RIGID FINITE ELEMENT AND LIMIT ANALYSIS

According to the lower-bound theorem of limit analysis the Rigid Finite Element Meth-od(RFEM)is applied to structural limit analysis and the linear programmings for limit analysis are deducedin this paper.Moreover,the Thermo-Parameter Method(TPM)and Parametric Variational principles(PVP)are used to reduce the computational effort while maintaining the accuracy of solutions.A better solution isalso obtained in this paper.

A pseudo-coupled numerical approach for stability analysis of frozen soil slopes based on finite element limit analysis method

To simplify the stability analysis of frozen soil slope, a pseudo-coupled numerical approach is developed. In this approach, the coupled heat transfer and water flow in frozen soils are simulated first, and based on the computed thermal-hydro field, the stability of frozen soil slope is evaluated. Although the shear strength for frozen soil is very complicated and is usually represented by a nonlinear MC failure criterion, a simple linear MC yield criterion is utilized. In this method, the internal friction angle is expressed as a function of volumetric ice content and the cohesion is fitted as a simple bilinear expression of Tand volumetric water content. To assess slope stability, the limit analysis is employed in conjunction with the recently developed a-section search algorithm. A frozen soil slope example is used to examine the proposed pseudo-coupled numerical approach, and numerical studies validate its effectiveness. Based on numerical results, it is seen that slope stability may be remarkably influenced by warming air （or grotmd surface） temperature. With increasing ground surface temperature, slope stability indicated by FOS may reduce to 1.0, implying that wanning air temperature could be a trigger of frozen soil slope failure.

Development of Finite Element Limiting Analysis Method and Its Applications in Geotechnical Engineering

The Finite Element Limiting Analysis Method(LELAM) has the advantage of combining a numerical analysis method with traditional limiting equilibrium methods.It is particularly applicable to the analysis and design of geotechnical engineering.In the early 20th century,FELAM has been developed vigorously in domestic geotechnical engineering over international common finite element procedures.It has made great achievements in basic theory research and computational precision,thus broadening the application fields in practical projects.In order to gradually make innovations in geotechnical design methods,some of our research results are presented,mainly including geotechnical safety factor definitions,the principles for use of the method concerned,the overall failure criterion,the deduction and selection of the yield criterion,and the measurement to improve the computational precision,etc..The application field has been broadened from two-dimensional to three-dimensional,from soil slope to jointed rock slope and foundation,from stable seepage to non-stable seepage,from slope and foundation to tunnel.This method has also been used in search of many hidden sliding surfaces of complex landslides,conducting the structural support design considering the interaction between the soil and the structure,and computing simulation foundation bearing plates load tests,etc..

PLASTIC LIMIT ANALYSIS OF INCOMPATIBLE FINITE ELEMENT METHOD

This paper describes an incompatible finite element model satisfying the consistency condition of energy to solve the numerical precision problem of finite element solution in perfectly plastic analysis. In this paper the reason and criterion of the application of the model to plastic limit analysis are discussed, and an algorithm of computing plastic limit load is given.

Finite element analysis of slope stability by expanding the mobilized principal stress Mohr's circles-Development, encoding and validation

In recent years,finite element analysis is increasingly being proposed in slope stability problems as a competitive method to traditional limit equilibrium methods(LEMs)which are known for their inherent deficiencies.However,the application of finite element method(FEM)to slope stability as a strength reduction method(SRM)or as finite element limit analysis(FELA)is not always a success for the drawbacks that characterize both methods.To increase the performance of finite element analysis in this problem,a new approach is proposed in this paper.It consists in gradually expanding the mobilized stress Mohr’s circles until the soil failure occurs according to a prescribed non-convergence criterion.The present approach called stress deviator increasing method(SDIM)is considered rigorous for three main reasons.Firstly,it preserves the definition of the factor of safety(FOS)as the ratio of soil shear strength to the mobilized shear stress.Secondly,it maintains the progressive development of shear stress resulting from the increase in the principal stress deviator on the same plane,on which the shear strength takes place.Thirdly,by introducing the concept of equivalent stress loading,the resulting trial stresses are checked against the violation of the actual yield criterion formed with the real strength parameters rather than those reduced by a trial factor.The new numerical procedure was encoded in a Fortran computer code called S^(4)DINA and verified by several examples.Comparisons with other numerical methods such as the SRM,gravity increasing method(GIM)or even FELA by assessing both the FOS and contours of equivalent plastic strains showed promising results.

