New Multidimensional Visualization Technique for Limit-State Surfaces in Nonlinear Finite-Element Reliability Analysis

Structural reliability problems involving the use of advanced finite-element models of real-world structures are usually defined by limit-states expressed as functions (referred to as limit-state functions) of basic random variables used to characterize the pertinent sources of uncertainty. These limit-state functions define hyper-surfaces (referred to as limit-state surfaces) in the high-dimensional spaces of the basic random variables. The hyper-surface topology is of paramount interest, particularly in the failure domain regions with highest probability density. In fact, classical asymptotic reliability methods, such as the first- and second-order reliability method (FORM and SORM), are based on geometric approximations of the limit-state surfaces near the so-called design point(s) (DP). This paper presents a new efficient tool, the multidimensional visualization in the principal planes (MVPP) method, to study the topology of high-dimensional nonlinear limit-state surfaces (LSSs) near their DPs. The MVPP method allows the visualization, in particularly meaningful two-dimensional subspaces denoted as principal planes, of actual high-dimensional nonlinear limit-state surfaces that arise in both time-invariant and time-variant (mean out-crossing rate computation) structural reliability problems. The MVPP method provides, at a computational cost comparable with SORM, valuable insight into the suitability of FORM/SORM approximations of the failure probability for various reliability problems. Several application examples are presented to illustrate the developed MVPP methodology and the value of the information provided by visualization of the LSS.     

Reliability-Based Optimal Design of Series Structural Systems

A robust approach for approximately solving reliability-based optimal design problems, for series structural systems, is developed. The approach reformulates the problems by replacing reliability terms with deterministic functions. The reformulated problems can be solved by existing semiinfinite optimization algorithms, producing solutions that are identical to those of the original problems, when the limit-state functions are affine, or when first-order reliability approximations are used. An important advantage of the approach is that the required reliability and optimization calculations are completely decoupled, allowing flexibility in the choice of the optimization algorithm and the reliability method. Three sets of examples demonstrate applications of the approach.     

The Rule of Equivalent States in Limit-State Analysis of Soils

Soil is typically regarded as a frictional or cohesive-frictional material in limit-state considerations. Often the solution to a limit-state problem (for instance, the bearing capacity of footings) for a purely frictional soil is easier to obtain than the solution for a cohesive-frictional material. A theorem was presented that makes it possible to obtain a solution for cohesive-frictional soil through a transformation of a known solution for purely frictional soil. However, application of the transformation rule based on this theorem is shown to have limitations. This rule appears to be applicable for boundary-value problems where boundary stresses have only normal components and principal stress trajectories are not altered by the transformation. With modern computational tools the correspondence rule is bypassed. However, its applicability is a consequential issue in soil mechanics education, even if of a somewhat historical nature. An example of limit loads on a strip footing is presented, a solution to inclination coefficients is produced, and the consequences of the rule of corresponding states are discussed. Finally, the application of the rule of correspondence in the kinematic approach of limit analysis is investigated. A convenient method is developed for calculations of the energy dissipation rate, which does not require tedious calculations of dissipation on all velocity discontinuity surfaces or in continually deforming regions.     

Strength and Serviceability of FRP Grid Reinforced Bridge Decks

The research presented in this paper evaluates the flexural performance of bridge deck panels reinforced with 2D fiber-reinforced polymer (FRP) grids. Two different FRP grids were investigated, one reinforced with a hybrid of glass and carbon fibers and a second grid reinforced with carbon fibers only. Laboratory measured load-deflection, load-strain (reinforcement and concrete), cracking, and failure behavior are presented in detail. Conclusions regarding failure mode, limit-state strength, serviceability, and deflection compatibility relative to AASHTO mandated criteria are reported. Test results indicate that bridge decks reinforced with FRP grids will be controlled by serviceability limit state and not limit-state ultimate strength. The low axial stiffness of FRP results in large service load flexural deflections and reduced shear strength. In as much as serviceability limits design, overreinforcement is recommended to control deflection violation. Consequently, limit-state flexural strength will be compression controlled for which reduced service stresses or ACI unified compression failure strength reduction factors are recommended.     

