Investigation of Linear and Nonlinear Buckling of Orthotropic Graphene Sheets with Nonlocal Elasticity Theories
محورهای موضوعی : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیکمصطفی صادقیان 1 , مهرداد جبارزاده 2
1 - دانشجوی کارشناسی ارشد، دانشکده مکانیک، دانشگاه آزاد اسلامی مشهد
2 - استادیار، دانشکده مکانیک، دانشگاه آزاد اسلامی مشهد
کلید واژه: Buckling, Orthotropic, Graphene sheets, Nonlocal elasticity theories, Method of differential quadrature (DQ),
چکیده مقاله :
In this paper, analysis of linear and nonlinear buckling of relatively thick orthotropic graphene sheets is carried out under mechanical load based on elasticity theories. With the help of nonlocal elasticity theory, the principle of virtual work, first order shear theory and Von-Karman nonlinear strain, the dominant relationship in terms of obtained displacements has been obtained, and the method of differential quadrature (DQ) with non-uniform distribution points (Chebyshev -Gauss-Lobato) has been used. To check the validity, the obtained results have been compared with other resources, and the effects of nonlocal coefficient, thickness, radius and elastic base on the dimensionless buckling loads were calculated and investigated. Moreover, the results of analysis using nonlocal and local theory were compared together. It can be noticed that the dimensionless buckling loads on graphene sheets increased more with a decrease in flexibility as far boundary condition is concerned. Additionally, with an increase in the sheet radius, the variation between nonlocal and local analysis results will be more.
در این مقاله، تحلیل خطی و غیرخطی کمانش صفحات نسبتا ضخیم دایروی/حلقوی گرافن با خواص ارتوتروپیک بر پایه الاستیک تحت بار مکانیکی مورد بررسی قرار میگیرد. به کمک ﺗﺌﻮری اﻻﺳﺘﯿﺴﯿﺘﻪ ﻏﯿﺮﻣﻮﺿﻌﯽ، اصل کار مجازی، تئوری مرتبه اول برشی و کرنشهای غیرخطی فون-کارمن، روابط حاکم برحسب جابجایی–ها بدست آمده و از روش مربعات دیفرانسیلی (DQ) همراه با توزیع غیریکنواخت نقاط (چیبشف-گوس-لوباتو) استفاده شده است. برای اعتبار سنجی، نتایج بدست آمده با نتایج کمانش در مراجعدیگر مقایسه شده و اثرات ضریب غیرموضعی، ضخامت، شعاع و پایه الاستیک، بر بارهای بی بعد کمانش مورد بررسی قرار گرفته است و همچنین نتایج تحلیل به روش تئوری غیر موضعی و موضعی با یکدیگر مقایسه شده اند. از نتایج مشاهده میشود که بار بیبعد کمانش صفحات گرافن با کاهش انعطاف پذیری از نظر شرط مرزی، با افزایش ضریب غیرموضعی، افزایش بیشتری مییابد و همچنین با افزایش شعاع صفحه، اختلاف نتایج تحلیل غیر موضعی و موضعی بیشتر میشود.
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