Optimal topology and configuration design of trusses with stress and buckling constraints

A heuristic algorithm for optimal design of trusses is presented with account for stress and buckling constraints. The design variables are constituted by cross-sectional areas, configuration of nodes and the number of nodes and bars. Similarly to biological growth models, it is postulated that the structure evolves with the characteristic size parameter and the bifurcation of topology occurs with the generation of new nodes and bars in order to minimize the cost function. The first-order sensitivity derivatives provide the necessary information on topology variation and the optimality conditions for configuration and cross-sectional parameters.     

Selecting highly optimal architectural feature sets with Filtered Cartesian Flattening

Feature modeling is a common method used to capture the variability in a configurable application. A key challenge developers face when using a feature model is determining how to select a set of features for a variant that simultaneously satisfy a series of resource constraints. This paper presents an approximation technique for selecting highly optimal feature sets while adhering to resource limits. The paper provides the following contributions to configuring application variants from feature models: (1) we provide a polynomial time approximation algorithm for selecting a highly optimal set of features that adheres to a set of resource constraints, (2) we show how this algorithm can incorporate complex configuration constraints; and (3) we present empirical results showing that the approximation algorithm can be used to derive feature sets that are more than 90%+ optimal.     

Artificial neural networks for 3-D motion analysis. I. Rigid motion

Proposes an approach applying artificial neural net techniques to 3D rigid motion analysis based on sequential multiple time frames. The approach consists of two phases: (1) matching between every two consecutive frames and (2) estimating motion parameters based on the correspondences established. Phase 1 specifies the matching constraints to ensure a stable and coherent feature correspondence establishment between two sequential time frames and configures a 2D Hopfield neural net to enforce these constraints. Phase 2 constructs a 3-layer net to estimate parameters through supervised learning. The method performs motion analysis based on sequential multiple time frames. It represents an effective way to achieve optimal matching between two frames using neural net techniques. The energy function of the Hopfield net is designed to reflect the matching constraints and the minimization of this function leads to the optimal feature correspondence establishment. The approach introduces the learning concept to motion estimation. The structure of the net provides the flexibility in estimating motion parameters based on information from multiple frames.     

Sensitivity of plastic optimal structures to imperfections and non-linear geometrical effects

The sensitivity of optimal plastic design with respect to geometric imperfections and post-critical deformations is discussed. It is shown that the concept of optimal plastic design should be modified in order to provide a proper safety factor against collapse for a specified range of imperfections and configuration changes. The optimal design of two-story frames is analysed in detail.     

Optimum configurational and dimensional design of truss structures

The feasibility of simultaneous optimization of member sizing and structural configuration of truss structures is demonstrated. The structural analysis is treated by the finite element displacement method and the optimization accomplished by the steepest descent method. Inequality constraints including limitations on both state variables (stress and displacement) and design variables (element cross sectional areas and nodal point placement) are included.The computational results show that in the presence of displacement constraints, the configuration of the optimum design sometimes differs considerably from the fully stressed design. The techniques can be extended to other structures such as beams, frames, plates, etc. and to include the possibility of Euler buckling.     

The effects of rehabilitation objectives on near optimal trade-off relation between minimum weight and maximum drift of 2D steel X-braced frames considering soil-structure interaction using a cluster-based NSGA II

A cluster-based non-dominated sorting genetic algorithm (NSGA) II has been considered to investigate the effects of rehabilitation objectives on multi-objective design optimization of two-dimensional (2D) steel X-braced frames in the presence of soil-structure interaction. The substructure elasto-perfect plastic model has been adopted for modeling of the soil-structure interaction and the nonlinear pushover analysis is used to evaluate the performance level of the frames for a specified hazard level. Cross-sections of grouped elements of the frames are considered to be discontinuous design variables of the problem. Via implementing some of the constraints, which are independent of doing the time-consuming nonlinear analysis, input population of the optimization technique has been clustered. By using the nonlinear analysis technique in conjunction with the cluster-based NSGA II, near optimal trade-off relation between minimum weight and maximum story drifts of the frames are obtained. The allowable rotations, geometry, and resistance constraints of the structural elements are considered in the optimization design of the frames. The effects of the enhanced basic safety and limited selective rehabilitation objectives on optimum design of the frame are studied. The results show differences between the optimum results of the three mentioned rehabilitation objectives and effects of soil types.

