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Speadsheet for 2-Dimensional Linear Elastic Problem

1. Purpose

This spreadsheet analyzes 2-dimensional linear elastic problems using Pronciple

2. Modelling

Modelling concept is same as finite element analysis.

The element types available in this speadsheet are Rod element, Trianglar eleme

3. Limitation

Number of Grids: 110 If you modify the spreadsheet, this limitation will be

Number of Elements: No limitation

Material Property: Orthotropic Materials

Element Types: Rod with 2 end points, "ROD"

Traiangular element with 3 grid points, "TRIA3"

Quadrilateral element with 4 grid points, "QUAD4"

Spring elements, "SPRING"

4. Instruction

4.1 Modelling

Modelling method is same as common finite element analysis.

(1) Grid Data

Define grid points.Input grid point coordinates (global coordinate system) in worksheet "grid_data".

(2) Element Data

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(2) Element Data

Put zeros "0" in "Displacement" columns in worksheet "grid_data".

Fill pink color to the "Displacement" columns with constraint.

(4) External Forces

Input external force data in "External Forces" columns (J and K) of worksheet "gri

4.2 Performing Analysis

Prepare "Solver". You need to add-in "Solver".

Select "Solver" in "Tool" fuction in worksheet "grid_data".

Set parameter columns for optomization in"Solver" setup. The columns are filled iExecute "Solver".

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Prepared by Toshimi Taki 5-May-07

f Minimum Potential Energy.

t, Quadrilateral element, and Spring element.

eliminated.

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_data".

pink color in Section 4.1 (3).

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2-Dimensional Linear Elastic Problem Grid Points and Result

Title: Truss -- Figure A2.22, Bruhn, p.A2.11Potential Energy by External Loa 212.8673

Total Strain Energy: 106.4337

Total Potential energy: -106.434

Grid No.

x y u v x' y' x

1 0 0 0 0 0 0 1

2 30 20 0.025213 -0.05422 30.02521264 19.94577578

3 30 0 0.0078 -0.05562 30.0078 -0.055624224

4 60 30 0.0244 -0.07392 60.02439951 29.92607921

5 60 0 0.0162 -0.07362 60.0162 -0.07362079

6 90 30 0.0175 -0.07407 90.0174995 29.92592823

7 90 0 0.0243 -0.07407 90.0243 -0.074071771

8 120 20 0.015415 -0.05503 120.0154155 19.94497431

9 120 0 0.0324 -0.05663 120.0324 -0.056625694

10 150 0 0.0396 0 150.0396 0

11

12

13

14

1516

17

18

Data

Instruction

Coordinates of Grid ConsCoordinates of Grid after

DeformationDisplacement

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34

35

36

37

38

39

40

41

42

4344

45

46

47

48

49

5051

52

53

54

55

56

5758

59

60

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75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

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5-May-07 by Toshimi Taki

Columns you need to input data

Target Column for "Solver"

Parameter Columns for "Solver". You need to change.

Potential Energy

by External Load

y x y Px Py

1 0 -500.0 1400.0

0 0.0 0.0

-500 27.81211195 0.0 -500.0

-1000 73.92079033 0.0 -1000.0

0 0.0 0.0

500 -1000 82.82152441 500.0 -1000.0

0 0.0 0.0

0 0.0 0.0

-500 28.31284711 0.0 -500.0

1 0 0.0 1600.0

traint External Forces and Reactions

(Output)

External Forces

(Input)

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Magnification of

Displacement: 50

x' y'

0 0

31.26063182 17.28878886

30.38999988 -2.781211195

61.21997533 26.30396048

60.80999993 -3.681039516

90.87497519 26.29641138

91.21499979 -3.703588554

120.7707726 17.24871531

121.6199999 -2.831284711

151.98 0

Data for Figure

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2-Dimensional Linear Elastic Problem Rod Elements on

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32 0 0 0 0 0 0 0 0

33 0 0 0 0 0 0 0 0

34 0 0 0 0 0 0 0 0

35 0 0 0 0 0 0 0 0

36 0 0 0 0 0 0 0 0

37 0 0 0 0 0 0 0 0

38 0 0 0 0 0 0 0 0

39 0 0 0 0 0 0 0 0

40 0 0 0 0 0 0 0 0

41 0 0 0 0 0 0 0 0

42 0 0 0 0 0 0 0 0

43 0 0 0 0 0 0 0 0

44 0 0 0 0 0 0 0 0

45 0 0 0 0 0 0 0 0

46 0 0 0 0 0 0 0 0

47 0 0 0 0 0 0 0 0

48 0 0 0 0 0 0 0 0

49 0 0 0 0 0 0 0 0

50 0 0 0 0 0 0 0 0

51 0 0 0 0 0 0 0 0

52 0 0 0 0 0 0 0 0

53 0 0 0 0 0 0 0 0

54 0 0 0 0 0 0 0 0

55 0 0 0 0 0 0 0 0

56 0 0 0 0 0 0 0 0

57 0 0 0 0 0 0 0 0

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73 0 0 0 0 0 0 0 0

74 0 0 0 0 0 0 0 0

75 0 0 0 0 0 0 0 0

76 0 0 0 0 0 0 0 0

77 0 0 0 0 0 0 0 0

78 0 0 0 0 0 0 0 0

79 0 0 0 0 0 0 0 0

80 0 0 0 0 0 0 0 0

81 0 0 0 0 0 0 0 0

82 0 0 0 0 0 0 0 0

83 0 0 0 0 0 0 0 0

84 0 0 0 0 0 0 0 0

85 0 0 0 0 0 0 0 0

86 0 0 0 0 0 0 0 0

87 0 0 0 0 0 0 0 0

88 0 0 0 0 0 0 0 0

89 0 0 0 0 0 0 0 0

90 0 0 0 0 0 0 0 0

91 0 0 0 0 0 0 0 0

92 0 0 0 0 0 0 0 0

93 0 0 0 0 0 0 0 0

94 0 0 0 0 0 0 0 0

95 0 0 0 0 0 0 0 0

96 0 0 0 0 0 0 0 0

97 0 0 0 0 0 0 0 0

98 0 0 0 0 0 0 0 0

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use Rod elements, put "on" in this column. If you don't use Rod elements, put "off" in

Total Strain Energy

Type of Elemet

Element No.

