رابطه‌سازی و بهینه‌سازی توپولوژی مفصل‌های خمشی با تغییرشکل‌های کوچک بر اساس معیار انرژی کرنشی

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مهندسی، گروه مهندسی مکانیک، دانشگاه فردوسی مشهد، مشهد، ایران

چکیده

مفصل‌های خمشی یکی از پرکاربردترین و مهم‌ترین المان‌های طراحی در طراحی سازوکارهای دقیق هستند. این مفصل‌ها به دلیل ساختار یک‌پارچه و ارتجاعی خود امکان ایجاد حرکت‌های دقیق را فراهم می‌کنند. در این پژوهش یک مدل کینتوالاستیک برای طراحی انواع مفصل‌های خمشی یک و چند درجه آزادی ارائه ‌شده است. برای کاهش هزینه محاسباتی، دو رویکرد رابطه‌سازی مفید برای بیان تابع هدف و قیدهای مسئله ارائه شده‌اند که تنها بر اساس معیار انرژی کرنشی و جابه‌جایی‌های ازپیش‌تعیین‌شده تعریف شده‌اند. این روش دارای خاصیت خود‌الحاقی است که با کاهش حجم محاسبات برای تحلیل حساسیت، همگرایی بالایی را نیز به همراه دارد. برای یافتن پاسخ‌های مسئله بهینه‌سازی از تحلیل اجزای محدود، مدل‌سازی مواد با استفاده از روش جامد همسان‌گرد با جریمه و روش مبتنی بر گرادیان حرکت مجانب‌های متحرک استفاده شده است. مسئله‌ی بهینه‌سازی توپولوژی در نرم‌افزار متلب برنامه‌نویسی و مثال‌های متعددی برای طراحی مفصل‌های خمشی یک و چند درجه آزادی در فضای دوبعدی حل شده است. در نهایت نتایج به‌دست‌آمده از دو رویکرد بهینه‌سازی ارائه‌شده در این پژوهش با یک‌دیگر مقایسه شده‌اند. نتایج به‌دست‌آمده از این پژوهش انواع مختلف مفصل‌های خمشی در فضای دوبعدی را پوشش می‌دهد. در برخی از این مفصل‌ها، نسبت سفتی سازه به میزان قابل توجهی، تا 208 برابر، افزایش یافته است که این امر نشان‌دهنده کاربردی بودن و اثربخشی این روش در بهینه‌سازی توپولوژی مفصل‌های خمشی است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Formulation and Topology optimization of flexure joints with small deformations based on strain energy criteria

نویسندگان [English]

  • Qaem Maloonezhadabsardi
  • Behrooz Hassani
  • Nima Yaghoobi
Faculty of Engineering, Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
چکیده [English]

Flexure joints are one of the most widely used and crucial elements in the design of precision mechanisms. Owing to their monolithic and elastic structure, these joints facilitate highly precise movements. In this study, we present a kinetoelastic model for designing various types of flexure joints with single and multiple degrees of freedom. To reduce computational costs, two beneficial approaches for defining the objective function and constraints are presented, based solely on the strain energy criterion and predetermined displacements. The resulting self-adjoint optimization problem exhibits computational efficiency and improved convergence. The topology optimization problem utilizes the Finite Element Method and the Solid Isotropic Material with a Penalization model, employing the Method of Moving Asymptotes to solve and identify the optimal topology. A comprehensive mathematical framework, including the relevant two-dimensional boundary conditions and sensitivity analysis, is meticulously developed and extensively examined. For this purpose, MATLAB code is developed for designing two-dimensional flexure joints with single and multiple degrees of freedom. Finally, the results obtained from the comparison of two optimization approaches presented in this study are discussed. In these joints, the stiffness ratio of the structure has increased significantly, up to 208 times, indicating the practicality and effectiveness of this method in the topology optimization of flexure joints.

کلیدواژه‌ها [English]

  • Flexure joints
  • topology optimization
  • strain energy
  • the Method of Moving Asymptotes
  • predetermined displacements
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