Optimum shape design of cold-formed thin-walled steel sections

The algorithm presented in this study obtains the optimum cross-sectional dimensions of cold-formed thin-walled steel beams subjected to general loading. It has the flexibility of considering different cross-sectional shapes such as symmetrical or unsymmetrical channel, lipped channel or Z-sections. The algorithm treats the cross-sectional dimensions such as width, depth and wall thickness as design variables and considers the displacement as well as stress limitations. The presence of torsional moments causes warping of thin-walled sections. The effect of warping in the calculation of normal stresses is included using Vlasov theorems. These theorems require the computation of sectorial properties of cross-sections. A general numerical procedure is presented for obtaining these properties. The optimum design problem of thin-walled open sections subjected to combined loading turns out to be a highly nonlinear problem. It is shown that optimality criteria method can effectively be used to obtain its solution. A number of design examples are presented to demonstrate the application of the algorithm.     

Harmony search based algorithm for the optimum design of grillage systems to LRFD-AISC

Harmony search based optimum design method is presented for the grillage systems. This numerical technique imitates the musical performance process that takes place when a musician searches for a better state of harmony. Jazz improvisation seeks to find musically pleasing harmony similar to the optimum design process which seeks to find the optimum solution. The design algorithm considers the serviceability and ultimate strength constraints which are implemented from Load and Resistance Factor Design—American Institute of Steel Construction (LRFD-AISC). It selects the appropriate W-sections for the transverse and longitudinal beams of the grillage system out of 272 discrete W-section designations given in LRFD-AISC. This selection is carried out such that the design limitations described in LRFD-AISC are satisfied and the weight of the system is the minimum. Many design examples are considered to demonstrate the efficiency of the algorithm presented.     

The application of the thin-walled box beam element to multibox bridge analysis

An application of the recently developed thin-walled box beam element to the analysis of multibox bridges which arises in practical design, is presented. The thin-walled box beam element, which also takes account of warping distortional effects, when combined with traditional beam elements into a grillage model may adequately represent the three-dimensional behaviour of multibox superstructure. Equivalent sectional properties for the transverse grillage members across individual boxes are computed from a frame analysis. A numerical iterative procedure is introduced to take account of the interaction due to distortion.Comparisons with other numerical methods and model experiments demonstrate the accuracy and economy of the proposed method.     

Geometry and topology optimization of geodesic domes using charged system search

Dome structures provide cost-effective solutions for covering large areas without intermediate supports. In this article, simple procedures are developed to reach the configuration of the geodesic domes. A new definition of dome optimization problems is given which consists of finding optimal sections for elements (size optimization), optimal height for the crown (geometry optimization) and the optimum number of elements (topology optimization) under determined loading conditions. In order to find the optimum design, the recently developed meta-heuristic algorithm, known as the Charged System Search (CSS), is applied to the optimum design of geodesic domes. The CSS takes into account the nonlinear response of the domes. Using CSS, the optimum design of the geodesic domes is efficiently performed.     

Applications of linear programming in structural layout and optimization

Various computer methods have been developed for the optimal design of indeterminate structures, but it is not possible to guarantee that the result of any method will be a global optimum, rather than merely a local optimum. By temporarily neglecting the conditions of elastic compatibility and formulating a mathematical optimization problem based on the equilibrium conditions and the stress constraints, it is possible to obtain an approximate design which avoids merely local optima. In the cases examined, this design is close to the exact global optimum obtained by enforcing the compatibility conditions and is therefore a good starting point for an optimizing procedure. Examples include a graphical solution of a simple grillage known to have multiple local optima, and a sequence of planar trusses under alternate loading conditions. Linear programming is used to find the minimum weight truss designs satisfying equilibrium; this method eliminates extraneous members and leads to better indeterminate truss configurations than does a stress-ratio type algorithm.     

