Discrete minimum weight design of steel structures using EC3 code

The paper presents a practical method of the discrete minimum weight design of steel structures. It is based on a concept of removal of the redundant material by successive diminishing of the size of the least stressed member. It is assumed that the member sizes are available from the European Steel Profiles Catalogues, and the design constraints are given by the rules of the code EC3 for nonsway buildings. Two numerical examples are presented: the classical benchmark problem of a ten-bar truss made of circular hollow sections (24 element catalogue, buckling taken into account) and a portal frame made of HEB sections with broad parallel flanges (11 element catalogue). The proposed method gives, after a reasonable calculation time, a very good approach to the exact optimum solution. Received January 21, 2000     

Optimal decision for the target value of performance-based structural system reliability

The optimal decision model of the target value of performance-based structural system reliability is established according to the cost-effectiveness criterion in the present paper. Three types of optimal decision models are studied: the conceptive model, the parameter programming model and the constraint relaxation model. The conceptive model is inoperable because the objective function must be expressed as the function of the structural target reliability. The parameter programming and constraint relax models are proved to be equivalent with Kuhn–Tucker conditions when the performance-based structural system reliability constraints are all active. Finally the numerical examples of RC-frames for different earthquake-resistant performance are calculated. Received February 5, 2000     

基于自适应距离度量的分类器设计方法

通过对欧氏距离度量的分析,提出了自适应距离度量.首先利用训练样本建立自适应距离度量模型,该模型保证了训练样本到相同模式类的距离最近,到不同模式类的距离最远,根据该模型建立目标函数,求解目标函数,得到最优权重.基于最小距离分类器和K近邻分类器,采用UCI标准数据库中部分数据,对提出的自适应距离度量和欧氏距离度量进行了实验比较,实验结果表明自适应距离度量更有效.     

Controlled mutation in evolutionary structural optimization

The paper deals with minimum weight design applying Evolutionary Strategy (ES), improved by controlled mutation. Applied selection and crossover are typical for ES. Mutations, however, are controlled by state variables, in this case by stresses. After crossover, from each population, a voted number of chromosomes are inspected from the point of view of stresses occurring in structural members (genes). Changes of cross-sectional areas are introduced depending on the minimum, or maximum stresses. 124 runs of the algorithm were performed on a bench-mark problem, with known optimum solution. The number of exact solutions, applying controlled mutation, was four times larger than in the case of a simple ES algorithm. Received January 27, 2000     

A mixed design approach for probabilistic structural durability

In this paper, a mixed approach for probabilistic structural durability design of mechanical systems is proposed. In this approach, a deterministic design optimization that considers structural crack initiation and crack propagation lives at critical points of the structural component as design constraints is performed first. After an optimal design is obtained, a reliability analysis is performed to ascertain if the deterministic optimal design is reliable. If the probability of the failure of the deterministic optimal design is found to be acceptable, a reliability-based design approach that employs a set of interactive design steps, such as trade-off analysis and what-if study, is used to obtain a near-optimal design that is reliable with an affordable computational cost. A 3-D tracked vehicle roadarm is employed to demonstrate the feasibility of the proposed approach.     

Effects of microscale material randomness on the attainment of optimal structural shapes

Classical procedures of shape optimization of engineering structures implicitly assume the existence of a hypothetical perfectly homogeneous continuum – they do not recognize the presence of any microscale material randomness. By contrast, the present study investigates this aspect for the paradigm of a Michell truss with minimum compliance (maximum stiffness) that has a prescribed weight. The problem involves a stochastic generalization of the topology optimization method implemented in the commercial Altairs OptiStruct computer code. In particular, this generalization allows for the dependence of each finite elements stiffness matrix on the actual microstructure contained in the given elements domain. Contrary to intuition, stochastic material properties may improve the compliance of optimal design. This is because the optimization is performed on a given random distribution, so that the design process has an opportunity to choose stiffer cells and discard those with weaker material. The paper does not aim for a robust design process, but tries to answer a simpler intermediate question: how the random fluctuation of material properties influences a structure that has been designed using classical continuum-based optimization algorithms.     

