-
Notifications
You must be signed in to change notification settings - Fork 196
/
12.5.2.out
24 lines (24 loc) · 6.69 KB
/
12.5.2.out
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Mapping Functions
x = 0.25*eta + 1.5*xi + 1.75
y = -0.2*eta*xi + 1.3*eta + 0.3*xi + 1.8
Gradient of the Map
J = Matrix([[1.50000000000000, 0.250000000000000], [0.3 - 0.2*eta, 1.3 - 0.2*xi]])
J^-1 = Matrix([[(1.95 - 0.3*xi)/(0.075*eta - 0.45*xi + 2.8125), (0.3*eta - 0.45)/(0.075*eta - 0.45*xi + 2.8125)], [-0.25/(0.05*eta - 0.3*xi + 1.875), 1.5/(0.05*eta - 0.3*xi + 1.875)]])
B = Matrix([[(1.65*eta - 0.15*xi - 1.5)/(0.3*eta - 1.8*xi + 11.25), 0, (-2.25*eta + 0.15*xi + 2.4)/(0.3*eta - 1.8*xi + 11.25), 0, (2.25*eta - 0.75*xi + 1.5)/(0.3*eta - 1.8*xi + 11.25), 0, (-1.65*eta + 0.75*xi - 2.4)/(0.3*eta - 1.8*xi + 11.25), 0], [0, (-0.0625*eta + 0.375*xi - 0.3125)/(0.05*eta - 0.3*xi + 1.875), 0, (0.0625*eta - 0.375*xi - 0.4375)/(0.05*eta - 0.3*xi + 1.875), 0, (-0.0625*eta + 0.375*xi + 0.3125)/(0.05*eta - 0.3*xi + 1.875), 0, (0.0625*eta - 0.375*xi + 0.4375)/(0.05*eta - 0.3*xi + 1.875)], [(-0.0625*eta + 0.375*xi - 0.3125)/(0.05*eta - 0.3*xi + 1.875), (1.65*eta - 0.15*xi - 1.5)/(0.3*eta - 1.8*xi + 11.25), (0.0625*eta - 0.375*xi - 0.4375)/(0.05*eta - 0.3*xi + 1.875), (-2.25*eta + 0.15*xi + 2.4)/(0.3*eta - 1.8*xi + 11.25), (-0.0625*eta + 0.375*xi + 0.3125)/(0.05*eta - 0.3*xi + 1.875), (2.25*eta - 0.75*xi + 1.5)/(0.3*eta - 1.8*xi + 11.25), (0.0625*eta - 0.375*xi + 0.4375)/(0.05*eta - 0.3*xi + 1.875), (-1.65*eta + 0.75*xi - 2.4)/(0.3*eta - 1.8*xi + 11.25)]])
Stiffness Matrix
K = Matrix([[0.323, 0.100, -0.254, 0.000187, -0.101, -0.144, 0.0320, 0.0433], [0.100, 0.390, 0.0277, 0.0887, -0.144, -0.137, 0.0159, -0.341], [-0.254, 0.0277, 0.713, -0.302, -0.0500, 0.0319, -0.409, 0.242], [0.000187, 0.0887, -0.302, 0.785, 0.0594, -0.434, 0.242, -0.440], [-0.101, -0.144, -0.0500, 0.0594, 0.391, 0.0868, -0.240, -0.00249], [-0.144, -0.137, 0.0319, -0.434, 0.0868, 0.467, 0.0250, 0.104], [0.0320, 0.0159, -0.409, 0.242, -0.240, 0.0250, 0.617, -0.283], [0.0433, -0.341, 0.242, -0.440, -0.00249, 0.104, -0.283, 0.676]])
k_{Full Integration} = Matrix([[0.322589737926487, 0.100264451314756, -0.253618645387425, 2.37938681509675e-18*sqrt(3) + 7.74655624329143e-5, -0.101186538823098 - 3.02484916338375e-18*sqrt(3), -0.143610223005978 + 5.94846703774188e-19*sqrt(3), 0.0322154462840355 - 1.58222879315458e-17*sqrt(3), 0.0432683061287894 - 2.37938681509675e-18*sqrt(3)], [0.100264451314756, 0.38896890135662 - 2.97831302240861e-17*sqrt(3), 0.0275499930349604, 2.79216845850808e-18*sqrt(3) + 0.0895588956741735, -0.143610223005978 - 1.18969340754838e-18*sqrt(3), -0.138009391040836 + 6.74774044139452e-18*sqrt(3), 0.0157957786562619, -0.340518405989957], [-0.253618645387425, 0.0275499930349604, 0.712013086896493 - 1.48915651120431e-17*sqrt(3), -0.301881216160633 + 2.03164420275255e-18*sqrt(3), -0.0495334272310621 - 1.86144563900538e-18*sqrt(3), 4.7587736301935e-18*sqrt(3) + 0.0318003712807132, -0.408861014278006 - 1.11686738340323e-17*sqrt(3), 2.37938681509675e-18*sqrt(3) + 0.242530851844959], [2.37938681509675e-18*sqrt(3) + 7.74655624329143e-5, 2.79216845850808e-18*sqrt(3) + 0.0895588956741735, -0.301881216160633 + 2.03164420275255e-18*sqrt(3), 0.783882080124238, 0.0592728987532407, -0.433180379029631 - 7.44578255602154e-18*sqrt(3), 5.94846703774188e-18*sqrt(3) + 0.242530851844959, -0.440260596768781 - 8.37650537552423e-18*sqrt(3)], [-0.101186538823098 - 3.02484916338375e-18*sqrt(3), -0.143610223005978 - 