روش دوبخشی و بهینه‌سازی مقدار میانگین شتاب‌دهنده پویا در مقایسه با رویکردهای مختلف بهینه‌سازی توپولوژی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی مکانیک، دانشکده فنی و مهندسی، دانشگاه زابل، زابل، ایران

2 گروه مهندسی عمران، دانشکده فنی و مهندسی، دانشگاه زابل، زابل، ایران

چکیده

از آنجایی که بهینه­سازی توپولوژی قطعی یا به اختصار بهینه­سازی توپولوژی (TO) عدم قطعیت در سازه شامل مواد، بارگذاری و ابعاد هندسی را در نظر نمی­گیرد، ممکن است به یک طراحی بهینه با کمترین حالت اعتماد و ایمنی منجر شود. برای رفع این مشکل از بهینه‌سازی توپولوژی مبتنی بر قابلیت اطمینان (RBTO) استفاده می‌شود که در حقیقت ترکیب روش‌های بهینه­سازی توپولوژی با روش‌های طراحی مبتنی بر قابلیت اطمینان (RBDO) بر اساس یک چارچوب و فرایند ریاضی است. در این مقاله با به کارگیری چهار روش بهینه­سازی توپولوژی شامل: آستانه سطح ایزو پویا (MIST) ، روش SIMP، روش تکاملی بهینه‌سازی سازه‌ای- اجزای محدود توسعه‌یافته (XFEM-ESO) و تنظیم سطح (LS) و با درنظرگرفتن یک قید یا تابع هدف به روش دوبخشی یک کسر حجمی (Vf) بهینه برای بهینه­سازی توپولوژی به دست می‌آید. سپس به کمک کسر حجمی متوسط (Vf)، بهینه‌سازی توپولوژی انجام‌گرفته و نتایج بهینه آن توسط روش پیشرفته تحلیل قابلیت اطمینان مقدار متوسط شتاب‌ دهنده پویا (ADMV) و با درنظرگرفتن عدم‌قطعیت‌ها و انحراف معیار جهت استخراج محتمل‌ترین نقاط احتمال (MPP) مورد استفاده قرار می‌گیرد. با ‌داشتن محتمل‌ترین نقطه احتمال و قید، الگوریتم دوبخشی مجدد مورد استفاده قرار گرفته و کسر حجمی بهینه برای مدل بهینه‌سازی توپولوژی مبتنی بر قابلیت اطمینان و درنتیجه شکل بهینه روش بهینه‌سازی توپولوژی مبتنی بر قابلیت اطمینان به دست می‌آید. مثال‌های متعددی برای اعتبارسنجی و تأیید قابلیت بهینه‌سازی روش بهینه‌سازی توپولوژی مبتنی بر قابلیت اطمینان با یک سازه مدل و روش‌های ذکر شده بهینه­سازی توپولوژی ارائه می‌شوند و نتایج با هم مقایسه می‌شوند. نتایج نشان می‌دهند که ترکیب روش‌های طراحی مبتنی بر قابلیت اطمینان و بهینه­سازی توپولوژی می‌تواند به سازه­های مستحکم، پایدار، ایمن و مطمئن کاملاً متفاوت از نتایج بهینه­سازی توپولوژی منجر شود.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

The Bisection Method and the Accelerated Dynamical Mean Value Optimization Method in Comparison of Different Topology Optimization Approaches

نویسندگان [English]

  • Mahmoud َAlfouneh 1
  • Behrouz Keshtegar 2
1 Mechanical Engineering Department, University of Zabol, Zabol, Iran
2 Civil Engineering Department, University of Zabol, Zabol, Iran
چکیده [English]

Since deterministic topology optimization (TO) does not consider the uncertainties in the structure, including materials, loading and geometric dimensions, it may provide the optimal designs with the lowest state of reliability and safety. To 
solve this problem, reliability-based topology optimization (RBTO) is used, which is actually a combination of TO methods with reliability-based design methods (RBDO) based on a mathematical framework and process. In this article, by considering four TO methods including moving iso-surface threshold (MIST), SIMP, evolutionary structural optimization-extended finite element (XFEM-ESO) and level-set (LS), and considering a constraint or objective function, an optimal volume fraction (Vf) is obtained for TO by the bisection method. Then, with the aid of mean volume fraction, TO is performed and its optimized results are applied by an advanced reliability analysis method, i.e. accelerated dynamical mean value (ADMV), taking into account the uncertainties and their standard deviations to extract the most probable probability point (MPP). Having the MPP and the constraint, the bisection algorithm is used again and the optimized volume fraction for the RBTO model, and thereby the optimal layout for the RBTO solution, is achieved. Several examples are presented to validate and highlight the optimization capability of the RBTO method using a structural model and the mentioned TO methods, and the results are compared together. Based on the results, it is shown that the combination of RBDO and TO approach is able to result in powerful, stable, safe, and reliable structures completely different from the TO results.


کلیدواژه‌ها [English]

  • Deterministic topology optimization
  • Reliability-based topology optimization
  • Bisection method
  • MIST method
  • Level-set method
  • SIMP
  • XFEM-ESO method

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