نویسندگان
مهندسی مکانیک، دانشگاه آزاد اسلامی واحد مشهد، مشهد
چکیده
در این مقاله، تحلیل خمش غیرخطی نانوصفحات دایروی سوراخ‌دار به کمک تئوری الاستیسیته سه‌بعدی و تنش کوپل اصلاح شده، بررسی شده است. به این منظور معادلات تعادل با در نظر گرفتن عبارت‌های غیرخطی کرنش به روش حداقل انرژی پتانسیل محاسبه و به روش عددی نیمه‌تحلیلی چندجمله‌ای حل شده است. طبق بررسی‌های انجام شده، تاکنون، تحقیقی که در آن به روش الاستیسیته سه‌بعدی تمام شرایط مرزی به روش عددی محاسبه شده باشند، ملاحظه نشد. به‌طور معمول، تحقیقات در زمینه الاستیسیته سه‌بعدی یا به‌صورت المان محدود بوده و یا اکثراً فقط برای شرط مرزی مفصلی انجام شده است. در این تحقیق، برای اولین مرتبه، تحلیل غیرخطی خمش به کمک الاستیسیته سه‌بعدی برای انواع شرط مرزی ارائه شده است. همچنین، به کمک تئوری تنش کوپل اصلاح شده، نتایج در مقیاس نانو بررسی شده است. در ادامه، ضمن اعتبارسنجی نتایج، بررسی تغییرات خیز نسبت به پارامتر مقیاس برای انواع شرط مرزی، اثر تغییر پارامتر مقیاس در ضخامت‌های مختلف و اثر پارامتر مقیاس بر نتایج خطی و غیرخطی بررسی شده است.
کلیدواژه‌ها
عنوان مقاله [English]
The Nonlinear Bending Analysis for Circular Nano Plates Based on Modified Coupled Stress and Three- Dimensional Elasticity Theories
نویسندگان [English]
- Z. Barouei
- M. Jabbarzadeh
چکیده [English]
In this paper, the nonlinear bending analysis for annular circular nano plates is conducted based on the modified coupled stress and three-dimensional elasticity theories. For this purpose, the equilibrium equations, considering nonlinear strain terms, are calculated using the least energy potential method and solved by the numerical semi-analytical polynomial method. According to the previous works, there have been no studies calculating all boundary conditions numerically based on three-dimensional elasticity. Typically, the research done on three-dimensional elasticity is either finite element or only for a simply-supported boundary condition. In this research, for the first time, the nonlinear analysis of bending is calculated with the help of three-dimensional elasticity for a variety of boundary conditions. Also, with the help of the modified couple stress theory, the results on the nano-scale scale have been studied. In the following, while validating the results, we investigate the changes in the scale parameter for the types of boundary conditions, the effect of changing the parameter of scale in different thicknesses, and the impact of the parameter of scale on the linear and nonlinear results.
کلیدواژه‌ها [English]
- Nonlinear bending
- Circular Nano plates
- Three-dimensional elasticity theory
- Modified coupled stress
- Semi-analytical polynomial method
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