پایان نامه تحلیل کمانش نانو صفحات کامپوزیتی چند لایه گرفن قرار گرفته بر روی بستر الاستیک بوسیله ی تئوری غیر محلی و روش DQ

فهرست:

چکیده : ...............................................................................................................................1

1.  فصل  اول:کلیات تحقیق.. 2

1-1-مقدمه.. ............................................................................................................................................2

1-2-سیستم های میکرو/نانوالکترومکانیکی.. 4

1-3-اهداف پژوهش و روند انجام پروژه. 5

2.  فصل دوم :ادبیات تحقیق.. .....8

2-1-مباحث نظری.. 8

2-2-روش های مختلف مدلسازی در مقیاس های مختلف.... 8

2-2-1- روش مدل سازی اتمی.. 8

2-2-2- روش های چند مقیاسی.. 9

2-2-3- روش اتمی پیوسته.. 9

2-2-4- مکانیک کوانتومی.. 11

2-2-5- دینامیک مولکولی.. 12

2-2-6- روش مونت کارلو. 12

2-2-7- دینامیک نابجایی.. 13

2-2-8- روش مکانیک مولکولی.. 13

2-2-9- تئوری های مرتبه بالای محیط پیوسته.. 14

2-2-9-1-تئوری کسرات و نظریه تنش های تزویجی...................................................................................16 

2-3-الاستیسیته ی غیرموضعی.. 18

2-4-معرفی تئوری های ورق. 21

2-5-تئوری کلاسیک ورق. 22

2-6-تئوری تغییر شکل برشی مرتبه اول.. 23

2-7-تئوری مرتبه سوم برشی.. 23

2-8-ساختارهای نانو. 24

2-9-نانولوله های کربنی را به پنج دسته می‌توان تقسیم کرد. 24

2-10-محیط الاستیک.... 26

2-11-پیشینه ی پژوهش.... 27

2-12- جمع بندی فصل دوم  .................................................................................................................31

3..... فصل سوم:روابط وفرمول ها 32

3-1-مدلسازی نانو صفحه و ارائه راه حل عددی.. 32

3-2-تئوری الاستیسیته ی غیرموضعی.. 32

3-3-استخراج معادلات حرکت... 35

3-4-حل تحلیلی.. 51

3-5-حل عددی.. 52

3-5-1- روش عددی GDQ... 52

3-5-1-1 تعیین مختصات گره ها ......................................................................................................................55

3-5-1-2 تعیین ضرایب وزنی ..............................................................................................56

4.  فصل چهارم::شبیه سازی نتایج.. 59

4-1-نتایج عددی.. 59

4-2-صحت سنجی.. 61

4-3-کمانش نانو صفحه.. 63

4-3-1- تاثیر ابعاد صفحه بر نیروی کمانش.... 64

4-3-2- تاثیر پارامتر ابعادی وشرایط مرزی بر روی نیروی کمانش.... 67

4-4-تاثیر پارامتر ابعادی بر روی مودهای مختلف.... 68

4-4-1- تاثیر مدول وینکلر بر نیروی کمانش.... 70

4-4-2- بررسی اثر ضریب وینکلر بر روی مودهای مختلف.... 72

4-5-تاثیر ضریب وینکلر بر نیروی کمانش برای طول های مختلف.... 73

4-5-1- تاثیر ضریب برشی پسترناک بر روی نیروی کمانش.... 75

4-5-2- تاثیر ضریب برشی پسترناک بر مودهای مختلف نیروی کمانشی.. 75

5.  فصل پنجم: نتیجه گیری و پیشنهادات.. 77

5-1-پیشنهاد پژوهش های آتی.. 78

6.  منابع. 80

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