     

Design of non-linear steel frames for stress and displacement constraints with semi-rigid connections via genetic optimization

A genetic-algorithm-based optimum design method is presented for non-linear steel frames with semi-rigid connections and column bases. The design algorithm obtains the minimum total cost, which comprises total member plus connection costs, by selecting suitable sections from a standard set of steel sections such as American Institute of Steel Construction (AISC) wide-flange (W) shapes. A genetic algorithm is employed as the optimization method, which utilizes reproduction, crossover and mutation operators. Displacement and stress constraints of AISC Allowable Stress Design (ASD) specification and size constraints for beams and columns are imposed on the frame. The algorithm requires a large number of non-linear analyses of frames. The analyses cover both the non-linear behavior of beam-to-column connection and P- effects of beam-column members. The Frye and Morris polynomial model is used for modeling semi-rigid connections. Two design examples with various types of connections are presented to demonstrate the application of the algorithm. The semi-rigid connection and column base modeling results in more economical solutions than rigid connection modeling, but increases the sway of frames.     

A family of homogeneous analysis models for the design of scalable structures

Research in optimum structural design has shown that mathematical programming techniques can be employed efficiently only in conjunction with explicit approximate constraints. In the course of time a well-established approximation for homogeneous functions (scalable structures) has emerged based on the linear Taylor expansion of the displacement functions in the compliance design space (Reciprocal approximation). It has been shown that the quality of this approximation is based on the property that homogeneity of the constraints is maintained and consequently the approximation is exact along the scaling line.The present paper presents a new family of approximations of homogenous functions which have the same properties as the Reciprocal approximation and which produce more accurate models in most of the tested cases. The approximations are obtained by mapping the direct linear Taylor expansion of the constraints unto a space spanned by intervening variables (original design variables to a powerm). Taking the envelope of these constraints along the scaling line yields a new family of approximations governed by the parameterm. It is shown that the Reciprocal approximation is a particular member of this family of approximations (m = –1).The new technique is illustrated with classical examples of truss optimization. An optimal plate design is also reported. A parametric study of the results for various values of the exponentm is presented. It is shown that for special values of the exponentm the new approximations usually yield better models than those based on the Reciprocal approximation.     

A comparison of simulated annealing and genetic algorithm for optimum design of nonlinear steel space frames

In this article, two algorithms are presented for the optimum design of geometrically nonlinear steel space frames that are based on simulated annealing and genetic algorithm. The design algorithms obtain minimum weight frames by selecting suitable sections from a standard set of steel sections such as the American Institute of Steel Construction (AISC) wide-flange shapes. Stress constraints of AISC Load and Resistance Factor Design (LRFD) and AISC Allowable Stress Design (ASD) specifications, maximum (lateral displacement) and interstorey drift constraints, and also size constraints for columns were imposed on frames. The algorithms were applied to the optimum design of three space frame structures, which have a very small amount of nonlinearity. The unconstrained form of objective function was applied in both optimum design algorithms, and constant penalty factors were used instead of gradually increasing ones. Although genetic algorithm took much less time to converge, the comparisons showed that the simulated annealing algorithm yielded better designs together with AISC-LRFD code specification.     

考虑可靠性和鲁棒性的机械接头有限元设计优化

为从实际工程角度获得最优的产品设计方案,对考虑应力约束条件下最优结构参数配置的机械接头进行有限元结构优化.以Abaqus为有限元计算软件,寻找出在应力约束条件下的理论值;通过OPTIMUS软件进行最优结构参数配置,并考虑结构加工制造公差和材料性能波动所产生的可靠性和鲁棒性因素,分析并重新进行结构的参数设计.示例表明该方法具有一定的参考价值.     

