文献翻译混合整数非线性规划的优化对结构的合成方法.docx

1、文献翻译混合整数非线性规划的优化对结构的合成方法ABSTRACT Part III of this three-part series of papers describes the synthesis of roller and sliding hydraulic steel gate structures performed by the Mixed-Integer Non-linear Programming (MINLP) approach. The MINLP approach enables the determination of the optimal number of ga

2、te structural elements (girders, plates), optimal gate geometry, optimal intermediate distances between structural elements and all continuous and standard crossectional sizes. For this purpose, special logical constraints for topology alterations and interconnection relations between the alternativ

3、e and fixed structural elements are formulated. They have been embedded into a mathematical optimization model for roller and sliding steel gate structures GATOP. GATOP has been developed according to a special MINLP model formulation for mechanical superstructures (MINLP-MS), introduced in Parts I

4、and II. The model contains an economic objective function of self-manufacturing and transportation costs of the gate. As the GATOP model is non-convex and highly non-linear, it is solved by means of the Modified OA/ER algorithm accompanied by the Linked Two-Phase MINLP Strategy, both implemented in

5、the TOP computer code. An example of the synthesis is presented as a comparative design research work of the already erected roller gate, the so-called Intake Gate in Aswan II in Egypt. The optimal result yields 29)4 per cent of net savings when compared to the actual costs of the erected gate. . 19

6、98 John Wiley & Sons, Ltd. KEY WORDS: structural synthesis; optimization; topology optimization; discrete variable optimization; Mixed-Integer Non-linear Programming; MINLP; the Modified OA/ER algorithm; MINLP strategy; hydraulic gate; sliding gate; roller gate; Aswan 1. INTRODUCTION This paper desc

7、ribes the Mixed-Integer Non-linear Programming (MINLP) approach to the synthesis of roller and sliding gate structures, i.e. the simplest types among vertical-lift hydraulic steel gates, see Figure 1. Roller and sliding gates are also regarded as the most frequently manufactured types of hydraulic s

8、teel gates for headwater control. They are used to regulate the water stream on hydro-electric plants, dams or spillways. As hydraulic steel gates are very special structures, only a few authors have discussed their optimization, e.g. Kravanja et al.,1D. Jongeling and Kolkman. as well as Almquist et

9、 al. Particular interest was shown in the optimization not of these (roller and sliding gates) but of similar structures. In such investigations, Vanderplaats and Weisshaar. as well as Gurdal et al. optimized stiffened laminated composite panels, Butler. and Ringertz. optimized stiffened panels, Far

10、kas and Jarmai1. optimized welded rectangular cellular plates, Finckenor et al.1. treated skin stringer cylinders and Gendy et al.1. stiffened plates. Almost all authors used Non-linear Programming (NLP) techniques. Gurdal et al. proposed the genetic algorithm, while Kravanja et al.1D. introduced MI

11、NLP algorithms and strategies to the simultaneous topology and parameter optimization of the gate. In Parts I of this three-part series of papers, a general view of the MINLP approach to the simultaneous topology and parameter optimization of structures is presented. Part II describes the extension

12、to the simultaneous standard dimension optimization. Based on the superstructure approach defined in Parts I and II, the main objective of this paper (Part III) is the MINLP synthesis of roller and sliding hydraulic steel gate structures, obtained at minimal gate costs and subjected to defined desig

13、n, material, stress, deflection and stability constraints. As the MINLP approach enables simultaneous topology, parameter and standard dimension optimization, a number of gate structural elements (girders and plates), the gate global geometry, intermediate distances between structural elements and a

14、ll continuous and standard dimensions are obtained simultaneously. This last part of the three-part series of papers is divided into three main sections: 1. Section 2 describes how different topology and standard dimension alternatives are postulated and how their interconnection relations are formu

15、lated by means of explicit logical constraints in order to perform topology and standard dimension alterations within the optimization procedure. 2. Section 3 represents a general MINLP optimization model for roller and sliding gate structures GATOP. 3. Finally, in Section 4, the proposed superstruc

16、ture MINLP approach is applied to the synthesis of an already erected roller gate, the so-called Intake Gate in Aswan II in Egypt. 2. SUPERSTRUCTURE ALTERNATIVES AND THE MODELLING OF THEIR DISCRETE DECISIONS 2.1. Postulation of topology and standard dimension alternatives The first step in the synth

