8/16/2019 Structural analysis with finite elements.pdf

1/413

Structural analysis withfinite elements

Paolo Rugarli

Castalia

8/16/2019 Structural analysis with finite elements.pdf

2/413

8/16/2019 Structural analysis with finite elements.pdf

3/413

 

 

8/16/2019 Structural analysis with finite elements.pdf

4/413

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

5/413

 

 

 

 

 

   

   

   

   

   

   

   

   

   

   

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

   

   

   

   

   

   

   

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

     

   

   

   

v 

8/16/2019 Structural analysis with finite elements.pdf

6/413

Structural analysis with finite elements 

vi

 

 

 

 

 

 

 

 

 

 

 

   

   

   

   

   

   

   

   

   

   

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

   

   

   

   

   

   

 

 

   

   

 

 

 

 

 

 

 

 

 

 

 

 

 

       

 

   

 

 

 

 

 

 

 

 

 

 

   

   

8/16/2019 Structural analysis with finite elements.pdf

7/413

Contents 

vii

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

   

   

   

   

   

   

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

   

   

   

   

   

   

   

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    

   

   

   

8/16/2019 Structural analysis with finite elements.pdf

8/413

Structural analysis with finite elements 

viii

   

   

   

   

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

   

   

   

   

   

   

   

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

 

 

 

   

   

 

 

 

 

 

 

 

 

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

9/413

 

 

         

 

 

 

ix 

8/16/2019 Structural analysis with finite elements.pdf

10/413

8/16/2019 Structural analysis with finite elements.pdf

11/413

 

 

 

 

 

 

xi

8/16/2019 Structural analysis with finite elements.pdf

12/413

Structural analysis with finite elements © Tomas elford 2010

    

 

  

 

 

 

   

 

8/16/2019 Structural analysis with finite elements.pdf

13/413

Structural analysis with finite elements 

2

 

 

      

   

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

14/413

Introduction

3

 

      

 

 

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

15/413

Structural analysis with finite elements 

4

 

 

 

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

16/413

Structural analysis with finite elements © Tomas elford 2010

   

 

 

        

8/16/2019 Structural analysis with finite elements.pdf

17/413

Structural analysis with finite elements 

6

 

 

 

 

     

     

8/16/2019 Structural analysis with finite elements.pdf

18/413

Overview 

7

 

 

 

 

 

 

         

 

8/16/2019 Structural analysis with finite elements.pdf

19/413

Structural analysis with finite elements 

8

 

  

 

 

               

   

8/16/2019 Structural analysis with finite elements.pdf

20/413

Overview 

9

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

21/413

Structural analysis with finite elements 

10

 

 

   

8/16/2019 Structural analysis with finite elements.pdf

22/413

Overview 

11

 

 

 

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

23/413

Structural analysis with finite elements 

12

 

 

 

      

 

8/16/2019 Structural analysis with finite elements.pdf

24/413

Overview 

13

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

25/413

Structural analysis with finite elements 

14

 

    

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

26/413

Overview 

15

   

 

 

 

   

 

     

8/16/2019 Structural analysis with finite elements.pdf

27/413

Structural analysis with finite elements 

16

 

 

   

 

 

   

8/16/2019 Structural analysis with finite elements.pdf

28/413

Overview 

17

 

 

   

 

     

 

8/16/2019 Structural analysis with finite elements.pdf

29/413

Structural analysis with finite elements 

18

 

   

 

 

8/16/2019 Structural analysis with finite elements.pdf

30/413

Overview 

19

   

           

 

8/16/2019 Structural analysis with finite elements.pdf

31/413

Structural analysis with finite elements 

20

        

 

  

 

 

         

           

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

32/413

Overview 

21

 

     

     

 

8/16/2019 Structural analysis with finite elements.pdf

33/413

Structural analysis with finite elements 

22

 

   

   

 

          

 

                 

 

 

8/16/2019 Structural analysis with finite elements.pdf

34/413

Overview 

23

 

   

 

   

 

               

         

 

8/16/2019 Structural analysis with finite elements.pdf

35/413

Structural analysis with finite elements 

24

          

 

 

    

   

   

    

 

 

   

 

 

 

   

    

            

 

 

8/16/2019 Structural analysis with finite elements.pdf

36/413

Overview 

25

  

 

 

 

 

 