Analysis and design of parallel mechanisms with flexure joints

Flexure joints are frequently used in precision-motion stages and microrobotic mechanisms due to their monolithic construction. The joint compliance, however, can affect the static and dynamic performance of the overall mechanism. In this paper, we consider the analysis and design of general platform-type parallel mechanisms containing flexure joints. Based on static performance measures such as task-space stiffness and manipulability, and constraints such as joint stress, mechanism size, and workspace volume, we pose the design problem as a multiobjective optimization. We first calculate the Pareto frontier, which can then be used to select the desired design parameters based on secondary criteria, such as performance sensitivity and dynamic characteristics. To facilitate design iteration, we apply the pseudo rigid-body approach with a lumped approximation of the flexure joints. A planar mechanism is used to illustrate the analysis and design techniques.     

A Study on Network Design Problems for Multi-modal Networks by Probit-based Stochastic User Equilibrium

This paper develops a multi-modal transport network model considering various travel modes including railway, bus, auto, and walking. Travellers are assumed to choose their multi-modal routes so as to minimise their perceived disutilities of travel following the Probit Stochastic User Equilibrium (SUE) condition. Factors influencing the disutility of a multi-modal route include actual travel times, discomfort on transit systems, expected waiting times, fares, and constants specific to transport modes. The paper then deals with the multi-modal network design problem (NDP). The paper employs the method of sensitivity analysis to define linear approximation functions between the Probit SUE link flows and the design parameters, which are then used as constraints in the sub-problem of the NDP instead of the original SUE condition. Based on this reformulated NDP, an efficient algorithm for solving the problem is proposed in the paper. Two instances of this general NDP formulation are then presented in the paper: the optimal frequency design problem for public transport services (FDP), and the anti-freezing admixture dispersion problem (AADP).     

Optimal topology design of structures under dynamic loads

When elastic structures are subjected to dynamic loads, a propagation problem is considered to predict structural transient response. To achieve better dynamic performance, it is important to establish an optimum structural design method. Previous work focused on minimizing the structural weight subject to dynamic constraints on displacement, stress, frequency, and member size. Even though these methods made it possible to obtain the optimal size and shape of a structure, it is necessary to obtain an optimal topology for a truly optimal design. In this paper, the homogenization design method is utilized to generate the optimal topology for structures and an explicit direct integration scheme is employed to solve the linear transient problems. The optimization problem is formulated to find the best configuration of structures that minimizes the dynamic compliance within a specified time interval. Examples demonstrate that the homogenization design method can be extended to the optimal topology design method of structures under impact loads.Presented at WCSMO-2, held in Zakopane, Poland, 1997     

A review of optimization of structures subjected to transient loads

Various aspects of structural optimization techniques under transient loads are extensively reviewed. The main themes of the paper are treatment of time-dependent constraints, calculation of design sensitivity, and approximation. Each subject is reviewed with corresponding papers that have been published since the 1970s. The treatment of time-dependent constraints in both the direct method and the transformation method is discussed. Two ways of calculating design sensitivity of a structure under transient loads are discussed—direct differentiation method and adjoint variable method. The approximation concept mainly focuses on the response surface method in crashworthiness and local approximation with the intermediate variables. Especially, a method using the equivalent static load is discussed as an approximation method. It takes advantage of the well-established static response optimization. The structural optimization in flexible multibody dynamic systems is reviewed in the viewpoint of the above three themes.     

覆盖表生成的遗传算法配置参数优化

覆盖表生成是组合测试的关键问题,很多数学方法、贪心算法以及演化搜索方法等被应用于生成各种覆盖表.针对演化搜索方法的性能受到方法本身配置参数影响很大这一实际问题,文中以二维覆盖表生成为实例,系统地对典型的演化搜索方法——遗传算法的种群规模、进化代数、交叉概率、变异概率以及遗传算法的变种算法等因素进行探索,设计了pair-wise法、Base choice法和爬山法3条实验路线探索遗传算法的这些配置参数及其相互作用对算法生成二维覆盖表效果的影响,并回答两个问题:对于特定二维覆盖表生成问题,是否存在遗传算法的最优参数配置;对于一般的二维覆盖表生成问题,是否存在通用的遗传算法最优参数配置.     