淤地坝水资源调控三维仿真系统

淤地坝对水资源调控过程是一种动态变化的过程,只用文字描述,无法给研究人员形象直观的展示,本文提出一种基于Unity3D的降雨过程与淤地坝调控水资源过程的模拟方法。采用3DsMax对淤地坝系主要模型进行三维建模,使用Unity3D引擎进行场景交互设计,采用粒子系统进行降雨的模拟,设计并实现了水资源收集仿真算法,利用多层次细节技术和剔除遮挡技术等进行渲染优化。借助这一方法,开发了淤地坝水资源调控虚拟再现仿真系统。实例表明,该方法可以形象逼真的再现降雨径流过程,还能表现淤地坝等组件对于水资源的调控过程,使展示的效果更加逼真。     

Optimum design of steel frames using harmony search algorithm

In this article, harmony search algorithm was developed for optimum design of steel frames. Harmony search is a meta-heuristic search method that has been developed recently. It bases on the analogy between the performance process of natural music and searching for solutions to optimization problems. The objective of the design algorithm is to obtain minimum weight frames by selecting suitable sections from a standard set of steel sections such as American Institute of Steel Construction (AISC) wide-flange (W) shapes. Strength constraints of AISC load and resistance factor design specification and displacement constraints were imposed on frames. The effectiveness and robustness of harmony search algorithm, in comparison with genetic algorithm and ant colony optimization-based methods, were verified using three steel frames. The comparisons showed that the harmony search algorithm yielded lighter designs.     

Garment pattern generation from body scan data

An automatic garment pattern design system using three-dimensional body scan data has been developed. A body model has been generated from massive body scan data using segmentation and the Fourier series expansion method. The surface geometry of a standard garment model used in the apparel industry was reconstructed by stereovision technique and converted into a mesh structure. Surface warping algorithm was used to make an equalized geometry of two models, and multi-resolution mesh generation along with optimum planar pattern mapping algorithm were used to generate the optimum two-dimensional patterns of the garment.     

Cross-section optimal design of composite laminated thin-walled beams

This paper aims to perform optimal design of cross-section properties of thin-walled laminated composite beams. These properties are expressed as integrals based on the cross-section geometry, on the warping functions for torsion, shear bending and shear warping, and on the individual stiffness of the laminates constituting the cross-section. The finite element method is used in discretizing the theory. For design sensitivity calculations, the cross-section is modelled throughout design elements. Geometrically, these elements may coincide with the laminates that constitute the cross-section. The developed formulation is based on the concept of adjoint structure. After a warping function is calculated for the cross-section, an adjoint problem may be formulated for each of the properties and a corresponding adjoint warping is determined. It can be applied in a unified way to open, closed or hybrid cross-sections. Design optimization is performed by nonlinear programming techniques. Laminate thickness and lamina orientations are considered as design variables.     

Optimum topological design of geometrically nonlinear single layer latticed domes using coupled genetic algorithm

Single layer latticed domes are lightweight and elegant structures that provide cost-effective solutions to cover the large areas without intermediate supports. The topological design of these structures present difficulty due to the fact that the number of joints and members as well as the height of the dome keeps on changing during the design process. This makes it necessary to automate the numbering of joints and members and the computation of the coordinates of joints in the dome. On the other hand the total number of joints and members in a dome is function of the total number of rings exist in the dome. Currently no study is available that covers the topological design of dome structures that give the optimum number of rings, the optimum height of crown and the tubular cross-sectional designations for the dome members under the given general external loading. The algorithm presented in this study carries out the optimum topological design of single layer lattice domes. The serviceability and strength requirements are considered in the design problem as specified in BS5950. The algorithm takes into account the nonlinear response of the dome due to effect of axial forces on the flexural stiffness of members. The optimum solution of the design problem is obtained using coupled genetic algorithm. Having the total number of rings and the height of crown as design variables provides the possibility of having a dome with different topology for each individual in the population. It is shown in the design example considered that the optimum number of joints, members and the optimum height of a geodesic dome under a given external loading can be determined without designer’s interference.     