Limit load and failure mechanisms of a vertical Hoek-Brown rock slope

The problem considered in this short note is the limit load determination of a vertical rock slope.The classical limit theorem is employed with the use of adaptive finite elements and nonlinear programming to determine upper and lower bound limit loads of a Hoek-Brown vertical rock slope.The objective function of the mathematical programming problem is such as to optimize a boundary load,which is known as the limit load,resembling the ultimate bearing capacity of a strip footing.While focusing on the vertical slope,parametric studies are carried out for several dimensionless ratios such as the dimensionless footing distance ratio,the dimensionless height ratio,and the dimensionless rock strength ratio.A comprehensive set of design charts is presented,and failure envelopes shown with the results explained in terms of three identified failure mechanisms,i.e.the face,the toe,and the Prandtl-type failures.These novel results can be used with great confidence in design practice,in particularly noting that the current industry-based design procedures for the presented problem are rarely found.

Arc-length technique for nonlinear finite element analysis

Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.

Finite element analyses of slope stability problems using non-associated plasticity

In recent years, finite element analyses have increasingly been utilized for slope stability problems. In comparison to limit equilibrium methods, numerical analyses do not require any definition of the failure mechanism a priori and enable the determination of the safety level more accurately. The paper compares the performances of strength reduction finite element analysis(SRFEA) with finite element limit analysis(FELA), whereby the focus is related to non-associated plasticity. Displacement-based finite element analyses using a strength reduction technique suffer from numerical instabilities when using non-associated plasticity, especially when dealing with high friction angles but moderate dilatancy angles. The FELA on the other hand provides rigorous upper and lower bounds of the factor of safety(FoS) but is restricted to associated flow rules. Suggestions to overcome this problem, proposed by Davis(1968), lead to conservative FoSs; therefore, an enhanced procedure has been investigated. When using the modified approach, both the SRFEA and the FELA provide very similar results. Further studies highlight the advantages of using an adaptive mesh refinement to determine FoSs. Additionally, it is shown that the initial stress field does not affect the FoS when using a Mohr-Coulomb failure criterion.

Strength reduction and step-loading finite element approaches in geotechnical engineering

The finite element limit analysis method has the advantages of both numerical and traditional limit equilibrium techniques and it is particularly useful to geotechnical engineering.This method has been developed in China,following well-accepted international procedures,to enhance understanding of stability issues in a number of geotechnical settings.Great advancements have been made in basic theory,the improvement of computational precision,and the broadening of practical applications.This paper presents the results of research on（1） the efficient design of embedded anti-slide piles,（2） the stability analysis of reservoir slopes with strength reduction theory,and（3） the determination of the ultimate bearing capacity of foundations using step-loading FEM（overloading）.These three applications are evidence of the design improvements and benefits made possible in geotechnical engineering by finite element modeling.

RIGID FINITE ELEMENT AND ITS APPLICATIONS IN ENGINEERING

Rigid Finite Element Method (RFEM) was proposed to simulate the mechanical behavior of discontinuous structures such as rock and soil structures. The authors' work on the theory and applications of RFEM is summarized in this paper. Based on the theory of RFEM, the Elastic Body-Seams Model (EBSM) is proposed to take the deformation and damage of rock masses into account.