 

 

 

 

 

 

    

 

         

8/16/2019 Structural analysis with finite elements.pdf

37/413

Structural analysis with finite elements 

26

 

     

   

  

  

 

   

 

8/16/2019 Structural analysis with finite elements.pdf

38/413

Overview 

27

 

8/16/2019 Structural analysis with finite elements.pdf

39/413

Structural analysis with finite elements 

28

   

 

 

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

40/413

Overview 

29

 

8/16/2019 Structural analysis with finite elements.pdf

41/413

Structural analysis with finite elements © Tomas elford 2010

 

 

 

 

   

 

8/16/2019 Structural analysis with finite elements.pdf

42/413

Structural analysis with finite elements 

32

  

 

  

 

     

8/16/2019 Structural analysis with finite elements.pdf

43/413

Elasticity: special formulations 

33

          

 

 

 

 

     

8/16/2019 Structural analysis with finite elements.pdf

44/413

Structural analysis with finite elements 

34

 

  

 

       

      

 

 

8/16/2019 Structural analysis with finite elements.pdf

45/413

Elasticity: special formulations 

35

 

 

    

 

   

   

   

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

46/413

Structural analysis with finite elements 

36

 

  

   

               

        

   

8/16/2019 Structural analysis with finite elements.pdf

47/413

Elasticity: special formulations 

37

   

      

 

   

       

       

      

 

 

 

    

  

 

   

8/16/2019 Structural analysis with finite elements.pdf

48/413

Structural analysis with finite elements 

38

 

 

 

   

8/16/2019 Structural analysis with finite elements.pdf

49/413

Elasticity: special formulations 

39

 

      

    

   

   

    

 

    

 

    

  

8/16/2019 Structural analysis with finite elements.pdf

50/413

Structural analysis with finite elements 

40

       

          

 

          

 

 

8/16/2019 Structural analysis with finite elements.pdf

51/413

Elasticity: special formulations 

41

 

 

 

   

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

52/413

Structural analysis with finite elements 

42

 

 

 

     

8/16/2019 Structural analysis with finite elements.pdf

53/413

Elasticity: special formulations 

43

 

 

 

  

          

    

  

       

          

8/16/2019 Structural analysis with finite elements.pdf

54/413

Structural analysis with finite elements 

44

 

 

       

 

 

    

8/16/2019 Structural analysis with finite elements.pdf

55/413

Elasticity: special formulations 

45

 

     

    

     

  

 

8/16/2019 Structural analysis with finite elements.pdf

56/413

8/16/2019 Structural analysis with finite elements.pdf

57/413

Elasticity: special formulations 

47

 

 

   

   

    

    

  

   

     

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

58/413

Structural analysis with finite elements 

48

  

 

 

 

 

 

     

  

 

             

 

   

       

      

8/16/2019 Structural analysis with finite elements.pdf

59/413

Elasticity: special formulations 

49

   

 

   

 

   

 

    

  

    

    

 

            

8/16/2019 Structural analysis with finite elements.pdf

60/413

Structural analysis with finite elements 

50

   

  

    

    

 

   

   

   

 

8/16/2019 Structural analysis with finite elements.pdf

61/413

Elasticity: special formulations 

51

 

            

 

   

   

      

  

  

 

  

   

8/16/2019 Structural analysis with finite elements.pdf

62/413

Structural analysis with finite elements 

52

  

 

 

     

           

 

    

8/16/2019 Structural analysis with finite elements.pdf

63/413

Elasticity: special formulations 

53

 

  

 

8/16/2019 Structural analysis with finite elements.pdf

64/413

Structural analysis with finite elements 

54

 

 

 

 

    

  

 

  

  

 

 

   

    

    

         

    

 

       

 

8/16/2019 Structural analysis with finite elements.pdf

65/413

Elasticity: special formulations 

55

   

 

   

   

 

 

  

 

    

    

  

 

   

 

8/16/2019 Structural analysis with finite elements.pdf

66/413

Structural analysis with finite elements 

56

   

    

  

 

 

    

 

 

 

 

 

 

    

 

 

   

8/16/2019 Structural analysis with finite elements.pdf

67/413

Elasticity: special formulations 

57

 

   

   

   

 

  

 

 

 

 

 

 

 

 

 

  

  

 

 

      

 

   

  

   

 