Addendum to: An energy model for the optimal design of linear continuum structures

The original paper of the above title presents an analytical model for problems in the optimal design of linearly elastic continuum structures, where the material modulus tensor has the role of design variable. Both internal (strain) energy and the expression of generalized cost are represented conveniently there, in a form where the modulus tensor is transformed into vector coordinates. The general design of linear continuum structures is stated as a max-min problem. Optimality conditions for the transformed design problem have particularly simple form.¶Both local properties, represented by the relative values of components of the modulus tensor, and the global distribution of structural resource (material) are variable in the design.With some modification to the original formulation, these separate aspects of design can be represented explicitly in the model. This modified form, which directly facilitates study of the role of local properties in the prediction of optimal design, and which ultimately serves as the basis for schemes to perform computational solution, is described and substantiated here.     

Optimum cost design of welded box beams with longitudinal stiffeners using advanced backtrack method

The use of longitudinal stiffeners in box girders loaded in bending results in savings in weight and cost. To study these savings the optimized box beams without and with stiffeners are compared to each other. The minimum cross-sectional area design can be solved analytically. A cost function is defined containing material and fabrication (welding) costs. This function is nonlinear in the structural dimensions to be optimized, therefore an advanced backtrack method is worked out and applied. An illustrative numerical example shows the savings. Received June 30, 1999     

A comparative study on reliability-index and target-performance-based probabilistic structural design optimization

Probabilistic structural design optimization enables designers and engineers to quantitatively take into account the uncertainties observed in the structural and environmental properties. In this paper, two approaches to determine the satisfaction of probabilistic constraints are discussed. One is the conventional reliability-index-based approach and the other is a more recently proposed target-performance-based approach. An algorithm, which detects and eliminates the excessive zigzagging iterations during the searches for the most probable failure point and the minimum performance target point, was incorporated.The number of iterations required by the two approaches was investigated in three examples: a cantilever beam, a three-bar truss and a ten-bar truss structure. Based on the results, the target-performance-based approach was found to be superior to the reliability-index-based one in view of both computational efficiency and numerical stability.     

Generic methodology for the probabilistic reliability assessment of some structural properties: a graph theoretical approach

The graphical characterisation of many important structural properties, such as controllability, observability, diagnosability of many kinds of structured systems, uses mainly four types of elementary graphical conditions: connectivity, complete matching, linking and distance conditions. Since structural properties depend on different associations of elementary conditions, it is interesting to study elementary conditions. This paper is the first part of this global approach based on elementary graphical conditions and we choose to study the so-called connectivity and complete matching conditions. Starting from the graphical representation associated with a system, the paper provides Boolean expressions of the connectivity and complete matching conditions based on the edges validity, which can be linked to the physical components operating state. These expressions can then be used to define and compute the reliability of a structural property knowing the reliability of the system physical components. This knowledge can be important during both conception and exploitation stages. The proposed methods are quite intuitive and simple to implement and have basically polynomial complexity orders. This makes our approach well suited to analyse large-scale systems.     

Spelling correction using probabilistic methods

A probabilistic procedure is suggested for the automatic correction of spelling and typing errors in printed English texts. The heart of the procedure is a probabilistic model for the generation of the garbled word from the correct word. The garbler can delete or insert symbols in the word or substitute one or more symbols by other symbols. An expression is derived for $\text{P(Y ? X)}$, the probability of generating a garbled word Y from a correct word X. The model is probabilistically consistent. Using the expression for $\text{P(Y ? X)}$, we can derive an estimate of the correct word from the garbled word Y so as to minimize the average probability of error in the decision. One of the important features of the expression $\text{P(Y ? X)}$ is that it can be computed recursively. Experiments conducted using the dictionary of 1025 most common English words indicate that the accuracy of correction by this scheme is substantially greater than that which can be obtained by other algorithms especially while dealing with garbled words derived from relatively short words of length less than 6.     

A new two-point approximation approach for structural optimization

The objective of this work is to build up a high-quality approximation scheme to realize computational savings for the solution of structural optimization problems. To this end, a newly developed two-point approximation scheme is proposed. This scheme is constructed by the linear combination of Taylor expansions in terms of both original and reciprocal variables. The coefficients of the combination are determined by utilizing both the function and gradient information of two different design points obtained during the process of optimization. Based on this approach, the accuracy of the existing constraint approximation methods can be improved. The effectiveness of the proposed approach is demonstrated on a number of numerical examples. The numerical results are also compared with those of previously published work. Received April 2, 1999     

