[toggle title=”عنوان انگلیسی”]
Optimization of stay cables in cable-stayed bridges using finite element, genetic algorithm, and B-spline combined techniqu
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چکیده
مقدمه
توصیف پل
بارهای طراحی
محدودیت های طراحی
روش بهینه سازی
عملگرهای ژنتیکی
اجزاء محدود، الگوریتم ژنتیکی، و روش ترکیبی نوار مبنا
نتایج و بحث
تعداد بهینه نقاط کنترل
بررسی تابع هدف چند بهینه ای
اشکال بهینه سازی توابع مساحت کابل
خلاصه و نتیجه گیری
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[toggle title=”ترجمه چکیده”]
به طور مرسوم، از روش آزمون و خطا برای طراحی سطح مقطع کابل های نگه دارنده در پل کابلی استفاده می شود. فرایند طراحی، خسته کننده، پر هزینه و وقت گیر است و قادر به یافتن راه حل بهینه طراحی نیست. هدف از این مطالعه، توسعه یک روش بهینه سازی طراحی قوی به منظور دستیابی به حداقل سطح مقطع کابل نگهدارنده است. روش بهینه سازی توسعه یافته، روش اجزاء محدود، منحنی های نوار مبنا، و الگوریتم ژنتیکی را با هم ادغام می کند. قابلیت و کارآیی این روش بهینه سازی با کاربرد در پل کابلی در اندازه عملی و مورد آزمایش و ارزیابی قرار گرفت.
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[toggle title=”ترجمه مقدمه”]
پل های کابلی به دلیل جاذبه زیبایی شناسی، سهولت نصب، کاربرد پر بازده مواد ساختاری، و دیگر مزیت های قابل توجه، در چند دهه گذشته کاربرد گسترده ای در سراسر جهان داشته است [1]. این نوع پل ها به تازگی وارد دوره جدیدی شده اند که فاصله بین دو تیر اصلی آنها بیش از 1000 متر است. در پل های کابلی جدید با دهانه طولانی، مانند پل سوتنگ در چین ( 2088 متر)، برای رسیدن به توزیع مناسب گشتاور خمشی در طول سکوی پل، به تعداد زیادی کابل های نگهدارنده نیاز است. هزینه واحد کابل های نگهدارنده در مقایسه با دیگر مصالح ساختمانی نسبتاً زیاد است؛ بنابراین، برای تعیین حداقل هزینه کابل های نگهدارنده در پل های کابلی، یک روش بهینه سازی باید توسعه داده شود.
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[toggle title=”مقدمه انگلیسی”]
Because of their aesthetic appeal, ease of erection, efficient utilization of structural materials, and other notable advantages, cable-stayed bridges have found wide applications all over the world in the last few decades [1]. Bridges of this type have recently entered a new era with main spans exceeding a value of 1000 m. In modern long-span cable-stayed bridges, such as the Sutong Bridge in China (2088 m), a large number of stay cables would be required in order to achieve reasonable distribution of bending moments along the bridge deck. The unit cost of stay cables is relatively high compared to other construction materials; therefore, there is a need for the development of an optimization technique to determine the minimum cost of stay cables in cable-stayed bridges. In the current practice, the design process of stay cables is performed in two stages. The first stage involves the determination of initial post-tensioning cable forces, which are evaluated corresponding to zero vertical deflections of the deck and zero horizontal deflections of the pylons’ tops under only self-weight of the bridge. These forces are required to determine the initial configuration of the bridge. In the second stage, the cross-sectional areas of stay cables are determined under the combined effect of self-weight, initial post-tensioning cable forces, and live load cases. To date, this design stage is based on a trial-and-error procedure, which depends on the designer’s experience and skills [2] and [3]. A set of cross-sectional areas of stay cables is first assumed. Structural analysis for the bridge is then carried out in order to obtain the bridge deflections and stresses. If the deflections and stresses satisfy the requirements imposed by design codes, the assumed cross-sectional areas of stay cables are adopted. Otherwise, the cross-sectional areas are modified and the structural process is repeated until all the design criteria are met. The previous iterative design procedure is expensive, tedious, and time consuming. Moreover, it does not guarantee that the final solution will be the best of all the possible design solutions that satisfy the requirements of design codes There have been many studies concerning the determination of the optimum post-tensioning cable forces under self-weight [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14] and [15]; however, there have been only a few attempts to determine the optimum cross-sectional areas of stay cables under self-weight, initial post-tensioning cable forces, and live load cases. One of the first attempts was conducted by [16]. In their study, a convex scalar function was used to minimize the cost of a box-girder deck cable-stayed bridge. The proposed function combines dimensions of the cross-sections of the bridge and post-tensioning cable forces. This method is very sensitive to the constraints, which should be imposed very cautiously to obtain a practical output [8]. In the research done by [3], the optimization module implemented in MATLB (fmincon), together, with the commercial finite element software, ABAQUS, are employed to evaluate the minimum cost of stay cables for cable stayed bridges. It should be noted that the two previous studies are based on direct search optimization techniques. The drawback of these direct techniques is that they begin the search procedure with a guess solution, which is often chosen randomly in the search space. If the guess solution is not chosen close enough to the global minimum solution, the optimization technique will be trapped in local minima. As a result, the final solutions of these previous studies may not be the global minimum [3]. On the other hand, the cross-sectional areas of stay cables are considered as discrete design variables in both studies. With the increase in the number of stay cables, the number of design variables becomes quite large leading to potential numerical problems in the optimization technique. In addition, the increase in the number of stay cables makes the final distribution of the cross-sectional areas of stay cables non-smooth. Hence, the resulting values from these methods may be impractical in such cases. The objective of the current study is to present a powerful optimization design technique in order to achieve the optimum cross-sectional areas of stay cables, which is directly proportional to the cost of the material. The proposed study focuses on the second design stage, where self-weight, initial post-tensioning cable forces, and live load cases are applied to the bridge. The proposed optimization technique involves interaction between three numerical schemes: finite element method (FEM), B-spline curves, and Real Coded Genetic Algorithm (RCGA). The novelty of this combined technique lies in the adoption of the B-spline curves to represent the distribution of cross-sectional areas of stay cables along the bridge length, which significantly reduces the number of design variables. In addition, RCGA, which is a global optimization method, is capable of finding the global optimal solution. The remainder of the paper is organized as follows. In the next section, the geometry, finite element modeling, and design loads of the bridge chosen for the study are described. In Section 3, a description of the design variables, design constraints, objective function, and optimization technique is presented. A detailed description of the optimization design technique that involves a combination between the FEM, B-spline curves, and RCGA is presented in Section 4. In Section 5, detailed presentation and discussion of the numerical optimization results are given. Finally, Section 6 presents the main conclusions drawn from the study.
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[toggle title=”منبع”]
Journal : Engineering Structures, Volume 49, April 2013, Pages 643–654
Publisher : Science Direct (Elsevier)
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فایل مقاله : 12 صفحه PDF
فایل ترجمه : 27 صفحه WORD
سال انتشار : 2013
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