The use of the node-based smoothed finite element method to estimate static and seismic bearing capacities of shallow strip footings

The node-based smoothed finite element method(NS-FEM)is shortly presented for calculations of the static and seismic bearing capacities of shallow strip footings.A series of computations has been performed to assess variations in seismic bearing capacity factors with both horizontal and vertical seismic accelerations.Numerical results obtained agree very well with those using the slip-line method,revealing that the magnitude of the seismic bearing capacity is highly dependent upon the combinations of various directions of both components of the seismic acceleration.An upward vertical seismic acceleration reduces the seismic bearing capacity compared to the downward vertical seismic acceleration in calculations.In addition,particular emphasis is placed on a separate estimation of the effects of soil and superstructure inertia on each seismic bearing capacity component.While the effect of inertia forces arising in the soil on the seismic bearing capacity is non-trivial,and the superstructure inertia is the major contributor to reductions in the seismic bearing capacity.Both tables and charts are given for practical application to the seismic design of the foundations.

A MATHEMATICAL PROGRAMMING ALGORITHM FOR LIMIT ANALYSIS

This paper deals with the limit analyses of perfect rigid-plastic continua.Based on the kinematic theorem of the limit analysis theory,a mathematical programming finite element formula for determining the upper bound load multiplier has been established,and an iteration algorithm proposed accordingly.In this algorithm the plastic and rigid zones are distinguished for every iteration step,and the goal function is modified gradually.The difficulties caused by the nonsmoothness of the goal function are over- come.Some examples solved by this algorithm are presented.

Lower Bound Limit Analysis of Anisotropic Soils

Previous approaches can only tackle anisotropic problems with cohesion varying with direction.A novel linearization of the Mohr-Coulomb yield criterion associated with plane strain problem has been achieved by simulating the Mohr’s circle with orientation lines inσ-τspace,which allows for lower bound solution of soils with cohesion and friction coefficient varying with direction.The finite element lower limit analysis formulation using the modified anisotropic yield criterion is then developed.Several examples are given to illustrate the capability and effectiveness of the proposed numerical procedure for computing rigorous lower bounds for anisotropic soils.

Upper Bound Limit Analysis of Anisotropic Soils

In this paper,a novel discretization method inσ-τspace is developed to calculate the upper bound limit loads and failure modes of anisotropic Mohr-Coulomb materials.To achieve this objective,the Mohr-Coulomb yield criterion is linearized inσ-τspace,which allows for upper bound solution of soils whose cohesion and friction coefficient varying with direction.The finite element upper limit analysis formulation using the modified anisotropic yield criterion is then developed.Several examples are given to illustrate the capability and effectiveness of the proposed numerical procedure for computing rigorous upper bounds for anisotropic soils.

Current Limiting Characteristic Analysis of Magnetic-controlled Switcher Type Fault Current Limiter

A novel magnetic-controlled switcher type fault current limiter (FCL) based on the topology of the saturated iron core high temperature superconducting FCL is proposed. The magnetic field distribution of the FCL iron core is analyzed by FEA software ANSYS. The current limiting characteristic is investigated by both 3-D field-circuit coupled simulation and Matlab. The experiments on the 220 V/50 A test model show that the FCL can limit the fault current swiftly and effectively,and the FCL has the advantages of simple and reliable structure, flexible control strategy. The simulation and experimental results prove that the theoretical expectation and current limiting performance is satisfactory for practical use.

基于网格自适应加密策略的隧道稳定性三维极限分析下限有限元法研究

网格分布形式对三维极限分析下限有限元法的计算精度影响较大,为获取精确下限解,通常需对破坏区域进行密集网格划分,从而极易导致计算规模过大,求解效率低下。针对上述问题,提出一种基于单元应力的三维极限分析下限有限元“后验”网格自适应加密策略。首先,构建基于Mohr-Coulomb(M-C)准则和半定规划技术的三维极限分析下限有限元模型,避免了屈服准则的近似处理。其次,引入基于M-C准则的网格自适应加密策略,通过判断各个单元应力接近屈服的程度,确定加密点的坐标。然后,将加密点与原先节点组合构成新的点集,并重新划分网格,建立新的下限有限元计算模型。最后,利用所提方法研究隧道稳定性问题,表明利用所提网格自适应加密策略能够以较少单元精确模拟破坏区域应力分布,从而获取高精度下限解。