8/16/2019 Structural analysis with finite elements.pdf

68/413

Structural analysis with finite elements 

58

         

  

  

     

    

         

     

 

 

 

 

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

69/413

Elasticity: special formulations 

59

 

 

 

 

 

 

  

   

 

 

      

    

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

70/413

Structural analysis with finite elements 

60

     

   

       

      

 

   

 

 

  

  

  

    

    

   

                 

                 

    

 

  

 

 

8/16/2019 Structural analysis with finite elements.pdf

71/413

Elasticity: special formulations 

61

    

      

    

    

    

   

   

 

 

 

 

 

  

 

  

      

 

    

   

 

          

       

 

  

  

 

 

              

 

8/16/2019 Structural analysis with finite elements.pdf

72/413

Structural analysis with finite elements 

62

 

 

 

               

  

  

 

 

 

             

 

  

    

    

 

  

 

   

   

   

 

      

 

  

     

8/16/2019 Structural analysis with finite elements.pdf

73/413

Elasticity: special formulations 

63

   

     

      

        

    

      

    

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

74/413

Structural analysis with finite elements 

64

 

  

 

8/16/2019 Structural analysis with finite elements.pdf

75/413

Elasticity: special formulations 

65

 

   

   

 

 

      

     

 

 

     

 

  

  

 

 

           

 

  

  

 

 

           

 

  

  

 

 

           

 

8/16/2019 Structural analysis with finite elements.pdf

76/413

Structural analysis with finite elements 

66

 

  

  

 

 

             

 

  

  

 

 

              

    

   

  

 

 

 

   

   

 

  

 

 

          

    

  

    

 

          

    

  

    

 

           

8/16/2019 Structural analysis with finite elements.pdf

77/413

Elasticity: special formulations 

67

 

 

 

 

 

 

 

  

  

  

 

 

 

  

   

  

 

 

 

 

   

  

  

  

  

 

 

8/16/2019 Structural analysis with finite elements.pdf

78/413

Structural analysis with finite elements 

68

  

 

 

                            

              

 

 

  

 

 

   

 

 

  

 

 

   

  

    

  

  

  

 

8/16/2019 Structural analysis with finite elements.pdf

79/413

Elasticity: special formulations 

69

 

   

        

 

  

     

 

 

  

       

 

  

 

8/16/2019 Structural analysis with finite elements.pdf

80/413

Structural analysis with finite elements 

70

 

 

 

     

    

   

    

   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  

  

 

 

 

 

  

 

 

 

 

 

 

 

  

  

  

 

8/16/2019 Structural analysis with finite elements.pdf

81/413

Elasticity: special formulations 

71

 

 

 

 

 

  

 

 

 

     

 

 

  

 

 

  

 

 

 

  

  

  

  

  

 

 

  

8/16/2019 Structural analysis with finite elements.pdf

82/413

Structural analysis with finite elements 

72

 

 

 

 

  

 

 

 

 

 

  

  

  

  

  

     

 

 

 

 

  

  

  

 

 

  

   

 

 

 

       

 

  

   

 

 

 

       

 

8/16/2019 Structural analysis with finite elements.pdf

83/413

Elasticity: special formulations 

73

    

 

8/16/2019 Structural analysis with finite elements.pdf

84/413

Structural analysis with finite elements 

74

   

 

     

 

    

 

 

  

 

 

 

   

            

8/16/2019 Structural analysis with finite elements.pdf

85/413

Elasticity: special formulations 

75

   

       

 

   

 

 

  

 

 

  

 

 

  

 

 

 

  

 

     

 

   

   

 

        

    

 

  

 

   

      

 

8/16/2019 Structural analysis with finite elements.pdf

86/413

Structural analysis with finite elements 

76

 

  

 

   

     

 

 

 

 

 

   

 

     

 

  

 

  

      

     

   

 

      

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

87/413

Elasticity: special formulations 

77

      

 

 

 

  

 

   

 

8/16/2019 Structural analysis with finite elements.pdf

88/413

Structural analysis with finite elements © Tomas elford 2010

 

 

 

 

  

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

89/413

Structural analysis with finite elements 

80

 

 

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

90/413

8/16/2019 Structural analysis with finite elements.pdf

91/413

Structural analysis with finite elements 

82

 

   

 