Probabilistic Stability Analyses of Embankments Based on Finite-Element Method

Conventional limit equilibrium methods are commonly used to assess the stability of embankments. The finite-element method, as an alternative to limit equilibrium methods, is being increasingly used in the deterministic stability analysis of slopes or embankments. In this paper, a practical procedure for integrating the finite-element method and the limit equilibrium methods into probabilistic stability analysis for embankments is presented. The response surface method is adopted to approximate the performance function for the stability problems and the first-order reliability method is used to calculate the reliability index based on an intuitive expanding ellipsoid perspective. The advantages of the response surface method as a bridge between stand-alone numerical packages and spreadsheet-based reliability analysis via automatic constrained optimization are demonstrated and discussed through a hypothetical two-layer slope and an actual case of the James Bay Dykes. The results show the ease and successful implementation of the proposed procedure for reliability analysis of embankments.     

Bond Tests of Short NSM-FRP and Steel Bar Anchorages

Performance of near-surface mounted (NSM) bars as additional reinforcement in strengthening of existing reinforced-concrete construction largely depends on the development capacity of the bar inside the groove. This is controlled primarily by the surface characteristics of the bar and its interaction with the surrounding groove filler and the cover concrete. In this paper, the bond strength of short NSM-bar anchorages is explored experimentally, using a modified eccentric pullout test specimen designed to alleviate some of the deficiencies associated with bond testing. A total of 45 tests were conducted to study the influence of the most important technological parameters of this upgrading method, namely the groove dimensions, the embedment length, and the surface pattern of the bars. NSM bars were 12?mm diameter rods: CFRP bars used had a sandblasted surface and winding helical lengthwise indentations. Steel bars were either standard deformed bars or smooth reinforcement. The variety of bar type considered was intended to highlight and to quantify through the tests the bond strength that may be mobilized by postinstalled reinforcement according to surface profile and stiffness. Test results are used to establish a limit-state bond-slip model for near-surface mounted bars, so as to enable implementation of this emerging technology in practical design.     

Contemporary Trends in Formwork Standards—A Case Study

One expression of the renewed attention gained recently by formwork for concrete is the current revision of formwork standards. This paper presents the new Israeli formwork standard as a case study for contemporary trends in formwork standardization. The main novelty in the new standard is its similar treatment of the design of temporary structures to that of permanent structures, resulting in the replacement of the traditional allowable-stress approach with the concept of limit-state design and partial safety factors. The paper presents this concept and discusses its applicability to formwork design. In addition, the paper highlights several other issues of a contemporary nature, which appear to be worth debate by standardization committee members from the industry and academia. In the course of the preparation of the new Israeli standard, American, European, and Australian standards and similar documents were closely studied; some comparisons of design and loading data that may affect construction safety and economy are also presented in this paper.     

Reliability-Based Optimal Design of Truss Structures Using Particle Swarm Optimization

In this work, the particle swarm optimization method is employed for the reliability-based optimal design of statically determinate truss structures. Particle swarm optimization is inspired by the social behavior of flocks (swarms) of birds and insects (particles). Every particle’s position represents a specific design. The algorithm searches the design space by adjusting the trajectories of the particles that comprise the swarm. These particles are attracted toward the positions of both their personal best solution and the best solution of the swarm in a stochastic manner. In typical structural optimization problems, safety is dealt with in a yes/no manner fulfilling the set of requirements imposed by codes of practice. Considering uncertainty for the problem parameters offers a measure to quantify safety. This measure provides a rational basis for the estimation of the reliability of the components and of the entire system. Incorporating the reliability into the structural optimization framework one can seek a reliability-based optimal design. For the problems examined herein, the reliability indexes of the structural elements are obtained from analytical expressions. The structure is subsequently analyzed as a series system of correlated elements and the Ditlevsen bounds are used for the calculation of its reliability index. The uncertain-random parameters considered in this work are the load, the yield-critical stress; and the cross sections of the elements. The considered design variables of the optimization problem are the cross-sectional areas of the groups, which control the size of the truss, and the heights and lengths that control the shape of the truss. The results of the optimization are presented for a 25-bar truss and a 30-bar arch and the robustness of the optimization scheme is discussed.     

