نویسندگان
دانشکده مهندسی مکانیک، دانشگاه کاشان
چکیده
در مقاله حاضر به کمک یکی از روشهای بدون المان به تحلیل استاتیکی ورقهای نازک با اشکال هندسی گوناگون بر مبنای تئوری های کلاسیک میندلین پرداخته شده است. در این روش عددی دامنه مسئله، تنها توسط مجموعه ای از گره ها بیان می شود و به هیچگونه شبکه بندی یا المان نیاز نیست. برای بیان دامنه مسائل با اشکال هندسی گوناگون ابتدا مجموعه ای از گره ها در یک دامنه مستطیلی استاندارد تعریف می شوند، سپس توسط یک نگاشت مرتبه سه این گره ها به دامنه مسئله اصلی انتقال می یابند، بنابراین می توان ورقهای با اشکال هندسی مختلف را تحلیل کرد. از میان روش های عددی بدون شبکه، در اینجا از روش بدون شبکه گالرکین (EFG) استفاده می شود. روش مذکور از روشهای انتگرالی فرم ضعیف می باشد که از توابع شکل MLS جهت تقریب استفاده می کند. با توجه به عدم خاصیت دلتا در توابع شکل MLS نمی توان شرایط مرزی را بصورت مستقیم اعمال کرد، لذا برای اعمال شرایط مرزی از روش لاگرانژ استفاده می شود. در پایان برای نشان دادن صحت روش حل، جوابهای روش حاضر با جوابهای حاصل از حل تحلیلی ورقها و روشهای المان محدود مقایسه خواهد شد. و پس ار تایید صحت روش حل به حل چند نمونه جدید پرداخته خواهد شد.
کلیدواژه‌ها
عنوان مقاله [English]
Analysis of Thin Isotropic and Orthotropic Plates with Element-Free Galerkin Method and Various Geometric Shapes
نویسندگان [English]
- H. Edalati
- B. Soltani
چکیده [English]
Utilizing one of the mesh free methods, the present paper concerns static analysis of thin plates with various geometric shapes based on the mindlin classical plate theories. In this numerical method, the domain of issue is solely expressed through a set of nods and no gridding or element is required. To express the domain of issues with various geometric shapes, first a set of nodes are defined in a standard rectangular domain , then via a three-order map with, these nodes are transferred to the main domain of the original issue; therefore plates of various geometric shapes can be analyzed. Among meshfree numerical methods, Element Free Galerkin method (EFG) is utilized here. The method is one of the weak form integral methods that uses MLS shape functions for approximation. Regarding the absence of Delta feature in MLS functions, boundary conditions cannot be imposed directly; hence the Lagrangian method is utilized to impose boundary conditions. At the end, our outputs are compared with those of analytic and finite element methods for plates, in order to validate the exactness of our solution method, and then after reliability is established, a few new examples will be solved.
کلیدواژه‌ها [English]
- Element Free method of Galerkin (EFG)
- Plate’s theory
- weak form numerical solution
- Lagrange methode
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