Grid No.

x y Px Py Cross Section Area

0 0 -500.0 1400.0 Young's Modulus

0 0 0.0 0.0 Direction of Element Coordinates

0 -500 0.0 -500.0 Strain Energy

0 -1000 0.0 -1000.0 Grid Coorinates

0 0 0.0 0.0 - Global Coordinate System

500 -1000 500.0 -1000.0

0 0 0.0 0.0

0 0 0.0 0.0 Length of Rod

0 -500 0.0 -500.0 Grid Coorinates after Deformation


0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0 Center of Element


0 0 0.0 0.0 Stress - 1->2 Direction

0 0 0.0 0.0 Grid Point Force

0 0 0 0 0 0 - Element Coordinate System

External Forces and

Reactions

External Forces

(Input)

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0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.00 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.00 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.00 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

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0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.00 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.00 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.00 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.00 0 0.0 0.0

0 0 0.0 0.0

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Grid Point Force, y-direction

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Direction Cosine 1-->2

Grid Point Coordinates - Element Coordinate System

Displacement of Grid

- Element Coordinate System

Element Stiffness Matrix

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n=2

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this column,

106.434

ROD ROD ROD ROD ROD ROD ROD

1 2 3 4 5 6 7

1 1 1 2 2 3 3 4

2 2 3 3 4 4 5 5

A 1 1 1 1 1 1 1

E 1E+07 1E+07 1E+07 1E+07 1E+07 1E+07 1E+07

phi (deg) 33.6901 0 -90 18.4349 45 0 -90

U 11.4837 10.14 0.49 7.74759 0.16971 11.76 0.015

x1 0 0 30 30 30 30 60

y1 0 0 20 20 0 0 30

x2 30 30 30 60 60 60 60

y2 20 0 0 30 30 0 0

L 36.0555 30 20 31.6228 42.4264 30 30

x1' 0 0 30.0252 30.0252 30.0078 30.0078 60.0244

y1' 0 0 19.9458 19.9458 -0.0556 -0.0556 29.9261

x2' 30.0252 30.0078 30.0078 60.0244 60.0244 60.0162 60.0162

y2' 19.9458 -0.0556 -0.0556 29.9261 29.9261 -0.0736 -0.0736

x0 15 15 30 45 45 45 60

y0 10 0 10 25 15 0 15

f1 -2523.9 2600 700.001 -2213.6 -282.84 2800 -100

Fe 11 2523.89 -2600 -700 2213.6 282.843 -2800 100

12 0 0 0 0 0 0 0

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9 0.0 0.0 0.0 0.0 0.0 0.0 0.0

10 0.0 0.0 0.0 0.0 0.0 0.0 0.0

11 0.0 0.0 0.0 0.0 0.0 0.0 0.012 0.0 0.0 0.0 0.0 0.0 0.0 0.0

13 0.0 0.0 0.0 0.0 0.0 0.0 0.0

14 0.0 0.0 0.0 0.0 0.0 0.0 0.0

15 0.0 0.0 0.0 0.0 0.0 0.0 0.0

16 0.0 0.0 0.0 0.0 0.0 0.0 0.0

17 0.0 0.0 0.0 0.0 0.0 0.0 0.0

18 0.0 0.0 0.0 0.0 0.0 0.0 0.019 0.0 0.0 0.0 0.0 0.0 0.0 0.0

20 0.0 0.0 0.0 0.0 0.0 0.0 0.0

21 0.0 0.0 0.0 0.0 0.0 0.0 0.0

22 0.0 0.0 0.0 0.0 0.0 0.0 0.0

23 0.0 0.0 0.0 0.0 0.0 0.0 0.0

24 0.0 0.0 0.0 0.0 0.0 0.0 0.0

25 0.0 0.0 0.0 0.0 0.0 0.0 0.026 0.0 0.0 0.0 0.0 0.0 0.0 0.0

27 0.0 0.0 0.0 0.0 0.0 0.0 0.0

28 0.0 0.0 0.0 0.0 0.0 0.0 0.0

29 0.0 0.0 0.0 0.0 0.0 0.0 0.0

30 0.0 0.0 0.0 0.0 0.0 0.0 0.0

31 0.0 0.0 0.0 0.0 0.0 0.0 0.0

32 0.0 0.0 0.0 0.0 0.0 0.0 0.033 0.0 0.0 0.0 0.0 0.0 0.0 0.0

34 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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50 0.0 0.0 0.0 0.0 0.0 0.0 0.0

51 0.0 0.0 0.0 0.0 0.0 0.0 0.0

52 0.0 0.0 0.0 0.0 0.0 0.0 0.053 0.0 0.0 0.0 0.0 0.0 0.0 0.0

54 0.0 0.0 0.0 0.0 0.0 0.0 0.0

55 0.0 0.0 0.0 0.0 0.0 0.0 0.0

56 0.0 0.0 0.0 0.0 0.0 0.0 0.0

57 0.0 0.0 0.0 0.0 0.0 0.0 0.0

58 0.0 0.0 0.0 0.0 0.0 0.0 0.0

59 0.0 0.0 0.0 0.0 0.0 0.0 0.060 0.0 0.0 0.0 0.0 0.0 0.0 0.0

61 0.0 0.0 0.0 0.0 0.0 0.0 0.0

62 0.0 0.0 0.0 0.0 0.0 0.0 0.0

63 0.0 0.0 0.0 0.0 0.0 0.0 0.0

64 0.0 0.0 0.0 0.0 0.0 0.0 0.0

65 0.0 0.0 0.0 0.0 0.0 0.0 0.0

66 0.0 0.0 0.0 0.0 0.0 0.0 0.067 0.0 0.0 0.0 0.0 0.0 0.0 0.0

68 0.0 0.0 0.0 0.0 0.0 0.0 0.0

69 0.0 0.0 0.0 0.0 0.0 0.0 0.0

70 0.0 0.0 0.0 0.0 0.0 0.0 0.0

71 0.0 0.0 0.0 0.0 0.0 0.0 0.0

72 0.0 0.0 0.0 0.0 0.0 0.0 0.0

73 0.0 0.0 0.0 0.0 0.0 0.0 0.074 0.0 0.0 0.0 0.0 0.0 0.0 0.0

75 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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91 0.0 0.0 0.0 0.0 0.0 0.0 0.0