BEM Analysis of Two-Dimensional Elastodynamic Problems of Anisotropic Solids

A direct BEM (boundary element method) formulation and its numerical implementation for steady-state elastodynamic analysis of two-dimensional problems involving orthotropic and nonorthotropic solids of arbitrary shape is presented. The present formulation is developed by incorporating isoparametric quadratic boundary elements, a rigorous self-adapting numerical integration scheme, and the Green's functions of Wang and Rajapakse for two-dimensional orthotropic solids. The full-space as well as the half-space Green's functions have been implemented. The formulation is capable of treating multidomain problems by substructuring and satisfying the equilibrium and displacement compatibility at the interfaces. Thus, problems related to the layered media and soil-structure interaction can all be analyzed. The accuracy and reliability of the present BEM analysis are demonstrated through comparison of results obtained for a few example problems with published solutions. Finally, the applicability of this methodology is demonstrated by analyzing three types of problems, a rigid strip footing embedded in an orthotropic half-space, a strip footing resting on an orthotropic stratum overlaying an orthotropic half-space, and a rigid strip footing embedded in a nonorthotropic half-space.     

Assessment of Stability of Slopes under Drawdown Conditions

The traditional approach for estimating the stability of slopes under different submergence conditions is the charts of Morgernstern and, more recently, proprietary computer programs, both utilizing limit-state analyses. The chart approach is limited by geometry and material property considerations and the limit-state approach by assumptions about analysis method and failure mechanism. The finite-element method offers a powerful method for analyzing complex geometries and properties of slope stability problems, but may be unattractive for routine use by supervisory staff. By comparison a chart based approach is useful, particularly when setting operating conditions on, for example, drawdown rates for dams and reservoirs. This paper seeks to explore the use of the finite-element method to produce operating charts for such circumstances that should be applicable to real structures.     

Method of Adaptive-Gradient Elements for Computational Mechanics

For tackling high-gradient, localized, or singular boundary value problems, the concept of an adaptive-gradient (AG) element family is introduced to advance the utility of discretization methods. Capable of encompassing regular and singular elements as special cases, a basic but versatile family of AG elements for multidimensional applications is derived whose gradient and singularity can be controlled parametrically to handle a wide variety of functional behavior with standard mesh configurations. As illustrations, examples of usage and performance in a set of linear and nonlinear mixed-boundary value problems are presented.     

难溶氧化铂中铂的测定

研究了将难溶氧化铂通过水合肼还原成海绵铂,用王水溶解海绵铂,采用氯化铵沉淀法测定铂,从而建立了难溶氧化铂中铂含量的测定方法。对还原剂的选择、还原温度、还原酸度、还原后沉淀过滤洗涤方式及共存元素的干扰等条件进行了一系列实验,解决了难溶氧化铂中铂测定的难题。该方法易于操作,准确度高。将该方法应用于5个不同品位难溶氧化铂样品中铂的测定,相对标准偏差（RSD）为0．10％～0．30％（n=9）。采用该方法测定基准物质氧化铂（PtO2·H2O）中的铂含量,测定值和标准值相符合,从而证明该方法的可行性和可靠性。     

火花源原子发射光谱法测定银中铜铋铁铅锑钯硒碲

探讨了火花源原子发射光谱法分析银中杂质元素铜、铋、铁、铅、锑、钯、硒和碲的分析条件、样品处理方法, 确定了各杂质元素测定范围。采用对测定结果无明显影响的车床或压样机加工样品表面, 用盐酸(1+9)去除试样表面的沾污, 校准曲线采用仪器内置的纯银标准曲线, 并通过内部质量控制样品和校正样品监控。实验方法用于纯银标准样品中8种元素的分析, 测定值与认定值一致;对银锭样品进行分析, 各元素11次测定结果的相对标准偏差在1.0%~4.0％之间。方法可用于纯银和银锭中包括钯的杂质元素分析。     

激光诱导击穿光谱在铜精矿成分在线检测中的应用

目前铜精矿成分检测多为实验室离线取样检测,存在取样代表性差、检测时间长、检测结果滞后等问题。针对上述问题,实验利用基于激光诱导击穿光谱(LIBS)技术的激光成分分析仪对铜精矿中Cu、S、Fe和Si关键元素含量进行了在线检测,同时采用X射线荧光光谱仪(XRF)对相同样品采用离线检测进行对照。结果表明：激光成分分析仪在线检测结果与实验室X射线荧光光谱仪(XRF)离线检测结果相比,Cu、S、Fe和Si元素的平均绝对误差分别为0.50%、0.56%、0.65%和1.67%,平均相对误差分别为2.80%、2.28%、2.74%和12.89%,各元素重复性在线检测最大差值和相对标准偏差(RSD)均与以国家标准的化学湿法分析检测结果表征的样品不均匀性相吻合,在线检测具有较好的稳定性和重复性。基于LIBS技术的在线成分检测仪器可满足铜冶炼过程中铜精矿成分检测的实时性和可靠性要求,并为配料品质提升和冶炼工艺优化提供有力支撑。     

