بهینه‌سازی توپولوژی و ابعاد سازه خرپایی بر مبنای روش چگالی مواد و الگوریتم مجانب‌های پویا

نوع مقاله : پژوهشی اصیل (کامل)

نویسندگان
دکتر حسین قاسم نژاد مقری 1
سید مهدی توکلی 2
1 استادیار، گروه مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه آزاد اسلامی واحد آیت الله آملی، آمل، ایران
2 دانشیار، گروه مهندسی سازه، دانشکده مهندسی عمران، دانشگاه صنعتی شاهرود، شاهرود، ایران
10.22034/24.5.37
چکیده
در این مقاله روش مجانب های پویا MMA که یک روش برنامه‌ریزی ریاضی است برای حل مسئله بهینه سازی خرپا به کار گرفته شده است. اگرچه این روش در مسائل توپولوژی سازه‌های محیط پیوسته بسیار مورد استفاده قرار گرفته است، اما در مورد سازه‌های خرپایی کمتر مورد توجه بوده است. مسئله بهینه‌سازی مورد نظر در اینجا، مسئله حداقل سازی انرژی کرنشی سازه با در نظر گرفتن قید حجمی می‌باشد. برای اولین بار برای سازه خرپایی از مبانی روش SIMP و اعمال ضریب جریمه تابع چگالی برای بهینه سازی همزمان توپولوژی و ابعاد اعضای خرپا استفاده شده است. به منظور انجام بهینه‌سازی، تحلیل حساسیت تحلیلی انجام شده است. مسائل متنوعی در انتها حل شده‌اند و نتایج مورد بحث و بررسی قرار گرفته‌اند. نتایج نشان می‌دهند در صورت استفاده از ضریب جریمه مناسب، پاسخ بهینه درست برای مسائل معیار به دست می‌آید. همچنین برخی مسائل کاربردی‌تر نیز حل شده و نتایج مورد بحث قرار گرفته‌اند.

 

کلیدواژه‌ها

موضوعات

عنوان مقاله English

Topology and size optimization of truss structures based on material density approach and MMA

نویسندگان English

Hossein Ghasemnejad Moghri 1
seyed Mehdi Tavakkoli 2
1 assistant professor, department of civil engineering, faculty of Engineering and technology, Ayatollah Amolli branch, Azad university, Amol, Iran
2 Associate Professor, Department of Structural Engineering, Faculty of Civil Engineering, Shahrood University of Technology, Shahrood, Iran
چکیده English

In this article, MMA which is a mathematical programing method is utilized for solving truss optimization problem. Although this method has been widely used in topology optimization problems of continuous structures, it has received less attention in the case of truss structures. The optimization problem considered here is the problem of minimizing the strain energy of the structure by considering the volume constraint. For the first time, the basics of the SIMP method and the application of the penalty exponent of the density function have been used for simultaneous optimization of topology and size of the truss members.To solve the optimization problem, analytical sensitivity analysis has been performed. Various problems have been solved at the end of the paper and the results have been discussed. The results show that if the appropriate penalty exponent is chosen, the correct optimal solution is obtained for the benchmark problems. Also, some more practical problems have been solved and the results have been discussed.

کلیدواژه‌ها English

Topology optimization
size optimization
truss
Sensitivity Analysis
SIMP
MMA
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مهندسی عمران مدرس
دوره 24، شماره 5
آذر و دی 1403
صفحه 37-51