92 0.0 0.0 0.0 0.0 0.0 0.0 0.0

93 0.0 0.0 0.0 0.0 0.0 0.0 0.094 0.0 0.0 0.0 0.0 0.0 0.0 0.0

95 0.0 0.0 0.0 0.0 0.0 0.0 0.0

96 0.0 0.0 0.0 0.0 0.0 0.0 0.0

97 0.0 0.0 0.0 0.0 0.0 0.0 0.0

98 0.0 0.0 0.0 0.0 0.0 0.0 0.0

99 0.0 0.0 0.0 0.0 0.0 0.0 0.0

100 0.0 0.0 0.0 0.0 0.0 0.0 0.0101 0.0 0.0 0.0 0.0 0.0 0.0 0.0

102 0.0 0.0 0.0 0.0 0.0 0.0 0.0

103 0.0 0.0 0.0 0.0 0.0 0.0 0.0

104 0.0 0.0 0.0 0.0 0.0 0.0 0.0

105 0.0 0.0 0.0 0.0 0.0 0.0 0.0

106 0.0 0.0 0.0 0.0 0.0 0.0 0.0

107 0.0 0.0 0.0 0.0 0.0 0.0 0.0108 0.0 0.0 0.0 0.0 0.0 0.0 0.0

109 0.0 0.0 0.0 0.0 0.0 0.0 0.0

110 0.0 0.0 0.0 0.0 0.0 0.0 0.0

1 1400.0 0.0 0.0 0.0 0.0 0.0 0.0

2 -1400.0 0.0 700.0 700.0 0.0 0.0 0.0

3 0.0 0.0 -700.0 0.0 200.0 0.0 0.0

4 0.0 0.0 0.0 -700.0 -200.0 0.0 -100.05 0.0 0.0 0.0 0.0 0.0 0.0 100.0

6 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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22 0.0 0.0 0.0 0.0 0.0 0.0 0.0

23 0.0 0.0 0.0 0.0 0.0 0.0 0.0

24 0.0 0.0 0.0 0.0 0.0 0.0 0.025 0.0 0.0 0.0 0.0 0.0 0.0 0.0

26 0.0 0.0 0.0 0.0 0.0 0.0 0.0

27 0.0 0.0 0.0 0.0 0.0 0.0 0.0

28 0.0 0.0 0.0 0.0 0.0 0.0 0.0

29 0.0 0.0 0.0 0.0 0.0 0.0 0.0

30 0.0 0.0 0.0 0.0 0.0 0.0 0.0

31 0.0 0.0 0.0 0.0 0.0 0.0 0.032 0.0 0.0 0.0 0.0 0.0 0.0 0.0

33 0.0 0.0 0.0 0.0 0.0 0.0 0.0

34 0.0 0.0 0.0 0.0 0.0 0.0 0.0

35 0.0 0.0 0.0 0.0 0.0 0.0 0.0

36 0.0 0.0 0.0 0.0 0.0 0.0 0.0

37 0.0 0.0 0.0 0.0 0.0 0.0 0.0

38 0.0 0.0 0.0 0.0 0.0 0.0 0.039 0.0 0.0 0.0 0.0 0.0 0.0 0.0

40 0.0 0.0 0.0 0.0 0.0 0.0 0.0

41 0.0 0.0 0.0 0.0 0.0 0.0 0.0

42 0.0 0.0 0.0 0.0 0.0 0.0 0.0

43 0.0 0.0 0.0 0.0 0.0 0.0 0.0

44 0.0 0.0 0.0 0.0 0.0 0.0 0.0

45 0.0 0.0 0.0 0.0 0.0 0.0 0.046 0.0 0.0 0.0 0.0 0.0 0.0 0.0

47 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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63 0.0 0.0 0.0 0.0 0.0 0.0 0.0

64 0.0 0.0 0.0 0.0 0.0 0.0 0.0

65 0.0 0.0 0.0 0.0 0.0 0.0 0.066 0.0 0.0 0.0 0.0 0.0 0.0 0.0

67 0.0 0.0 0.0 0.0 0.0 0.0 0.0

68 0.0 0.0 0.0 0.0 0.0 0.0 0.0

69 0.0 0.0 0.0 0.0 0.0 0.0 0.0

70 0.0 0.0 0.0 0.0 0.0 0.0 0.0

71 0.0 0.0 0.0 0.0 0.0 0.0 0.0

72 0.0 0.0 0.0 0.0 0.0 0.0 0.073 0.0 0.0 0.0 0.0 0.0 0.0 0.0

74 0.0 0.0 0.0 0.0 0.0 0.0 0.0

75 0.0 0.0 0.0 0.0 0.0 0.0 0.0

76 0.0 0.0 0.0 0.0 0.0 0.0 0.0

77 0.0 0.0 0.0 0.0 0.0 0.0 0.0

78 0.0 0.0 0.0 0.0 0.0 0.0 0.0

79 0.0 0.0 0.0 0.0 0.0 0.0 0.080 0.0 0.0 0.0 0.0 0.0 0.0 0.0

81 0.0 0.0 0.0 0.0 0.0 0.0 0.0

82 0.0 0.0 0.0 0.0 0.0 0.0 0.0

83 0.0 0.0 0.0 0.0 0.0 0.0 0.0

84 0.0 0.0 0.0 0.0 0.0 0.0 0.0

85 0.0 0.0 0.0 0.0 0.0 0.0 0.0

86 0.0 0.0 0.0 0.0 0.0 0.0 0.087 0.0 0.0 0.0 0.0 0.0 0.0 0.0

88 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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104 0.0 0.0 0.0 0.0 0.0 0.0 0.0

