crack under various wind loads was calculated. The obtained results were com- pared with those obtained for a torsion problem of the same column without cracks to prove the applicability of the present method. The comparison showed that the detrimental effect of cracks in a column should be considered in marine engineering.

On the Adjacent Strong Edge Coloring of Outer Plane Graphs

A k-adjacent strong edge coloring of graph G(V, E) is defined as a proper k-edge coloring f of graph G(V, E) such that f[u] ≠ f[v] for every uv ∈ E(G), where f[u] = {f(uw)|uw ∈ E(G)} and f(uw) denotes the color of uw, and the adjacent strong edge chromatic number is defined as x'as(G) = min{k| there is a k-adjacent strong edge coloring of G}. In this paper, it has been proved that △ ≤ x'as(G) ≤ △ + 1 for outer plane graphs with △(G) ≥ 5, and X'as(G) = △ + 1 if and only if there exist adjacent vertices with maximum degree.

ON THE EMPTY CONVEX PARTITION OF A FINITE SET IN THE PLANE

The authors discuss the partition of a finite set of points in the plane into empty convex polygons, and improve some upper bound and lower bound in the related enumeration problems.

Analytic prediction for planar turbulent boundary layers

Analytic predictions of mean velocity profile(MVP) and streamwise(x) development of related integral quantities are presented for flows in channel and turbulent boundary layer(TBL), based on a symmetry analysis of eddy length and total stress. Specific predictions include the relations for momentum Reynolds number(Reθ) with friction Reτ and streamwise Re_x: Re_θ≈ 3.27Re_τ,and Re_x/Re_θ = 4.94(lnRe_θ + 1.88)~2 + 1; the streamwise development of the friction velocity u_τ: U_e/u_τ≈ 2.22 lnRe_x + 2.86. 3.83ln(lnRe_x), and of the boundary layer thickness δ_e: x/δ_e ≈ 7.27 lnRe_x.5.18.12.52ln(lnRe_x), which are fully validated by recent reliable data.