Bending Sector Graphene Sheet Based on the Elastic Winkler-Pstrnak with the Help of Nonlocal Elasticity Theory Using Developed Kantorovich Method
محورهای موضوعی : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیکشهریار دستجردی 1 , مهرداد جبارزاده 2
1 - کارشناس ارشد، دانشکده مکانیک، دانشگاه آزاد اسلامی واحد مشهد
2 - استادیار، دانشکده مکانیک، دانشگاه آزاد اسلامی واحد مشهد
کلید واژه: Sector graphene sheet, Nonlocal Continuum Field mechanic, Developed Kantorovich method, Elastic Winkler-Pstrnak,
چکیده مقاله :
In this study, the elastic bending of sector graphene sheet has been studied based on elasticity using Eringen Nonlocal Elasticity Theory. In order to do this, the balance equations governing the sector graphene sheet have been solved in terms of displacements with regard to nonlocal relationship of stress, shear theory of the first order, and obtained linear strains using developed Kantorovich method. In this method, the obtained partial differential equations are converted into two categories that can be solved using analytical and numerical methods. Developed Kantorovich method is a method with a high rate of convergence, in which the expected convergence is achieved with just three to four repetitions. With regard to the fact that no research has yet been conducted in this regard, the results, considering the nonlocal coefficient equal to zero, have been compared with other articles in order to check the validity. In the end, the effect of nonlocal coefficient variations on the results in terms of thickness, boundary conditions, hardness of elastic base and difference between nonlocal and local elasticity analysis has been studied.
در این تحقیق خمش صفحات قطاعی گرافن بر پایه الاستیک توسط تئوری مکانیک غیر موضعی ارینگن مورد بررسی قرار گرفته است. برای این منظور معادلات تعادل حاکم بر ورق قطاعی گرافن بر حسب جابجائیها، با در نظر گرفتن روابط غیرموضعی تنش و تئوری مرتبه اول برشی و کرنشهای خطی بدست آمده و با روش کانتروویچ توسعه یافته حل شده است. در این روش دستگاه معادلات دیفرانسیل جزئی بدست آمده به دو دسته دستگاه معادلات دیفرانسیل معمولی تبدیل میشود که قابل حل بروشهای مختلف تحلیلی و عددی میباشد. حل کانتروویچ توسعه یافته روشی با سرعت همگرائی بالا است که تنها پس از سه الی چهار مرحله تکرار همگرایی مورد انتظار بدست میآید. با توجه به اینکه تاکنون در این خصوص تحقیقی صورت نگرفته است نتایج با در نظر گرفتن ضریب غیرموضعی برابر با صفر با دیگر مقالات جهت اعتبار سنجی مقایسه شده است. در انتها اثر تغییرات ضریب غیرموضعی بر نتایج بر حسب تغییرات ضخامت، شرایط مرزی، مقدار سختی پایه الاستیک و اختلاف تحلیل الاستیسیته غیرموضعی و موضعی مورد بررسی قرار گرفته اند.
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