17、esis of the gate is the generation of an MINLP superstructure in which different topology/structure and standard dimension alternatives are embedded to be selected as the optimal result. The gate superstructure also contains the representation of structural elements which may construct each possible

18、 structure alternative as well as different sets of discrete values, defined for each standard dimension alternative. As both the roller and sliding gates have almost the same structure, it was reasonable to propose a superstructure, which could well be useful for both of them. 2.1.1. Topology alter

19、natives The gate superstructure typically includes a representation of main gate elements, where each gate element is composed of various structural elements, such as horizontal girders, vertical girders, stiffeners and plate elements of the skin plate, see Figure 2. The superstructure comprises n m

20、ain gate elements, n3N, each containing m horizontal girders, m3M, the (3#2v) number of vertical girders through the entire gate, v3., and the corresponding (m!1)(2#2v) number of skin-plate elements. To each mth horizontal girder of the nth main gate element an extra binary variable yn,m is assigned

21、. The number of horizontal girders and corresponding plate elements of the skin plate, distributed over the nth main gate element, can therefore be determined simply by. Note that the proposed minimal number of identical vertical girders is 3 and that they can take only odd numbers. If a binary vari

22、able yv is assigned to each v, vV., the number of vertical girders can be obtained by (3+2 vyv). In the same way an even number (2+2 .vyv) of equal horizontal partitions of the entire gate is proposed. In the case of vertical girders, we can see that the structural elements can also be determined by

23、 suitable linear combinations of binary variables. Among the maximal number Mmax of horizontal girders per each main gate element, the upper and lower girders together with the minimal number Mminof intermediate horizontal girders and the adjoining skin-plate elements are treated as fixed structural

24、 elements, which are always present in the optimization. All other (Mmax Mmin) intermediate horizontal girders with the corresponding number of adjoined skin-plate elements are then regarded as alternative structural elements, which may either disappear or be selected. Since only alternative structu

25、ral elements participate in the discrete optimization, the size of the discrete decisions is significantly reduced. Each possible combination between selected alternative structural elements and fixed structural elements forms an extra gate topology/structure alternative. 2.1.2. Standard dimension a

26、lternatives Four standard dimensions are additionally defined to represent the standard thicknesses of sheet-iron plates: the thickness of the skin-plate tsn for each nth main gate element, the .flange thickness of the horizontal girder tfn, the web thickness of the outer horizontal girder m=1or m=M

27、 ,and the web thickness of the inner horizontal girder,1(m(M. Since the thickness tsn has a common value for the entire skin-plate of the nth main gate element and the tare the same for all horizontal girders of the nth main gate element, i.e. they correspond to the common standard design variables

28、for the superstructure or its part from the special MINLP-MS model formulation in Part II. Similarly, the web thicknesses, which take a common value for both outer horizontal girders of the nth main gate element, and , which are the same for all the inner horizontal girders, correspond to the common

29、 standard design variables of the alternative structural elements. An extra set of discrete values of standard dimension alternatives and a special set of the same size of binary variables are introduced for each mentioned standard dimension. Each standard dimension tsn shall be expressed within the

30、 given i standard dimension alternatives, iI, standard dimension tfnby k alternatives, kK, standard dimension by p alternatives, pP, and standard dimension by r alternatives, rR. The vector of i binary variables yn,i and the vector of i discrete values qn,I are assigned to the variable tsn, the vect

31、ors of k elements yn,kand qn,kto the variable tfn, the vectors of p elements yn,pand qn,kto the variableand the vectors of r elements yn,vand qn,v to the variable Consequently, the overall vector of binary variables assigned to the gate superstructure is y=yn,m ,y,v,yn,I,yn,p,yn,v2.2. Modeling of di

32、screte decisions The postulated gate superstructure of topology and standard dimension alternatives can be formulated as an MINLP problem using a special MINLP model formulation (MINLP-MS) for simultaneous topology, parameter and standard dimension optimization of mechanical superstructures, describ

33、ed in Part II. As can be seen from the (MINLP-MS), the objective function is typically subjected to structural analysis and logical constraints. While structural analysis constraints represent a mathematical model of a synthesized structure, logical constraints are used for the explicit modeling of logical d