家电用热镀锌板减薄后的冲压成形性能

某家电厂将DC51D+Z钢冰箱用热镀锌板的厚度由0.3 mm减薄至0.27 mm,直接减薄时出现了冲压开裂问题。采用有限元仿真分析方法研究了零件冲压成形的要求,并提出了优化方案。结果表明:在材料不变、冲压工艺不变的前提下,直接减薄热镀锌板无法满足该零件冲压成形的要求;采用增加镀锌板碳元素含量、降低镀锌板硼元素含量、提高退火温度等方法,可以降低材料的屈服强度,提高材料的时效性能和冲压成形性能,改进后材料成形极限满足零件的冲压成形要求。

基于FELA的随机场方法在考虑降雨入渗的边坡开挖稳定性分析中的应用

黑山共和国南北高速公路项目部分路段处于复理石地区,降雨集中、空间变异性显著且分层分布的岩土体给道路边坡施工带来了挑战。条分法、常规有限元法等确定性分析方法不能考虑岩土材料的不确定性,给出的具有唯一性、确定性的结果不能反映边坡稳定的不确定性。以该工程某边坡为例,采用有限元极限分析方法(FELA),考虑岩土材料强度的空间变异性,利用上下限解法得出安全系数的分布区间。由勘察资料得到材料均值、标准差和空间相关长度并重建描述抗剪强度指标的二维随机场,同时考虑开挖岩层的节理分布,分析边坡在分级开挖过程中,各施工步骤的稳定性和破坏模式。与有限元分析结果相比,随机场条件下,部分情况开挖阶段安全系数低于限值,并出现局部破坏和整体破坏两种形式。结合不饱和土理论,模拟暴雨情况下雨水的入渗深度并在饱和区采用降低后的强度参数重新计算。通过蒙特卡洛模拟,得到各工况下安全系数、滑动体体积、挡墙弯矩和锚杆内力的概率密度分布函数。挡墙结构约束土体的变形,使得破坏模式趋向于整体破坏,安全系数分布区间变小。锚杆能带动更多土体进入工作状态,同样约束安全系数分布区间。旱季施工与雨季施工边坡破坏区域不同,同等支护条件下,雨季边坡安全系数分布区间更大,且均值明显降低。

Effects of cement-enhanced soil on the ultimate lateral resistance of composite pile in clayey soil

The composite pile consisting of core-pile and surrounding cement-enhanced soil is a promising pile foundation in recent years.However,how and to what extent the cement-enhanced soil influences the ultimate lateral resistance has not been fully investigated.In this paper,the ultimate lateral resistance of the composite pile was studied by finite element limit analysis(FELA)and theoretical upper-bound analysis.The results of FELA and theoretical analysis revealed three failure modes of laterally loaded composite piles.The effects of the enhanced soil thickness,strength,and pile-enhanced soil interface characteristics on the ultimate lateral resistance were studied.The results show that increasing the enhanced soil thickness leads to a significant improvement on ultimate lateral resistance factor(N P),and there is a critical thickness beyond which the thickness no longer affects the N P.Increasing the enhanced soil strength induced 6.2%-232.6%increase of N P.However,no noticeable impact was detected when the enhanced soil strength was eight times higher than that of the natural soil.The maximum increment of N P is only 30.5%caused by the increase of interface adhesion factor(a).An empirical model was developed to calculate the N P of the composite pile,and the results show excellent agreement with the analytical results.

基于光滑有限元的隧道掌子面稳定性分析

隧道掌子面稳定是影响地下工程施工安全的重要问题之一。基于塑性上限和下限定理的极限分析方法是分析掌子面稳定性常用方法之一。其中,自适应混合常应力-光滑应变极限分析(MCSE-LA)方法在计算精度、效率以及收敛性方法已被证明比传统有限元极限分析方法具有一定的优势。基于此,首先验证自适应MCSE-LA在隧道掌子面稳定分析中的可行性,发现该方法求出的隧道掌子面稳定指标(稳定数)与传统有限元上限和下限法相同,同时,还可以通过基于最大剪应变率自适应网格加密技术获得掌子面失稳模式。另外,还将该方法用于分析隧道开挖未支护段长度对掌子面稳定性的影响,通过分析总结了稳定数随未支护长度的变化规律,对指导地下工程施工具有一定的意义。