تعیین ضرایب شدت تنش در صفحات تابعی ارتوتروپیک با روش بدون المان گلرکین

نوع مقاله : مقاله پژوهشی

نویسندگان

1 عضو هیات علمی / دانشکدة مهندسی مکانیک، دانشگاه فردوسی مشهد

2 عضو هیات علمی/ دانشکدة مهندسی مکانیک، دانشگاه صنعتی شاهرود

3 عضو هیات علمی / گروه مهندسی رباتیک، دانشگاه صنعتی شاهرود

چکیده

روش‌های تولید مواد تابعی سبب می‌شود رفتار این مواد غیر ایزوتروپ باشد. در این مقاله از روش بدون ­المان گلرکین برای مطالعة شکست مواد تابعی ارتوتروپیک استفاده شده است. در این روش محاسبة عددی مشتق میدان­های اصلی و کمکی کرنش به‌سادگی انجام می­شود، حال آنکه روش المان محدود و فرم توسعه­یافتة آن با مشکلاتی همراه است. به‌علاوه در این مقاله یک انتگرال پایستار جدید برای محاسبة پارامترهای شکست در مواد غیرهمگن ارائه شده است که فرم یکسانی برای بارگذاری مکانیکی و حرارتی دارد. این شکل جدید از انتگرال برهم­کنش دارای ترم­هایی با تعبیر فیزیکی مشخص بوده و برای برهم­کنش میدان‌های خطی بر میدان الاستیک دارای ترم­های ثابت است و به‌طور سیستماتیک قابل تعمیم می­باشد. در این مقاله، ضرایب شدت تنش در مواد تابعی ارتوتروپیک با به‌کارگیری این انتگرال برهم‌کنش محاسبه شده است. برای گسسته­سازی معادلات حاکم از روش بدون المان گلرکین استفاده شده است. در چند مثال اثر تغییر خصوصیات مواد بر ضرایب شدت تنش بررسی شده است. مقایسة نتایج با مقادیر گزارش­شده در مقالات موجود بیانگر دقت قابل قبول رابطة ارائه‌شده است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Stress intensity factor calculation in orthotropic functionally graded layers using element-free Galerkin method

نویسندگان [English]

  • Mahmoud Shariati 1
  • Mohammad Bagher Nazari 2
  • Masoud Mahdizadeh Rokhi 3
چکیده [English]

Production methods of functionally graded materials cause anisotropic behavior. In this paper, the element-free Galerkin method is used to study of fracture behavior of orthotropic functionally graded materials. In this method, numerical calculation of the main and auxiliary strain fields is simply done while, in finite element and extended finite element methods, it is associated with difficulties. In addition to in this paper, a path-independent integral is presented to compute the fracture parameters in heterogeneous materials which has a unique form for mechanical and thermal loading. This new form of interaction integral includes terms with the certain physical interpretation. Also, the presented form of interaction integral has fixed term for interaction of linear fields on elastic field and it is systematically extensible. In this paper, the stress intensity factors in orthotropic functionally graded materials are obtained by using this interaction integral formula. The element-free Galerkin method is implemented to discrete the governing equations. The effect of materials characteristics on the stress intensity factors is studied in several examples. The obtained results are in good agreement with reported ones in existence papers.

کلیدواژه‌ها [English]

  • path-independent integral
  • crack
  • stress intensity factor
  • orthotropic functionally graded materials
  • element-free Galerkin method
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