افزایش سرعت محاسبات در تحلیل مدل‌های پری‌داینامیک خطی و غیرخطی تحت بارهای ضربه‌ای

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده‌ی مهندسی عمران و حمل و نقل، دانشگاه اصفهان، اصفهان، ایران

چکیده

تئوری پری‌داینامیک با فرمول­ بندی جدید در معادلات حرکت، روابط انتگرالی را جایگزین مشتقات مکانی می­ کند. با توجه به این قابلیت، شروع ترک در هر جهت بدون نیاز به افزودن معیارهای رشد ترک امکان­ پذیر می­ شود. یکی از اساسی ­ترین مشکلات در تئوری پری‌داینامیک، حجم بالای محاسبات به دلیل ماهیت دینامیکی آن است. برای حل این مشکل، در این مقاله با استفاده از تبدیل موجک، مسائل پری‌داینامیک تحت بار­های نامنظم یا تصادفی تحلیل شده است. هدف از این کار افزایش سرعت محاسبات به بیش از 80 درصد است. روش ارائه ‌شده در این مقاله بر روی دو مدل ماده یعنی Prototype brittle material و Micro-plastic material بررسی‌ شده است. در این راستا به تحلیل سازه­ ها با رفتار خطی و غیرخطی با در نظر گرفتن اثرات ناپیوستگی (مانند ترک) و بدون در نظر گرفتن اثرات ناپیوستگی پرداخته شده است. سازه­ های انتخاب شده شامل تیرهای یک سر گیردار و دو سر ساده می­شوند. هر تیر تحت دو بار ضربه ­ای نامنظم قرار می­ گیرد. تیرهای مورد نظر یک مرتبه با تابع اصلی موج ضربه تحلیل می­ شوند و یک بار هم با موج­ های تقریبی به دست آمده از روش موجک تحلیل می­ شوند. نتایج به دست آمده از نمونه‌های تحقیق حاضر نشان می­ دهد که روش موجک در سازه­ های پری­داینامیک با رفتار خطی کاهش هزینه­ ی 87 درصدی و در سازه­ های پری‌داینامیک با رفتار غیرخطی کاهش زمان محاسبات 94 درصدی ایجاد می­ کند. این در حالی است که خطای این روش نیز در حد قابل قبول است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Reducing computational efforts in linear and nonlinear analysis of peridynamic models under impact loads

نویسندگان [English]

  • Noorollah Majidi
  • Hossein Tajmir Riahi
  • Mahdi Zandi
Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan
چکیده [English]

Peridynamic theory, with a new formulation in the equations of motion, replaces the partial differential equations with integral equations. Due to this capability, it is possible to model crack initiation in any direction without the need to consider crack-growth criteria. One of the main problems in peridynamic theory is its high computational efforts due to its dynamic nature. If the critical time step of the numerical integration is greater than the loading time step, it will increase the cost of calculations. In this paper, using wavelet transform, peridynamic problems under irregular and random impact loads are analyzed. The aim of this study is to increase the computational speed for these problems. The method presented in this paper is investigated on two material models, namely Prototype brittle material and micro-plastic material. In this regard, structures with linear and nonlinear behavior have been analyzed considering the effects of discontinuities (such as cracks) and without considering the effects of discontinuities. The selected structures include two beams. Each beam is subjected to two types of irregular impact loading. The beams are analyzed once with the main impact (wave) function and once with the approximate impact (waves) functions obtained using wavelet transform. Based on the results of linear and nonlinear analyses of this study, it can be judged that the presented method reduces the computational cost by 87% in peridynamic models with linear behavior. It also bring a 94% reduction in computational costs in peridynamic models with nonlinear behavior.

کلیدواژه‌ها [English]

  • Peridynamic
  • Wavelet transform
  • Cracking
  • Crack line
  • Computational efforts
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