105 0.0 0.0 0.0 0.0 0.0 0.0 0.0

106 0.0 0.0 0.0 0.0 0.0 0.0 0.0107 0.0 0.0 0.0 0.0 0.0 0.0 0.0

108 0.0 0.0 0.0 0.0 0.0 0.0 0.0

109 0.0 0.0 0.0 0.0 0.0 0.0 0.0

110 0.0 0.0 0.0 0.0 0.0 0.0 0.0

m 0.83205 1 0 0.94868 0.70711 1 0

n 0.5547 0 -1 0.31623 0.70711 0 -1

xe1 0 0 0 0 0 0 0ye1 0 0 0 0 0 0 0

xe2 36.0555 30 20 31.6228 42.4264 30 30

ye2 0 0 0 0 0 0 0

xe1' 0 0 0.05422 0.00677 -0.0338 0.0078 0.07392

ye1' 0 0 0.02521 -0.0594 -0.0448 -0.0556 0.0244

xe2' 36.0464 30.0078 20.0556 31.6225 42.3914 30.0162 30.0736

ye2' -0.0591 -0.0556 0.0078 -0.0778 -0.0695 -0.0736 0.0162u1 0 0 0.05422 0.00677 -0.0338 0.0078 0.07392

v1 0 0 0.02521 -0.0594 -0.0448 -0.0556 0.0244

u2 -0.0091 0.0078 0.05562 -0.0002 -0.035 0.0162 0.07362

v2 -0.0591 -0.0556 0.0078 -0.0778 -0.0695 -0.0736 0.0162

[K]_e 11 277350 333333 500000 316228 235702 333333 333333

12 0 0 0 0 0 0 0

13 -277350 -333333 -500000 -316228 -235702 -333333 -33333314 0 0 0 0 0 0 0

21 0 0 0 0 0 0 0

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J

J-1

det[J]

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dN4/dy

[B]

[D][B]

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1

2

3

4

J

J-1

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dN1/dy

dN2/dy

dN3/dydN4/dy

[B]

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0.0 0.0 0.0 0.0 0.0 -300.0 2700.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 -2400.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.00.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0

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30 42.4264 30 30 31.6228 42.4264 30 20 36.0555

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333333 235702 333333 333333 316228 235702 333333 500000 277350

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0 0 0 0 0 0 0 0 0

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ROD

17

9

10

1

1E+07

0

8.64

120

0

150

0

30

120.032

-0.0566

150.04

0

135

0

2400

-2400

0

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-2400.0

2400.0

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0.0

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1

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2-Dimensional Linear Elastic Problem Triangular Elements off

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2 Dimensional Linear Elastic Problem Triangular Elements off

Grid No.

x y u v x' y' x

1 0 0 0 0 0 0 1

2 30 20 0.02521 -0.0542 30.02521264 19.94577578 0

3 30 0 0.0078 -0.0556 30.0078 -0.05562422 0

4 60 30 0.0244 -0.0739 60.02439951 29.92607921 0

5 60 0 0.0162 -0.0736 60.0162 -0.07362079 0

6 90 30 0.0175 -0.0741 90.0174995 29.92592823 0

7 90 0 0.0243 -0.0741 90.0243 -0.07407177 0

8 120 20 0.01542 -0.055 120.0154155 19.94497431 0

9 120 0 0.0324 -0.0566 120.0324 -0.05662569 0

10 150 0 0.0396 0 150.0396 0 0

11 0 0 0 0 0 0 0

12 0 0 0 0 0 0 0

13 0 0 0 0 0 0 0

14 0 0 0 0 0 0 0

15 0 0 0 0 0 0 0

16 0 0 0 0 0 0 0

17 0 0 0 0 0 0 0



32 0 0 0 0 0 0 0

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33 0 0 0 0 0 0 0

34 0 0 0 0 0 0 0

35 0 0 0 0 0 0 036 0 0 0 0 0 0 0

37 0 0 0 0 0 0 0

38 0 0 0 0 0 0 0

39 0 0 0 0 0 0 0

40 0 0 0 0 0 0 0

41 0 0 0 0 0 0 0

42 0 0 0 0 0 0 043 0 0 0 0 0 0 0

44 0 0 0 0 0 0 0

45 0 0 0 0 0 0 0

46 0 0 0 0 0 0 0

47 0 0 0 0 0 0 0

48 0 0 0 0 0 0 0

49 0 0 0 0 0 0 050 0 0 0 0 0 0 0

51 0 0 0 0 0 0 0

52 0 0 0 0 0 0 0

53 0 0 0 0 0 0 0

54 0 0 0 0 0 0 0

55 0 0 0 0 0 0 0

56 0 0 0 0 0 0 057 0 0 0 0 0 0 0

73 0 0 0 0 0 0 0

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74 0 0 0 0 0 0 0

75 0 0 0 0 0 0 0

76 0 0 0 0 0 0 077 0 0 0 0 0 0 0

78 0 0 0 0 0 0 0

79 0 0 0 0 0 0 0

80 0 0 0 0 0 0 0

81 0 0 0 0 0 0 0

82 0 0 0 0 0 0 0

83 0 0 0 0 0 0 084 0 0 0 0 0 0 0

85 0 0 0 0 0 0 0

86 0 0 0 0 0 0 0

87 0 0 0 0 0 0 0

88 0 0 0 0 0 0 0

89 0 0 0 0 0 0 0

90 0 0 0 0 0 0 091 0 0 0 0 0 0 0

92 0 0 0 0 0 0 0

93 0 0 0 0 0 0 0

94 0 0 0 0 0 0 0

95 0 0 0 0 0 0 0

96 0 0 0 0 0 0 0

97 0 0 0 0 0 0 098 0 0 0 0 0 0 0

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Total Strain Energy

Type of Element

Element No.

Grid No.

y x y Px Py

1 0 0 0.0 0.0 Thickness

0 0 0 0.0 0.0 Material Properties - Material Axis

0 0 -500 0.0 0.0

0 0 -1000 0.0 0.0

0 0 0 0.0 0.0

0 500 -1000 0.0 0.0 Direction of Material Axis - Global Coo

0 0 0 0.0 0.0 Direction of Element Coord.