1.18969340754838e-18*sqrt(3), -0.0495334272310621 - 1.86144563900538e-18*sqrt(3), 0.0592728987532407, 0.390713799189068, 0.08692729079438 - 9.02952979001131e-19*sqrt(3), -0.239993833134909, -0.0025899665416423 + 1.18969340754838e-18*sqrt(3)], [-0.143610223005978 + 5.94846703774188e-19*sqrt(3), -0.138009391040836 + 6.74774044139452e-18*sqrt(3), 4.7587736301935e-18*sqrt(3) + 0.0318003712807132, -0.433180379029631 - 7.44578255602154e-18*sqrt(3), 0.08692729079438 - 9.02952979001131e-19*sqrt(3), 1.48915651120431e-17*sqrt(3) + 0.466187212223014, 0.0248825609308852, 1.39608422925404e-18*sqrt(3) + 0.105002557847453], [0.0322154462840355 - 1.58222879315458e-17*sqrt(3), 0.0157957786562619, -0.408861014278006 - 1.11686738340323e-17*sqrt(3), 5.94846703774188e-18*sqrt(3) + 0.242530851844959, -0.239993833134909, 0.0248825609308852, 0.616639401128879, -0.283209191432106 - 5.41771787400679e-18*sqrt(3)], [0.0432683061287894 - 2.37938681509675e-18*sqrt(3), -0.340518405989957, 2.37938681509675e-18*sqrt(3) + 0.242530851844959, -0.440260596768781 - 8.37650537552423e-18*sqrt(3), -0.0025899665416423 + 1.18969340754838e-18*sqrt(3), 1.39608422925404e-18*sqrt(3) + 0.105002557847453, -0.283209191432106 - 5.41771787400679e-18*sqrt(3), 0.675776444911285]])
k_{Reduced Integration}= Matrix([[0.226648351648352, 0.119047619047619, -0.122252747252747, -0.0256410256410256, -0.226648351648352, -0.119047619047619, 0.122252747252747, 0.0256410256410256], [0.119047619047619, 0.280219780219780, 0.00183150183150182, 0.238461538461538, -0.119047619047619, -0.280219780219780, -0.00183150183150182, -0.238461538461538], [-0.122252747252747, 0.00183150183150182, 0.532142857142857, -0.266666666666667, 0.122252747252747, -0.00183150183150182, -0.532142857142857, 0.266666666666667], [-0.0256410256410256, 0.238461538461538, -0.266666666666667, 0.580000000000000, 0.0256410256410256, -0.238461538461538, 0.266666666666667, -0.580000000000000], [-0.226648351648352, -0.119047619047619, 0.122252747252747, 0.0256410256410256, 0.226648351648352, 0.119047619047619, -0.122252747252747, -0.0256410256410256], [-0.119047619047619, -0.280219780219780, -0.00183150183150182, -0.238461538461538, 0.119047619047619, 0.280219780219780, 0.00183150183150182, 0.238461538461538], [0.122252747252747, -0.00183150183150182, -0.532142857142857, 0.266666666666667, -0.122252747252747, 0.00183150183150182, 0.532142857142857, -0.266666666666667], [0.0256410256410256, -0.238461538461538, 0.266666666666667, -0.580000000000000, -0.0256410256410256, 0.238461538461538, -0.266666666666667, 0.580000000000000]])
Body Forces
ρ_b = Matrix([[0], [-1]])
Body Force Vetor
f_{Exact Integration} = Matrix([[0], [-1.95833333333333], [0], [-1.75833333333333], [0], [-1.79166666666667], [0], [-1.99166666666667]])
f_{Full Integration} = Matrix([[0], [-1.95833333333333], [0], [-1.75833333333333 - 2.46716227694479e-17*sqrt(3)], [0], [-1.79166666666667], [0], [-1.99166666666667 - 2.46716227694479e-17*sqrt(3)]])
f_{Reduced Integration}= Matrix([[0], [-1.87500000000000], [0], [-1.87500000000000], [0], [-1.87500000000000], [0], [-1.87500000000000]])
Traction Vectors
t_n = Matrix([[-1], [0]])
Spatial Coordinate System = 1.12805141726785
Nodal Forces due to Traction Forces
f_{Exact Integration} Matrix([[0], [0], [-1.12805141726785], [0], [-1.12805141726785], [0], [0], [0]])
f_{Full Integration} = Matrix([[0], [0], [-1.12805141726785], [0], [-1.12805141726785], [0], [0], [0]])
f_{Reduced Integration} Matrix([[0], [0], [-1.12805141726785], [0], [-1.12805141726785], [0], [0], [0]])