Improvement of the procedure for determining alumina in the electrolyte

A procedure for determining the weight fraction of alumina in electrolytes containing additives of magnesium fluoride, which increases the reliability of chemical analytical data, based on which the electrolytic production of aluminum is monitored, is developed. A physicochemical model allowing one to determine the content and forms of elements in the solution, solid phases, and gaseous products forming during the interaction of the electrolyte with the aqueous solution of aluminum chloride is presented. The example of using the physicochemical model as a method for matching the chemical analytical data is presented, and the accuracy of determining the alumina weight fraction in the electrolyte by the leaching method is verified.     

ICP-AES测定钒氮合金中杂质元素

研究了用ICP -AES测定钒氮合金中杂质元素硅、锰、磷、铬、镍、铜、铝的方法 ,建立了最佳工作条件。试样用硝酸、盐酸和高氯酸溶解 ,应用谱线干扰校正技术和基体匹配办法消除干扰元素影响 ,克服了繁琐的样品预处理过程。方法用于钒氮合金中 7个微量元素的测定 ,相对标准偏差为 0.44 %～ 1.79% ,标准加入回收率为 93.6%～ 109.7%。     

Double adenomas with different pathological and hormonal features in the left adrenal gland of a patient with Cushing''s syndrome

A simple method is presented for projecting the conformation of extended secondary structure elements of peptides and proteins that extend over four C alpha atoms onto a simple two-dimensional surface. A new set of two degrees of freedom is defined, a pseudodihedral involving four sequential C alpha atoms, as well as the triple scalar product for the vectors describing the orientation of the three intervening peptide groups. The method provides a reduction in dimensionality, from the usual combination of multiple phi,psi pairs to a single pair, yielding valuable information concerning the structure and dynamics of these important elements. The new two-dimensional surface is explored by reference to 63 selected protein crystal structures together with a comparison of model built peptides representing the common secondary structural elements. Dynamical aspects on this new surface are examined using a molecular dynamics trajectory of Basic Pancreatic Trypsin Inhibitor.     

Estimation of the surface tensions of binary liquid alloys

A simple method to estimate the surface tensions of binary alloys has been developed by assuming that the partial molar excess free energies are proportional to the number of nearest neighbors in both the bulk solution and in the surface itself. In order to estimate the surface tension of the alloys, excess free energies of the alloys and the surface tensions of the pure components are required. This method has been applied to ten alloys exhibiting positive, positive as well as negative, and negative deviations from ideal solution behavior. The method depends upon the reliability of the thermodynamic data for the bulk solutions, and, further, it is important to use an interpolation scheme that is consistent with the Gibbs-Duhem requirement, when the thermodynamic data are presented in tabular form as a function of composition. To accomplish this interpolation, a special calculation technique is presented.     

Observations on Limit Equilibrium–Based Slope Reliability Problems with Inclined Weak Seams

This study addresses the complexity of slope reliability problems based on limit equilibrium methods (LEMs). The main focus is on the existence of multiple failure modes that poses difficulty to many LEM-based slope reliability methods. In particular, when weak seams are present, the failure modes associated with those seams may be difficult to detect. A systematic way of searching the failure modes is proposed, and its robustness over slopes with or without weak seams is demonstrated. It is found that in the presence of weak seams, assuming circular slip surfaces may cause underestimation of slope failure probability. The conclusion of the study promotes the use of finite elements as the stability method for reliability evaluation because it is not necessary to search for failure surfaces in finite-element stability analysis.     

Efficient Evaluation of Reliability for Slopes with Circular Slip Surfaces Using Importance Sampling

Evaluating the reliability of a slope is a challenging task because the possible slip surface is not known beforehand. Approximate methods via the first-order reliability method provide efficient ways of evaluating failure probability of the “most probable” failure surface. The tradeoff is that the failure probability estimates may be biased towards the unconservative side. The Monte Carlo simulation (MCS) is a viable unbiased way of estimating the failure probability of a slope, but MCS is inefficient for problems with small failure probabilities. This study proposes a novel way based on the importance sampling technique of estimating slope reliability that is unbiased and yet is much more efficient than MCS. In particular, the critical issue of the specification of the importance sampling probability density function will be addressed in detail. Three examples of slope reliability will be used to demonstrate the performance of the new method.