0 0 0 0.0 0.0 Strain Energy

0 0 -500 0.0 0.0 Grid Coorinates before Deformation

1 0 0 0.0 0.0 - Global Coordinate System

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0 Grid Coorinates after Deformation

0 0 0 0.0 0.0 - Global Coordinate System

0 0 0 0 0 0 0

traint External Forces and

Reactions

External Forces

(Input)

0 0 0 0.0 0.0

0 0 0 0 0 0 0

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0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0 Grid Point Force0 0 0 0.0 0.0 - Global Coordinate System

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0 Grid Point Force, x-direction

0 0 0 0.0 0.00 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.00 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.00 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0 0 0 0

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0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.00 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.00 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.00 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.00 0 0 0.0 0.0

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Direction Cosine 1-->2

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Stiffeness - Material Axis

Stiffeness - Element Coordinate Syste

Element Stiffness Matrix

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nts, put "off" in this column,

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0

TRIA3

4

1 3

2 4

3 17

t 1

E1 7000

E2 7000

v12 0.3

G12 2692

theta (deg) 0

phi (deg) 45

U 4.608064

x1 30

y1 0

x2 60

y2 30

x3 0

y3 0

x1' 30.0078

y1' -0.05562

x2' 60 0244

22 152.448

31 56.21325

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32 248.6827

Fe 1x 199.12251y -368.162

2x -63.0261

2y 152.5679

3x -136.096

3y 215.594

1 0.0

2 0.03 199.1

4 -63.0

5 0.0

6 0.0

7 0.0

8 0.0

9 0.010 0.0

11 0.0

12 0.0

13 0.0

14 0.0

15 0.0

16 0.017 -136.1

33 0.0

34 0.0

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35 0.0

36 0.037 0.0

38 0.0

39 0.0

40 0.0

41 0.0

42 0.0

43 0.044 0.0

45 0.0

46 0.0

47 0.0

48 0.0

49 0.0

50 0.051 0.0

52 0.0

53 0.0

54 0.0

55 0.0

56 0.0

57 0.058 0.0

74 0.0

75 0.0

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76 0.0

77 0.078 0.0

79 0.0

80 0.0

81 0.0

82 0.0

83 0.0

84 0.085 0.0

86 0.0

87 0.0

88 0.0

89 0.0

90 0.0

91 0.092 0.0

93 0.0

94 0.0

95 0.0

96 0.0

97 0.0

98 0.099 0.0

5 0.0

6 0.0

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7 0.0

8 0.09 0.0

10 0.0

11 0.0

12 0.0

13 0.0

14 0.0

15 0.016 0.0

17 215.6

18 0.0

19 0.0

20 0.0

21 0.0

22 0.023 0.0

24 0.0

25 0.0

26 0.0

27 0.0

28 0.0

29 0.030 0.0

46 0.0

47 0.0

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48 0.0

49 0.050 0.0

51 0.0

52 0.0

53 0.0

54 0.0

55 0.0

56 0.057 0.0

58 0.0

59 0.0

60 0.0

61 0.0

62 0.0

63 0.064 0.0

65 0.0

66 0.0

67 0.0

68 0.0

69 0.0

70 0.071 0.0

87 0.0

88 0.0

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89 0.0

90 0.091 0.0

92 0.0

93 0.0

94 0.0

95 0.0

96 0.0

97 0.098 0.0

99 0.0

100 0.0

101 0.0

102 0.0

103 0.0

104 0.0105 0.0

106 0.0

107 0.0

108 0.0

109 0.0

110 0.0

m 0.707107n 0.707107

u2 -0.03502

v2 -0.06952

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u3 0

v3 0Q11 7692.308

Q12 2307.692

Q22 7692.308

Q66 2692

m 0.707107

n -0.70711

Qxx 7692Qxy 2308

Qxs -5.6E-14

Qyx 2308

Qyy 7692

Qys 5.55E-14

Qsx -5.6E-14

Qsy 5.55E-14Qss 2692.308

[K]_e 11 7980.692

12 3750.231

13 -3942.23

14 -2596.23

15 -4038.46

16 -115421 3750.231

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36 0

[D][B] 11 -181.302

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12 -163.2

13 181.302214 54.40008

15 -2.6E-15

16 108.8002

21 -54.4001

22 -543.907

23 54.40008

24 181.302225 2.62E-15

26 362.6044

31 -190.375

32 -63.4583

33 63.4583

34 63.4583

35 126.916636 2.62E-15

[D][B][d] 1 3.319538

2 11.72301

3 2.649918

[d][B]T 1 -2.8E-05

2 0.001533

3 0.000984[B]T[D][B] 11 17.73487

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2-Dimensional Linear Elastic Problem Quad. Elements off

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Grid No.

x y u v x' y' x y

1 0 0 0 0 0 0 1 1

2 30 20 0.02521 -0.0542 30.025213 19.945776 0 03 30 0 0.0078 -0.0556 30.0078 -0.0556242 0 0