A preference aggregation rule approach for structural optimization

In this paper, preference aggregation rules are used to define overall design evaluation measures in optimal design problems. A methodology for the efficient solution of the corresponding design optimization problems is presented. Each design criterion as well as the constraints imposed on the design variables and problem parameters are characterized by preference functions. The nondifferentiable nature of the optimization problems which arise in this formulation is coped with using a first-order algorithm combined with approximation concepts. High-quality approximations for the system response functions are constructed using the concepts of intermediate response quantities and intermediate variables. These approximations are used to replace the original problem by a sequence of approximate problems. Example problems are presented to study the performance of the proposed optimization technique as well as the methodology based on approximation concepts.     

面向产品线交互配置不一致性修复的差分IBEA算法

在大规模复杂系统产品线工程中,人工配置难免会导致配置的不一致,即,配置数据会违背预定义的约束(也可以称为一致性约束).对于大规模复杂系统产品线体系结构,比如信息物理系统产品线,往往存在成百上千的可变点以及约束,而且约束与可变点之间存在复杂的依赖关系,为不一致配置的修复带来很大的挑战.为了解决这个问题,针对前期提出的基于多目标搜索以及约束求解技术的自动不一致配置修复推荐框架(Zen-Fix),提出一种改进的IBEA算法(De IBEA).De IBEA通过将差分引入IBEA算法,搜索过程中,基于可行解和不可行解的差分变异产生后代,最终为用户推荐符合预定义约束并且对于配置效率来说最优的配置修复方案.基于一个工业案例海底油田采控系统产品线为例,通过模拟一个产品的配置过程,产生了10 189个优化问题,结果表明:Zen-Fix框架结合De IBEA算法,可以实时地为用户提供较优的不一致配置修复方案.此外,通过对这10 189个问题的推荐方案进行对比,证明了De IBEA算法无论从时间效率还是搜索性能上都优于原始的IBEA算法.     

Optimal design of frames with substructuring

This paper presents a formulation for optimal design of large scale, two and three dimensional framed structures. Von Mises equivalent stress constraints and displacement constraints are imposed at all points in the structure. Member size constraints and constraints based on Schilling's approach for member buckling are also imposed. Three example problems of varying degrees of difficulty are solved, using a gradient projection algorithm with state space design sensitivity analysis and substructuring. Results of these examples are analyzed and conclusions are presented.     

Mass customization design of engineer-to-order products using Benders’ decomposition and bi-level stochastic programming

Leveraging product differentiation and mass production efficiency in mass customization basically entails a configure-to-order paradigm. In the engineer-to-order (ETO) business, however, companies build unique products in response to ‘foreseeable’ customer specifications. The key challenge of ETO mass customization lies in the complexity of accommodating future design changes when customers are involved in customizing design specifications. This paper proposes a two-stage, bi-level stochastic programming framework to tackle ETO mass customization. At the first stage, product platform configuration is integrated with production reconfiguration, which is formulated as a shortest path problem with resource constraints (SPPRC) to optimize production delays within the capabilities of the process platform. Benders’ decomposition algorithm is applied to solve this optimal configuration problem owing to its high computational efficiency. The second stage scrutinizes the optimal configuration resulting from the first stage for scaling optimization of design parameters (DPs) for each module. All DPs are differentiated by standard or customizable DPs. A bi-level stochastic program is implemented to leverage conflicting goals between the producer (leader) and consumer (follower) surpluses. As a result, ETO customization design is anchored with optimal values of standard DPs and optimal value ranges of customizable DPs. A case study of ship engine and power generator ETO design is presented, demonstrating the feasibility and potential of the ETO mass customization framework.