پایان نامه تحلیل ارتعاشی یک ورق مرکب لایه‌ لایه به کمک تئوری دو متغیره‌ ی پالوده شده به روش المان‌ های محدود سلسله مراتبی

فهرست:

فهرست مطالب. هشت

چکیده. 1

فصل اول: مقدمه  7

1-1    تاریخچه‌ای به روش‌های حل مسایل ارتعاش آزاد ورق‌ها 8

1-2    روش‌ المان محدود سلسله مراتبی.. 21

1-2-1     مقدمه. 21

1-2-2     روش‌های المان محدود 22

1-2-3     مروری بر کارهای انجام گرفته در زمینه روش المان محدود سلسله مراتبی.. 23

1-2-4     ویژگی‌های روش المان محدود سلسله مراتبی.. 24

1-3    اهداف پژوهش.... 25

فصل سوم: تئوری‌های کلاسیک و تغییرشکل برشی مرتبه اول ورق  26

2-1    مقدمه. 26

2-2    تعریف ماده عمودسانگرد. 27

2-3    تئوری کلاسیک ورق لایه لایه. 27

2-3-1     میدان‌های جابجایی و کرنش... 28

2-3-2     رابطه‌های ساختاری تنش- کرنش... 29

2-3-3     فرمول‌بندی المان محدود 30

2-3-4     ماتریس سختی.. 31

2-3-5     تابع‌های درونیاب لاگرانژی. 32

2-3-6     تابع‌های شکل هرمیتی.. 33

2-3-7     ماتریس جرم. 36

2-3-8     روش المان محدود سلسله مراتبی برای ورق تئوری کلاسیک... 38

2-3-9     تابع‌های شکل سلسله مراتبی درون-صفحه. 38

2-3-10    تابع‌‌های شکل برون-صفحه. 41

2-3-11    استخراج ماتریس سختی وجرم. 43

2-3-12    حل عددی ورق با تئوری کلاسیک ورق. 43

2-4    تئوری تغییرشکل برشی مرتبه اول. 51

2-4-1     میدان‌های جابجایی و کرنش... 51

2-4-2     رابطه‌های ساختاری تنش- کرنش... 53

2-4-3     فرمول‌بندی المان محدود 53

2-4-4     ماتریس سختی.. 54

2-4-5     ماتریس جرم. 56

2-4-6     روش المان محدود سلسله مراتبی.. 57

فصل سوم: تئوری ورق دو‌متغیره پالوده شده 60

3-1    مقدمه. 60

3-2    فرضیات اساسی.. 61

3-3    رابطه‌های کرنش- جابجایی.. 62

3-4    معادله‌های ساختاری تنش-کرنش.... 63

3-5    معادله‌های حرکت... 65

3-6    فرمول‌بندی المان محدود. 68

3-6-1     ماتریس سختی.. 69

3-6-2     ماتریس جرم. 72

3-7    روش المان محدود سلسله مراتبی برای تئوری ورق دو‌متغیره پالوده شده. 73

3-7-1     تابع‌های شکل روش المان محدود سلسله مراتبی.. 74

3-7-1     نتیجه‌گیری. 75

نتیجه‌گیری و پیشنهاد 87

4-1    نتیجه گیری.. 87

4-2    پیشنهاد‌ها 88

روش المان محدود سلسله مراتبی  89

پ-1-1   تابع‌ها‌ی شکل سلسله مراتبی.............................................................................................................................89

پ-1-2   تابع‌ها‌ی شکل سلسله مراتبی یک‌بعدی..............................................................................................................92

پ-1-3   تابع‌ها‌ی شکل سلسله مراتبی المان میله..............................................................................................................96

پ-1-4   تابع‌ها‌ی شکل سلسله مراتبی المان تیر................................................................................................................98

پ-1-5   تابع‌های مثلثاتی یک‌بعدی.............................................................................................................................101

پ-1-6   تابع‌ها‌ی شکل سلسله مراتبی دوبعدی (المان مستطیلی).....................................................................................102

مراجع  104

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