4 60 30 0.0244 -0.0739 60.0244 29.926079 0 0

5 60 0 0.0162 -0.0736 60.0162 -0.0736208 0 0

6 90 30 0.0175 -0.0741 90.0175 29.925928 0 0

7 90 0 0.0243 -0.0741 90.0243 -0.0740718 0 0

8 120 20 0.01542 -0.055 120.01542 19.944974 0 0

9 120 0 0.0324 -0.0566 120.0324 -0.0566257 0 010 150 0 0.0396 0 150.0396 0 0 1

11 0 0 0 0 0 0 0 0

12 0 0 0 0 0 0 0 0

13 0 0 0 0 0 0 0 0

14 0 0 0 0 0 0 0 0

15 0 0 0 0 0 0 0 0

16 0 0 0 0 0 0 0 017 0 0 0 0 0 0 0 0

Coordinates of Grid ConstraintCoordinates of Grid after


32 0 0 0 0 0 0 0 0

33 0 0 0 0 0 0 0 0

34 0 0 0 0 0 0 0 0

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34 0 0 0 0 0 0 0 0

35 0 0 0 0 0 0 0 0

36 0 0 0 0 0 0 0 0

37 0 0 0 0 0 0 0 0

38 0 0 0 0 0 0 0 0

39 0 0 0 0 0 0 0 0

40 0 0 0 0 0 0 0 0

41 0 0 0 0 0 0 0 0

42 0 0 0 0 0 0 0 0

43 0 0 0 0 0 0 0 0

44 0 0 0 0 0 0 0 0

45 0 0 0 0 0 0 0 0

46 0 0 0 0 0 0 0 0

47 0 0 0 0 0 0 0 0

48 0 0 0 0 0 0 0 0

49 0 0 0 0 0 0 0 0

50 0 0 0 0 0 0 0 0

51 0 0 0 0 0 0 0 0

52 0 0 0 0 0 0 0 0

53 0 0 0 0 0 0 0 0

54 0 0 0 0 0 0 0 0

55 0 0 0 0 0 0 0 0

56 0 0 0 0 0 0 0 057 0 0 0 0 0 0 0 0

73 0 0 0 0 0 0 0 0

74 0 0 0 0 0 0 0 0

75 0 0 0 0 0 0 0 0

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75 0 0 0 0 0 0 0 0

76 0 0 0 0 0 0 0 0

77 0 0 0 0 0 0 0 0

78 0 0 0 0 0 0 0 0

79 0 0 0 0 0 0 0 0

80 0 0 0 0 0 0 0 0

81 0 0 0 0 0 0 0 0

82 0 0 0 0 0 0 0 0

83 0 0 0 0 0 0 0 0

84 0 0 0 0 0 0 0 0

85 0 0 0 0 0 0 0 0

86 0 0 0 0 0 0 0 0

87 0 0 0 0 0 0 0 0

88 0 0 0 0 0 0 0 0

89 0 0 0 0 0 0 0 0

90 0 0 0 0 0 0 0 0

91 0 0 0 0 0 0 0 0

92 0 0 0 0 0 0 0 0

93 0 0 0 0 0 0 0 0

94 0 0 0 0 0 0 0 0

95 0 0 0 0 0 0 0 0

96 0 0 0 0 0 0 0 0

97 0 0 0 0 0 0 0 0

98 0 0 0 0 0 0 0 0

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u use Quad. elements, put "on" in this column. If you don't use Quad. elements, p

Total Strain Energy

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gy

Type of ElemetElement No.

Grid No.

x y Px Py

0 0 0.0 0.0

0 0 0.0 0.0 Thickness0 -500 0.0 0.0 Material Properties - Material Axis

0 -1000 0.0 0.0

0 0 0.0 0.0

500 -1000 0.0 0.0

0 0 0.0 0.0 Direction of Material Axis - Global Coo

0 0 0.0 0.0 Direction of Element Coord.

0 -500 0.0 0.0 Strain Energy0 0 0.0 0.0 Grid Coorinates before Deformation


0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.00 0 0.0 0.0

External Forces and

Reactions

External Forces

(Input)


0 0 0.0 0.0


0 0 0 0 0 0 El t C di t S t

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0 0 0.0 0.0 - Element Coordinate System

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0



0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0 Grid Point Force, x-direction

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0 0 0 0

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0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

0 0 0.0 0.0

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Grid Point Force, y-direction

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Grid Point Coordinates after Defomati


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Displacement of Grid


Stiffeness - Material Axis

Stiffeness - Element Coordinate Syste

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Center of Element

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NumericaL Integration Points, n=2

NumericaL Integration Point 1

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[B][D]

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[B][D]