8/16/2019 Structural analysis with finite elements.pdf

92/413

Te finite element 

83

 

 

 

   

  

   

 

 

  

8/16/2019 Structural analysis with finite elements.pdf

93/413

Structural analysis with finite elements 

84

 

 

   

 

 

   

 

8/16/2019 Structural analysis with finite elements.pdf

94/413

Te finite element 

85

 

 

8/16/2019 Structural analysis with finite elements.pdf

95/413

Structural analysis with finite elements 

86

 

 

 

   

 

     

   

  

8/16/2019 Structural analysis with finite elements.pdf

96/413

Te finite element 

87

 

 

 

 

     

 

8/16/2019 Structural analysis with finite elements.pdf

97/413

Structural analysis with finite elements 

88

 

  

   

8/16/2019 Structural analysis with finite elements.pdf

98/413

Te finite element 

89

   

 

 

 

   

   

 

8/16/2019 Structural analysis with finite elements.pdf

99/413

Structural analysis with finite elements 

90

 

 

 

   

   

 

   

         

         

         

     

 

8/16/2019 Structural analysis with finite elements.pdf

100/413

Te finite element 

91

 

         

         

 

 

   

   

       

       

     

   

           

  

  

 

8/16/2019 Structural analysis with finite elements.pdf

101/413

Structural analysis with finite elements 

92

   

       

 

   

 

   

 

     

 

 

 

 

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

102/413

Te finite element 

93

   

 

 

 

 

 

 

     

 

     

   

          

8/16/2019 Structural analysis with finite elements.pdf

103/413

Structural analysis with finite elements 

94

  

     

 

 

      

 

 

 

   

        

 

 

8/16/2019 Structural analysis with finite elements.pdf

104/413

Te finite element 

95

 

    

  

 

 

 

    

 

 

  

   

8/16/2019 Structural analysis with finite elements.pdf

105/413

Structural analysis with finite elements 

96

             

   

     

   

  

  

 

 

 

   

  

 

 

 

    

    

 

  

 

   

   

  

 

8/16/2019 Structural analysis with finite elements.pdf

106/413

Te finite element 

97

 

  

       

 

 

 

  

 

    

   

         

 

           

        

       

  

        

8/16/2019 Structural analysis with finite elements.pdf

107/413

Structural analysis with finite elements 

98

         

     

     

     

   

   

     

       

 

 

         

     

    

    

8/16/2019 Structural analysis with finite elements.pdf

108/413

Te finite element 

99

  

 

  

                    

       

 

            

  

       

       

             

        

      

   

   

       

    

 

 

8/16/2019 Structural analysis with finite elements.pdf

109/413

Structural analysis with finite elements 

100

 

       

         

 

  

    

     

      

    

   

        

     

      

 

               

         

   

    

8/16/2019 Structural analysis with finite elements.pdf

110/413

Te finite element 

101

        

     

          

                 

     

         

    

   

 

 

8/16/2019 Structural analysis with finite elements.pdf

111/413

Structural analysis with finite elements 

102

 

 

   

 

8/16/2019 Structural analysis with finite elements.pdf

112/413

Te finite element 

103

   

       

  

 

8/16/2019 Structural analysis with finite elements.pdf

113/413

Structural analysis with finite elements 

104

 

 

 

 

   

 

 

8/16/2019 Structural analysis with finite elements.pdf

114/413

Te finite element 

105

 

    

 

     

   

 

 

 

 

  

   

 

    

 

     

8/16/2019 Structural analysis with finite elements.pdf

115/413

Structural analysis with finite elements 

106

 

 

  

8/16/2019 Structural analysis with finite elements.pdf

116/413

Te finite element 

107

 

 

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

117/413

Structural analysis with finite elements 

108

      

   

8/16/2019 Structural analysis with finite elements.pdf

118/413

Te finite element 

109

 

8/16/2019 Structural analysis with finite elements.pdf

119/413

Structural analysis with finite elements 

110

     

 

    

 

8/16/2019 Structural analysis with finite elements.pdf

120/413

Te finite element 

111

 

 

8/16/2019 Structural analysis with finite elements.pdf

121/413

Structural analysis with finite elements 

112

   

   

8/16/2019 Structural analysis with finite elements.pdf

122/413

Te finite element 

113

          

     

   

        

     

