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Elas4#

Plate with a hole subjected to uniform tensile loading.

  • TRI10: Ne = 104, Nn = 511
  • Boundary conditions
  • $ux$
  • $uy$
  • $\sigma_{vm}^{e}$
==================== Mesh ====================

Element type: TRI10
Ne = 104, Nn = 511

==================== Model ====================

Isotropic:
E = 2.10e+05, v = 0.3
planeStress = True
thickness = 1.00e+00

solver : scipy

============= Boundary Conditions =============

Unspecified.

=================== Results ===================


W def = 5.04

Svm max = 127.24

Evm max = 0.07 %

Ux max = 1.27e-02
Ux min = 0.00e+00

Uy max = 0.00e+00
Uy min = -4.89e-03

=================== TicTac ===================

Mesh : 19.989 ms
Boundary Conditions : 23.842 µs
Matrix : 12.647 ms
Solver : 14.188 ms
Display : 167.627 ms
PostProcessing : 1.047 ms


12 import matplotlib.pyplot as plt
13
14 from EasyFEA import Display, ElemType, Models, Simulations
15 from EasyFEA.Geoms import Point, Points, Domain, Circle
16
17 if __name__ == "__main__":
18     Display.Clear()
19
20     # ----------------------------------------------
21     # Configuration
22     # ----------------------------------------------
23
24     dim = 2
25     isSymmetric = True
26
27     # geom
28     a = 10
29     l = 50
30     h = 20
31     thickness = 1
32
33     # ----------------------------------------------
34     # Mesh
35     # ----------------------------------------------
36
37     meshSize = h / 4
38
39     if isSymmetric:
40         p0 = Point(0, 0, r=-a)
41         p1 = Point(l, 0)
42         p2 = Point(l, h)
43         p3 = Point(0, h)
44         contour = Points([p0, p1, p2, p3], meshSize)
45         inclusions = []
46     else:
47         p0 = Point(-l, -h)
48         p1 = Point(l, h)
49         contour = Domain(p0, p1, meshSize)
50         inclusions = [Circle(Point(), 2 * a, meshSize, isHollow=True)]
51
52     if dim == 2:
53         mesh = contour.Mesh_2D(inclusions, elemType=ElemType.TRI10)
54     else:
55         mesh = contour.Mesh_Extrude(
56             inclusions, [0, 0, thickness], [1], ElemType.PRISM18
57         )
58
59     # ----------------------------------------------
60     # Simu
61     # ----------------------------------------------
62     material = Models.Elastic.Isotropic(
63         dim, E=210000, v=0.3, planeStress=True, thickness=thickness
64     )
65     simu = Simulations.Elastic(mesh, material)
66
67     if isSymmetric:
68         nodes_x0 = mesh.Nodes_Conditions(lambda x, y, z: x == 0)
69         nodes_y0 = mesh.Nodes_Conditions(lambda x, y, z: y == 0)
70         nodes_xl = mesh.Nodes_Conditions(lambda x, y, z: x == l)
71         simu.add_dirichlet(nodes_x0, [0], ["x"])
72         simu.add_dirichlet(nodes_y0, [0], ["y"])
73         simu.add_surfLoad(nodes_xl, [800 / 20], ["x"])
74     else:
75         nodes_pl = mesh.Nodes_Conditions(lambda x, y, z: x == l)
76         nodes_ml = mesh.Nodes_Conditions(lambda x, y, z: x == -l)
77         nodes_y0 = mesh.Nodes_Conditions(lambda x, y, z: y == 0)
78         simu.add_dirichlet(nodes_y0, [0], ["y"])
79         simu.add_surfLoad(nodes_pl, [800 / 20], ["x"])
80         simu.add_surfLoad(nodes_ml, [-800 / 20], ["x"])
81
82     simu.Solve()
83
84     # ----------------------------------------------
85     # Results
86     # ----------------------------------------------
87     uxMax = simu.Result("ux").max()
88     Display.Plot_Mesh(simu, deformFactor=2 / uxMax)
89     Display.Plot_BoundaryConditions(simu)
90
91     Display.Plot_Result(simu, "ux", ncolors=10)
92     Display.Plot_Result(simu, "uy", ncolors=10)
93     Display.Plot_Result(simu, "Svm", ncolors=10, nodeValues=False, plotMesh=True)
94
95     print(simu)
96
97     plt.show()

Total running time of the script: (0 minutes 0.634 seconds)

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