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t "off" in this column,

0

QUAD4

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1

1 1

2 3

3 5

4 2

t 1

E1 7000

E2 7000

v12 0.3

G12 2692

theta (deg) 0

phi (deg) 0

U 2.40351

x1 0

y1 0

x2 30

y2 0

x3 60

y3 0

x4 30

y4 20

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24 0.0

25 0.0

26 0.0

27 0.0

28 0 0

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28 0.0

29 0.0

30 0.0

31 0.0

32 0.0

33 0.0

34 0.0

35 0.0

36 0.0

37 0.0

38 0.0

39 0.0

40 0.0

41 0.0

42 0.0

43 0.0

44 0.0

45 0.0

46 0.0

47 0.0

48 0.0

49 0.0

65 0.0

66 0.0

67 0.0

68 0.0

69 0 0

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69 0.0

70 0.0

71 0.0

72 0.0

73 0.0

74 0.0

75 0.0

76 0.0

77 0.0

78 0.0

79 0.0

80 0.0

81 0.0

82 0.0

83 0.0

84 0.0

85 0.0

86 0.0

87 0.0

88 0.0

89 0.0

90 0.0

106 0.0

107 0.0

108 0.0

109 0.0

110 0 0

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110 0.0

1 120.9

2 34.8

3 -257.6

4 0.0

5 101.8

6 0.0

7 0.0

8 0.0

9 0.0

10 0.0

11 0.0

12 0.0

13 0.0

14 0.0

15 0.0

16 0.0

17 0.0

18 0.0

19 0.0

20 0.0

21 0.0

37 0.0

38 0.0

39 0.0

40 0.0

41 0 0

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41 0.0

42 0.0

43 0.0

44 0.0

45 0.0

46 0.0

47 0.0

48 0.0

49 0.0

50 0.0

51 0.0

52 0.0

53 0.0

54 0.0

55 0.0

56 0.0

57 0.0

58 0.0

59 0.0

60 0.0

61 0.0

62 0.0

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xe4 30

ye4 20

xe1' 0

ye1' 0

xe2' 30 0078

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xe2' 30.0078

ye2' -0.0556

xe3' 60.0162

ye3' -0.0736

xe4' 30.0252

ye4' 19.9458

u1 0

v1 0

u2 0.0078

v2 -0.0556

u3 0.0162

v3 -0.0736

u4 0.02521

v4 -0.0542

Q11 7692.31

Q12 2307.69

Q22 7692.31

Q66 2692

m 1

n 0

Qxx 7692.31

Qxy 2307.69

21 0

22 3408.06

23 1346

24 -5918.8

25 2 1E 14

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25 2.1E-14

26 2510.73

27 -1346

28 0

31 -2446.4

32 1346

33 8930.7

34 0

35 -2446.4

36 -1346

37 -4038

38 0

41 1153.85

42 -5918.8

43 0

44 23376

45 -1153.8

46 -5918.8

47 0

48 -11538

51 -58.876

52 -4E-15

72 -1346

73 -4038

74 0

75 0

76 1346

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76 1346

77 4038

78 0

81 -1153.8

82 -2E-13

83 0

84 -11538

85 1153.85

86 -2E-13

87 0

88 11538.5

x 0

h 0

J 11 15

12 -5

21 15

22 5

J-1 11 0.03333

12 0.03333

21 -0.1

22 0.1

det[J] 150

dN4/dy 0.05

[B] 11 -0.0167

12 0

13 0

14 0

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14 0

15 0.01667

16 0

17 0

18 0

21 0

22 0

23 0

24 -0.05

25 0

26 0

27 0

28 0.05

31 0

32 -0.0167

33 -0.05

34 0

35 0

36 0.01667

37 0.05

38 0

[D][B] 11 -128.21

31 0

32 -44.867

33 -134.6

34 0

35 0

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35 0

36 44.8667

37 134.6

38 0

1 x -0.5774

h -0.5774

H 1

2 x 0.57735

h -0.5774

H 1

3 x -0.5774

h 0.57735

H 1

4 x 0.57735

h 0.57735

H 1

J 11 15

12 -2.1132

21 15

22 7.88675

J-1 11 0.05258

12 0.01409

dN1/dy 0

dN2/dy -0.05

dN3/dy 0

dN4/dy 0.05

[B] 11 -0 0263

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[B] 11 -0.0263

12 0

13 0.01925

14 0

15 0.00704

16 0

17 0

18 0

21 0

22 0

23 0

24 -0.05

25 0

26 0

27 0

28 0.05

31 0

32 -0.0263

33 -0.05

34 0.01925

35 0

36 0.00704

17 0

18 115.385

21 -60.667

22 0

23 44 4116

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23 44.4116

24 -384.62

25 16.2558

26 0

27 0

28 384.615

31 0

32 -70.77

33 -134.6

34 51.8076

35 0

36 18.9629

37 134.6

38 0

[B]*H*det[J] 11 797.447

12 0

13 -583.77

14 455.005

15 -213.68

16 0

17 0

18 -455

38 333.087

41 455.005

42 -204.3

43 -721.64

44 3034 17

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44 3034.17

45 -121.92

46 54.7411

47 388.557

48 -2884.6

51 -213.68

52 0

53 156.421

54 -121.92

55 57.2541

56 0

57 0

58 121.918

61 0

62 -74.778

63 -142.22

64 54.7411

65 0

66 20.0366

67 142.222

68 0

71 0

J 11 15

12 -2.1132

21 15

22 2.11325

J-1 11 0.03333

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J 1 11 0.03333

12 0.03333

21 -0.2366

22 0.2366

det[J] 63.3975

dN1/dx -0.3943

dN2/dx 0.39434

dN3/dx 0.10566

dN4/dx -0.1057

dN1/dh -0.1057

dN2/dh -0.3943

dN3/dh 0.39434

dN4/dh 0.10566

dN1/dx -0.0167

dN2/dx 0

dN3/dx 0.01667

dN4/dx 0

dN1/dy 0.0683

dN2/dy -0.1866

dN3/dy 0.0683

dN4/dy 0.05

[B] 11 -0.0167

31 0.0683

32 -0.0167

33 -0.1866

34 0

35 0.0683

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35 0.0683

36 0.01667

37 0.05

38 0

[B](d) 1 0.00027

2 0.00264

3 -0.0003

[D][B](d) 1 8.16927

2 20.9309

3 -0.8491

U2 1.83001

[D][B] 11 -128.21

12 157.618

13 0

14 -430.62

15 128.205

16 157.618

17 0

18 115.385

21 -38.462

22 525.394

23 0

13 -2175.2

14 455.005

15 660.703

16 27.735

17 582.835

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58 835

18 -121.92

21 -360.82

22 2322.43

23 530.778

24 -6215.5

25 -27.735

26 2227.62

27 -142.22

28 1665.43

31 -2175.2

32 530.778

33 5942.68

34 0

35 -2175.2

36 -530.78

37 -1592.3

38 0

41 455.005

42 -6215.5

43 0

44 16981

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16 -42.234

17 0

18 115.385

21 -38.462

22 -140.78

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23 0

24 -103.06

25 38.4615

26 -140.78

27 0

28 384.615

31 -49.26732 -44.867

33 -36.066

34 0

35 -49.267

36 44.8667

37 134.6

38 0[B]*H*det[J] 11 718.893

12 360.822

13 156.17

14 121.918

15 -292.23

16 -27.735

17 -582.84

37 -426.66

38 0

41 121.918

42 446.252

43 0

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44 326.679

45 -121.92

46 446.252

47 0

48 -1219.2

51 -292.23

52 27.73553 156.17

54 -121.92

55 718.893

56 -360.82

57 -582.84

58 455.005

61 -27.73562 432.665

63 -142.22

64 446.252

65 -360.82

66 786.517

67 530.778

68 -1665.4

88 4550.05

J 11 15

12 -7.8868

21 15

22 2.11325

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J-1 11 0.01409

12 0.05258

21 -0.1

22 0.1

det[J] 150

dN1/dx -0.1057

dN2/dx 0.10566

dN3/dx 0.39434

dN4/dx -0.3943

dN1/dh -0.1057

dN2/dh -0.3943

dN3/dh 0.39434

dN4/dh 0.10566

dN1/dx -0.007dN2/dx -0.0192

dN3/dx 0.02629

dN4/dx 0

dN1/dy 0

dN2/dy -0.05

dN3/dy 0

dN4/dy 0.05

28 0.05

31 0

32 -0.007

33 -0.05

34 -0.0192

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35 0

36 0.02629

37 0.05

38 0

[B](d) 1 0.00028

2 7E-05

3 5.7E-06[D][B](d) 1 2.28287

2 1.17486

3 0.01532

U4 0.05339

[D][B] 11 -54.186

12 0

13 -148.0414 -115.38

15 202.224

16 0

17 0

18 115.385

21 -16.256

22 0

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63 -530.78

64 -204.3

65 0

66 279.074

67 530.778

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68 0

71 0

72 -142.22

73 -1009.5

74 -388.56

75 0

76 530.77877 1009.5

78 0

81 -121.92

82 0

83 -333.09

84 -2884.6

85 455.00586 0

87 0

88 2884.62

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2-Dimensional Linear Elastic Problem Spring Elements off

Grid No.

x y u v x' y' x

1 0 0 0 0 0 0 1

2 30 20 0.02521 -0.0542 30.0252126 19.9457758 0

3 30 0 0.0078 -0.0556 30.0078 -0.0556242 0



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4 60 30 0.0244 -0.0739 60.0243995 29.9260792 05 60 0 0.0162 -0.0736 60.0162 -0.0736208 0