8/16/2019 Structural analysis with finite elements.pdf

123/413

Structural analysis with finite elements 

114

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

124/413

Te finite element 

115

  

 

  

 

 

 

 

 

 

 

  

 

   

  

 

 

    

 

     

 

           

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

125/413

Structural analysis with finite elements 

116

   

   

  

  

   

        

  

      

 

    

   

    

  

      

 

       

 

     

         

8/16/2019 Structural analysis with finite elements.pdf

126/413

Te finite element 

117

 

   

 

 

       

        

 

 

  

   

8/16/2019 Structural analysis with finite elements.pdf

127/413

8/16/2019 Structural analysis with finite elements.pdf

128/413

Te finite element 

119

 

   

       

 

   

 

      

              

  

 

  

8/16/2019 Structural analysis with finite elements.pdf

129/413

Structural analysis with finite elements 

120

 

 

    

 

 

 

 

     

 

                    

8/16/2019 Structural analysis with finite elements.pdf

130/413

Te finite element 

121

 

 

 

 

 

 

 

        

 

   

    

8/16/2019 Structural analysis with finite elements.pdf

131/413

8/16/2019 Structural analysis with finite elements.pdf

132/413

Structural analysis with finite elements © Tomas elford 2010

     

 

 

   

 

   

     

          

8/16/2019 Structural analysis with finite elements.pdf

133/413

Structural analysis with finite elements 

124

 

 

 

 

 

 

              

 

     

      

8/16/2019 Structural analysis with finite elements.pdf

134/413

 Assembly 

125

 

     

    

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

135/413

Structural analysis with finite elements 

126

   

      

  

 

 

    

   

 

   

   

 

  

  

8/16/2019 Structural analysis with finite elements.pdf

136/413

 Assembly 

127

 

         

          

       

                  

 

   

                     

       

       

        

8/16/2019 Structural analysis with finite elements.pdf

137/413

Structural analysis with finite elements 

128

             

                

   

               

   

        

         

      

    

    

      

 

  

       

8/16/2019 Structural analysis with finite elements.pdf

138/413

 Assembly 

129

       

 

   

 

       

     

           

      

 

    

         

       

  

              

      

    

                     

     

   

                  

        

8/16/2019 Structural analysis with finite elements.pdf

139/413

Structural analysis with finite elements 

130

 

        

 

    

 

   

 

    

       

   

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

140/413

 Assembly 

131

   

   

 

       

             

     

 

8/16/2019 Structural analysis with finite elements.pdf

141/413

Structural analysis with finite elements 

132

    

     

 

 

8/16/2019 Structural analysis with finite elements.pdf

142/413

 Assembly 

133

 

     

            

   

8/16/2019 Structural analysis with finite elements.pdf

143/413

Structural analysis with finite elements 

134

 

   

             

      

  

          

       

                               

                       

 

8/16/2019 Structural analysis with finite elements.pdf

144/413

 Assembly 

135

 

         

  

   

 

8/16/2019 Structural analysis with finite elements.pdf

145/413

Structural analysis with finite elements 

136

 

  

 

  

       

 

          

                                     

8/16/2019 Structural analysis with finite elements.pdf

146/413

 Assembly 

137

   

    

   

 

  

    

 

 

 

 

 

 

 

    

 

 

8/16/2019 Structural analysis with finite elements.pdf

147/413

Structural analysis with finite elements 

138

 

    

   

 

  

 

 

 

 

 

 

 

8/16/2019 Structural analysis with finite elements.pdf

148/413

 Assembly 

139

 

 

 

   

 

          

 

8/16/2019 Structural analysis with finite elements.pdf

149/413

Structural analysis with finite elements 

140

      

 

 

  

     

 

   

        

     

 

                               

 

8/16/2019 Structural analysis with finite elements.pdf

150/413

 Assembly 

141

    

 

8/16/2019 Structural analysis with finite elements.pdf

151/413

Structural analysis with finite elements 

142

     

 

   

8/16/2019 Structural analysis with finite elements.pdf

152/413

8/16/2019 Structural analysis with finite elements.pdf

153/413

Structural analysis with finite elements 

144

  

 

 

8/16/2019 Structural analysis with finite elements.pdf

154/413

 Actions 

145

 

    

8/16/2019 Structural analysis with finite elements.pdf

155/413

Structural analysis with finite elements 

146