Automated optimization of transverse frame layouts for ships by elastic-plastic finite element analysis

This paper presents a model for the optimum design of ship transverse frames. An elastic-plastic finite element analysis algorithm for plane frames has been incorporated in the model to evaluate the ultimate strength of the overall frame, and different effects of design loads. Using these strengths and load effects, appropriate design constraints are then formulated to prevent different failure categories; the overall collapse, ultimate limit state failures and serviceability failures. Possible instabilities and effects of combined loads are accounted for in formulating these constraints. Scantlings of the frame structure have been modelled as free design variables. The weight function and different constraint functions are then derived relating design variables in such a way that once parameters for finite element analysis are input, the scheme automatically forms the objective function and all constraints, and then interacts with the simplex algorithm through sequential linearization to find the optimum solution. Thus the scheme is almost automatic. Different layouts of the frame structure have been designed by executing this scheme, which demonstrates the capability of the model and the possibility of weight savings by choosing the appropriate layout. Finally, it is suggested how this model would interact with the design of longitudinal materials to ensure the overall optimality in ship hull module design, to prevent grillage buckling and to validate underlying assumptions in analysis.     

Using genetic algorithm for the optimization of seismic behavior of steel planar frames with semi-rigid connections

Beam-column connections have a significant role in the results of the analysis and the design of steel frames. In this paper, a genetic algorithm has been used for the non-linear analysis and design of steel frames. For minimizing the weight of frames, while satisfying the applied constraints and restraints such as the limits of normal and combined stresses, criteria such as target displacement(s) and the number and locations of plastic hinges were used. To analyze and design the frame elements, I and box-shaped standard sections were used for beams and columns, respectively. Finally, some clues for finding optimizing semi-rigid connection stiffness values for beam-to-column connections have been obtained. The degrees of these rigidities are obtained by a genetic algorithm during the procedure of optimization in order to reach a frame with the minimum weight. SAP2000 structural analysis program was used to perform modal analysis and linear and non-linear static solutions as well as the design of the elements. A MATLAB program was written for the process of optimization. The procedure of optimization was based on a weight minimization carried out for 9 steel frames. Thus, the optimum connection stiffness could be obtained for minimizing the weight of the structure. The results show that the non-linear analysis gives less weight for short period frames with semi-rigid connections compared to those of linear ones. However, by increasing the periods of frames, much less weights are obtained in the case of non-linear analysis with semi-rigid connections.     

Simultaneous size and geometry optimization of steel trusses under dynamic excitations

During the past decades, the main focus of the research in steel truss optimization has been tailored towards optimal design under static loading conditions and limited work has been devoted to investigating the optimum structural design considering dynamic excitations. This study addresses the simultaneous size and geometry optimization problem of steel truss structures subjected to dynamic excitations. Using the well-known big bang-big crunch algorithm, the minimum-weight design of steel trusses is conducted under both periodic and non-periodic excitations. In the case of periodic excitations, in order to examine the effect of the exciting period of the dynamic load on the final results, the design instances are optimized under different exciting periods and the obtained results are compared. It is observed that by increasing the excitation period of the considered sinusoidal loading as well as the finite rise time of the non-periodic step force, the optimization results approach the minimum design weight obtained under the static loading counterpart. However, in the case of the studied rectangular periodic excitation, the results obtained do not approach the optimum design associated with the static loading case even for higher values of the exciting period.     

时间序列数据挖掘中的动态时间弯曲研究综述

动态时间弯曲是一种重要的相似性度量方法,对时间序列数据挖掘的性能起着至为关键的作用,对其进行全面和深入的探索具有十分重要的理论意义和实际应用价值.首先简述动态时间弯曲算法的基本步骤,并分析其优点和存在的不足;然后,从动态时间弯曲度量效率的改进研究、度量效果的提升措施以及其在各个行业的应用研究等进行相关综述;最后,给出动态时间弯曲的进一步研究方向.通过对动态时间弯曲方法相关综述及分析,能为相似性度量、聚类和分类等时间序列数据挖掘技术提供必要的文献资料和理论基础.     