6 90 30 0.0175 -0.0741 90.0174995 29.9259282 0

7 90 0 0.0243 -0.0741 90.0243 -0.0740718 0

8 120 20 0.01542 -0.055 120.015415 19.9449743 0

9 120 0 0.0324 -0.0566 120.0324 -0.0566257 0

10 150 0 0.0396 0 150.0396 0 0

11 0 0 0 0 0 0 012 0 0 0 0 0 0 0

13 0 0 0 0 0 0 0

14 0 0 0 0 0 0 0

15 0 0 0 0 0 0 0

16 0 0 0 0 0 0 0

17 0 0 0 0 0 0 0

32 0 0 0 0 0 0 0

33 0 0 0 0 0 0 0

34 0 0 0 0 0 0 0

35 0 0 0 0 0 0 0

36 0 0 0 0 0 0 0

37 0 0 0 0 0 0 0

38 0 0 0 0 0 0 0

39 0 0 0 0 0 0 0

40 0 0 0 0 0 0 0

41 0 0 0 0 0 0 0

42 0 0 0 0 0 0 0

43 0 0 0 0 0 0 0

44 0 0 0 0 0 0 0

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44 0 0 0 0 0 0 0

45 0 0 0 0 0 0 0

46 0 0 0 0 0 0 0

47 0 0 0 0 0 0 0

48 0 0 0 0 0 0 0

49 0 0 0 0 0 0 0

50 0 0 0 0 0 0 0

51 0 0 0 0 0 0 0

52 0 0 0 0 0 0 0

53 0 0 0 0 0 0 0

54 0 0 0 0 0 0 0

55 0 0 0 0 0 0 0

56 0 0 0 0 0 0 0

57 0 0 0 0 0 0 0

73 0 0 0 0 0 0 0

74 0 0 0 0 0 0 0

75 0 0 0 0 0 0 0

76 0 0 0 0 0 0 0

77 0 0 0 0 0 0 0

78 0 0 0 0 0 0 0

79 0 0 0 0 0 0 0

80 0 0 0 0 0 0 0

81 0 0 0 0 0 0 0

82 0 0 0 0 0 0 0

83 0 0 0 0 0 0 0

84 0 0 0 0 0 0 0

85 0 0 0 0 0 0 0

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85 0 0 0 0 0 0 0

86 0 0 0 0 0 0 0

87 0 0 0 0 0 0 0

88 0 0 0 0 0 0 0

89 0 0 0 0 0 0 0

90 0 0 0 0 0 0 0

91 0 0 0 0 0 0 0

92 0 0 0 0 0 0 0

93 0 0 0 0 0 0 0

94 0 0 0 0 0 0 0

95 0 0 0 0 0 0 0

96 0 0 0 0 0 0 0

97 0 0 0 0 0 0 0

98 0 0 0 0 0 0 0

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0 0 -1000 0.0 0.00 0 0 0.0 0.0

0 500 -1000 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 -500 0.0 0.0

1 0 0 0.0 0.0

0 0 0 0.0 0.00 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0 0 0 0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

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0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

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0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

0 0 0 0.0 0.0

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u don't use Spring elements, put "off" in this column,

Total Strain Energy 0

Type of Elemet SPRING

Element No. 1

Degree of Freedom of Spring: x-->1, y-->2 1

Grid No. 1 2

2 6

Spring Constant K 449110

Strain Energy U 13.3593

Grid Coorinates x1 30

- Global Coordinate System y1 20

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x2 90

y2 30

Grid Coorinates after Deformation x1' 30.0252

- Global Coordinate System y1' 19.9458

x2' 90.0175

y2' 29.9259

Extension of Spring d -0.0077

Grid Point Force Fe 11 3464.05

- Element Coordinate System 12 0

21 -3464

22 0

Grid Point Force Fe 1x 3464.05

- Global Coordinate System 1y 0

13 0.0

14 0.0

15 0.0

16 0.0

17 0.0

18 0.0

19 0.0

20 0.0

21 0.0

22 0.0

23 0.0

24 0.0

25 0.0

26 0 0

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26 0.0

27 0.0

28 0.0

29 0.0

30 0.0

31 0.0

32 0.0

33 0.0

34 0.0

35 0.0

36 0.0

37 0.0

38 0.0

54 0.0

55 0.0

56 0.0

57 0.0

58 0.0

59 0.0

60 0.0

61 0.0

62 0.0

63 0.0

64 0.0

65 0.0

66 0.0

67 0 0

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67 0.0

68 0.0

69 0.0

70 0.0

71 0.0

72 0.0

73 0.0

74 0.0

75 0.0

76 0.0

77 0.0

78 0.0

79 0.0

95 0.0

96 0.0

97 0.0

98 0.0

99 0.0

100 0.0

101 0.0

102 0.0

103 0.0

104 0.0

105 0.0

106 0.0

107 0.0

108 0 0

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108 0.0

109 0.0

110 0.0

Grid Point Force, y-direction 1 0.0

2 0.0

3 0.0

4 0.0

5 0.0

6 0.0

7 0.0

8 0.0

9 0.0

10 0.0

26 0.0

27 0.0

28 0.0

29 0.0

30 0.0

31 0.0

32 0.0

33 0.0

34 0.0

35 0.0

36 0.0

37 0.0

38 0.0

39 0 0

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39 0.0

40 0.0

41 0.0

42 0.0

43 0.0

44 0.0

45 0.0

46 0.0

47 0.0

48 0.0

49 0.0

50 0.0

51 0.0

67 0.0

68 0.0

69 0.0

70 0.0

71 0.0

72 0.0

73 0.0

74 0.0

75 0.0

76 0.0

77 0.0

78 0.0

79 0.0

80 0 0

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80 0.0

81 0.0

82 0.0

83 0.0

84 0.0

85 0.0

86 0.0

87 0.0

88 0.0

89 0.0

90 0.0

91 0.0

92 0.0

108 0.0

109 0.0

110 0.0

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J-1

det[J]

dN1/dx

dN2/dx

dN3/dx

dN4/dx

dN1/dh

dN2/dh

dN3/dh

dN4/dh

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dN4/dh

dN1/dx

dN2/dx

dN3/dx

dN4/dx

dN1/dy

dN2/dy

dN3/dy

dN4/dy

[B]

[D][B]

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