بهینه‌سازی ایزوژئومتریک شکل سازه‌های دوبعدی با استفاده از تحلیل حساسیت کاملا تحلیلی

نوع مقاله : پژوهشی

نویسندگان

• سجاد نیکویی
• بهروز حسنی

گروه مکانیک، دانشکدۀ مهندسی، دانشگاه فردوسی مشهد.

10.22067/civil.v1i33.77532

چکیده

در اکثر روش‌های بهینه‌سازی سازه‌ای در تحلیل سازه و محاسبۀ حساسیت از روش اجزای محدود مرسوم استفاده شده است. به دلیل تغییر هندسه در هر مرحله از بهینه‌سازی، برای دست‌یابی به مدل محاسباتی نیاز به تولید شبکۀ اجزای محدود جدیدی است که سبب افزایش هزینه محاسباتی و اتلاف وقت می‌شود. برای مرتفع نمودن مشکلات این‌چنینی، روش تحلیل ایزو ژئومتریک بر مبنای توابع پایه نربز که ترکیبی از روش طراحی به کمک کامپیوتر (CAD) و اجزای محدود است، در اینجا استفاده می‌شود. در بهینه‌سازی شکل سازه‌ها از روش مجانب‌های پویا (MMA) که روشی گرادیان محور است، استفاده شده است. در بهره‌گیری ازاین‌روش نیاز به تحلیل حساسیت طرح نسبت به متغیرهای طراحی است. به همین منظور، با توجّه به ویژگی‌های توابع نربز روش تحلیل حساسیت کاملاً تحلیلی فرمول‌بندی و اجرا شده است. برای نشان دادن عملکرد روش پیشنهادی، مثال‌های عددی گوناگونی حل شده است.

کلیدواژه‌ها

• روش ایزوژئومتریک
• بهینه‌سازی شکل
• نربز
• حساسیت کاملا تحلیلی

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عنوان مقاله [English]

Isogeometric Shape Optimization of 2D Structures Using Fully Analytical Sensitivity Analysis

نویسندگان [English]

• sajjad nikoei
• Behroz hasani

Department of Aerospace Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

چکیده [English]

In most of the structural optimization approaches analysis and sensitivities are carried out by using the conventional finite element method. Due to the variations of the problem geometry within the shape optimization iterations, updating the computational model by several remeshings is required that is quite time consuming and computationally costly. As a remedy for this problem, the NURBS-based isogeometric analysis method is here adopted that combines the Computer Aided Design (CAD) and finite element techniques. In this study, in the shape optimization of the structures the Method of Moving Asymptotes (MMA), which is a gradient-based method, is employed and to calculate the required sensitivities a fully analytical approach is presented. To demonstrate the performance of the suggested approach, various numerical examples are solved.
 

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