Topological optimization of continuum structures with design-dependent surface loading – Part II: algorithm and examples for 3D problems

The problem of topology optimization of 3D structures with design-dependent loading is considered. An algorithm for generating the valid loading surface of the 3D structure is presented, constituting an extension of the algorithm for 2D structures developed in Part I of this paper on the basis of a modified isoline technique. In this way the complicated calculation of the fit of the loading surface of a 3D structure may be avoided. Since the finite element mesh is fixed in the admissible 3D design domain during the period of topology evolution, the design-dependent loading surface may intersect the elements as the design changes. Independent interpolation functions are introduced along the loading surface so that the surface integral for generating the loading on the surface of the 3D structure can be performed more efficiently and simply. The bilinear 4-node serendipity surface element is constructed to describe the variable loading surface, and this matches well with the 8-node isoparametric 3D elements which have been used for the discretization of the 3D design domain. The validity of the algorithm is verified by numerical examples for 3D problems. Results of designing with design-dependent loads and with corresponding fixed loads are presented, and some important features of the computational results are discussed.     

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.

     

Optimum design of pitched roof steel frames with haunched rafters by genetic algorithm

The pitched roof steel frames appear to be the simplest structural form used in single storey buildings. However, its design necessitates consideration of many different structural criteria that are required in the design of complex structures. In this paper, a genetic algorithm is used to develop an optimum design method for pitched roof steel frames with haunches for the rafters in the eaves. The algorithm selects the optimum universal beam sections for columns and rafters from the available steel sections tables. Furthermore, it determines the optimum depth of the haunch at the eaves and the length of the haunch required for reaching the most cost-effective form. Formulation of the design problem is based on the elastic design method. The serviceability and the strength constraints are included in the design problem as defined in BS 5950. Furthermore, the overall buckling of columns and rafters in the torsional mode between effective torsional restraints to both flanges is also checked. A pitched roof frame is designed by the algorithm developed to demonstrate its practical application.     

Optimum topology design of various geometrically nonlinear latticed domes using improved harmony search method

Domes are elegant and economical structures used in covering large areas. They are built in various forms. According to their form, they are given special names such as lamella, network, and geodesic domes. In this paper, optimum topological design algorithm is presented that determines the optimum number of rings, the optimum height of crown and tubular section designations for the member groups of these domes. The design algorithm developed has a routine that generates the data required for the geometry of these domes automatically. The minimum weight of each dome is taken as the objective function. The design constraints are implemented according to the provision of LRFD-AISC (Load and Resistance Factor Design–American Institute of Steel Constitution). The optimum topological design problem that considers these constraints turns out to be discrete programming problem. Improved harmony search algorithm is suggested to determine its optimum solution. The design algorithm also considers the geometric nonlinearity of these dome structures. Design examples are presented to demonstrate the effectiveness and robustness of the design optimization algorithm developed.     

Implications of failure criteria choices on the rapid concept design of composite grillage structures using multiobjective optimisation

Grillage topologies are commonly used in many composite structural applications to produce low mass designs that have a high stiffness. While composite failure criteria are being compared in many different simple structures, for example plates and tubes, literature must also compare more complicated applications, including grillages, as there are distinct differences in behaviour. This paper therefore performs analysis of grillage structures with more up to date failure criteria, taken from the world wide failure exercise, than previously investigated. The grillage theory selected is that of Navier theory with elastic equivalent properties due to its low computational expense for use with a genetic algorithm to optimise a composite structure. The results take an example from leisure boatbuilding showing the grillages produced from the different limit states, comparing the cost and mass. The final results show that the method allows a rapid analysis of grillages and that the selection of the limit state has an important effect on the optimised grillage topology.     

求解矩形packing问题的贪心算法

在货物装载、木材下料、超大规模集成电路设计等工作中提出了矩形packing问题。对这一问题,国内外学者提出了诸如模拟退火算法、遗传算法及其它一些启发式算法等求解算法。该文利用人类的智慧及历史上形成的经验,提出了一种求解矩形packing问题的贪心算法。并对21个公开测试实例进行了实算测试,所得结果的平均面积未利用率为0.28%,平均计算时间为17.86s,并且还得到了其中8个实例的最优解。测试结果表明,该算法对求解矩形packing问题相当有效。