Damage-reduction-based structural optimum design for seismic RC frames

The development of structural seismic design is briefly reviewed with an emphasis on different conceptual approaches and their success in practical engineering applications. The concept of damage-reduction-based seismic design is proposed, in which the whole structural system is either physically or functionally designed as two parts, the main-function part and the damage-reduction part. The main-function part satisfies the serviceability requirements of the structural system. The damage-reduction part is composed of several damage-reduction elements, which work under hazard loads to ensure the safety of the main-function part, and further maintain the serviceability of the structural system by specific damage-reduction techniques or even by failure of damage-reduction elements. The formulation of damage-reduction-based optimum design for seismic structures is presented and some related issues are addressed, including a simplified approach to reliability analysis, the evaluation of the structural loss expectation, and the modified enumeration method. Numerical examples of RC frames are examined. The results show that several measures of structural seismic performance, including the life-cycle cost, severe earthquake action, and the story-drift reliability index of the weakest story, can be improved by damage-reduction-based design compared with conventional design.     

Optimal structural topologies with transmissible loads

In optimal topological design of structures one obtains the configuration of optimal structures when the design domain, the displacement boundary conditions and the applied loads are specified. In the optimal structure one often notices a marked difference between the main bearing structure and the load transfer zones. The latter are composed of relatively light elements the exact nature of which is not always very distinct. The main purpose of this paper is to allow the main bearing part of the structure to emerge. Moreover the actual location of the load along its line of action is not always a design requirement. In order to include this relaxed condition regarding the loading position the concept of transmissible or sliding forces is introduced in topological design of structures. A transmissible force is a force of given magnitude and direction which can be applied at any point along the line of action of the force. The optimization formulation is similar to standard topological design procedure in addition to the condition of transmissability of the forces. It is shown that this condition reduces to an equal displacement constraint along the line of action of the forces. The method is illustrated by typical structural examples. It is observed that this numerical method produces indeed crisp images of the main structural components, unblurred by the secondary load transfer elements. It is also indicated that many results are often replicas of Prager structures which were previously obtained by analytical methods. Received March 3, 1999     

Michell cantilevers constructed within trapezoidal domains—Part I: geometry of Hencky nets

The present paper is the first part of the four-part work on Michell cantilevers transmitting a given point load to a given segment of a straight-line support, the feasible domain being a part of the half-plane contained between two fixed half-lines. The axial stress σ in the optimal cantilevers is assumed to be bounded by −σ _C ≤σ≤σ _T , where σ _C and σ _T represent the allowable compressive and tensile stresses, respectively. The work provides generalization of the results of the article of Lewiński et al. (Int J Mech Sci 36:375–398, 1994a) to the case of σ _T ≠σ _C . The present, first part of the work concerns the analytical formation of the Hencky nets or the lines of fibres filling up the interior of the optimal cantilevers corresponding to an arbitrary position of the point of application of the given concentrated force.     

移动环境下的连续概率Skyline查询

主要研究查询点固定,目标对象移动且移动对象在位置不确定的情况下,成为Skyline对象的可能性（采用概率形式表示）,并实现移动对象位置不确定条件下的连续Skyline查询。定义了影响P-Skyline集合的Events,提出了一个基于事件的算法E-CPS,该算法并通过计算,跟踪和处理Events来更新P-Skyline集合。该方法大大减少了算法的查找和计算开销,提高了运算效率。     

A global structural optimization technique using an interval method

This paper deals with a global optimization scheme for structural systems that require finite element analysis to evaluate the constraints or the objective function. The paper proposes a strategy for finding the global optimum using an interval method in conjunction with a multipoint function approximation. The highly nonlinear and nonconvex objective and constraint functions are first represented in the design space using linear and adaptive local approximations and these approximations are blended globally with the use of proper weighting functions. The interval method is then employed to trace the global optimum in the approximated function space. The procedure is tested with several examples with known global solutions and it is successfully applied to optimize the fiber-orientation angles of laminated composite plates for minimum deflections. Received December 22, 2000     

Saddlepoint approximation based structural reliability analysis with non-normal random variables

The saddlepoint approximation (SA) can directly estimate the probability distribution of linear performance function in non-normal variables space. Based on the property of SA, three SA based methods are developed for the structural system reliability analysis. The first method is SA based reliability bounds theory (RBT), in which SA is employed to estimate failure probability and equivalent normal reliability index for each failure mode firstly, and then RBT is employed to obtain the upper and the lower bo...