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LinearElasticity1#

A cantilever beam undergoing bending deformation.

Note that this simulation is also performed in examples/Elastic/Elas1.py.

$uy$
14 from EasyFEA import Display, ElemType, Models, Simulations, np
15 from EasyFEA.fem import Field, BiLinearForm, FeArray, Sym_Grad, Trace
16 from EasyFEA.Geoms import Domain
17
18 if __name__ == "__main__":
19     Display.Clear()
20
21     # ----------------------------------------------
22     # Configuration
23     # ----------------------------------------------
24
25     dim = 2
26
27     # geom
28     L = 120  # mm
29     h = 13
30
31     # load
32     F = -800  # N
33
34     # model
35     E = 210000  # MPa
36     v = 0.3
37
38     elastic = Models.ElasIsot(dim, E, v, planeStress=True, thickness=h)
39     lmbda = elastic.get_lambda()
40     mu = elastic.get_mu()
41
42     # ----------------------------------------------
43     # Mesh
44     # ----------------------------------------------
45
46     contour = Domain((0, 0), (L, h), h / 3)
47
48     if dim == 2:
49         mesh = contour.Mesh_2D([], ElemType.QUAD9, isOrganised=True)
50     else:
51         mesh = contour.Mesh_Extrude(
52             [], [0, 0, h], [3], ElemType.HEXA27, isOrganised=True
53         )
54
55     nodesX0 = mesh.Nodes_Conditions(lambda x, y, z: x == 0)
56     nodesXL = mesh.Nodes_Conditions(lambda x, y, z: x == L)
57
58     # ----------------------------------------------
59     # Formulations
60     # ----------------------------------------------
61
62     field = Field(mesh.groupElem, dim)
63
64     def S(u: Field) -> FeArray:
65         Eps = Sym_Grad(u)
66         return 2 * mu * Eps + lmbda * Trace(Eps) * np.eye(dim)
67
68     @BiLinearForm
69     def ComputeK(u: Field, v: Field):
70         Sig = S(u)
71         Eps = Sym_Grad(v)
72         return Sig.ddot(Eps)
73
74     weakForms = Models.WeakForms(field, ComputeK)
75
76     # ----------------------------------------------
77     # Simulations
78     # ----------------------------------------------
79
80     simu = Simulations.WeakFormSimu(mesh, weakForms)
81
82     simu.add_dirichlet(nodesX0, [0] * dim, simu.Get_unknowns())
83     simu.add_surfLoad(nodesXL, [F / h**2], ["y"])
84
85     simu.Solve()
86
87     # ----------------------------------------------
88     # Results
89     # ----------------------------------------------
90
91     Display.Plot_Result(simu, "uy", 10, plotMesh=True)
92
93     Display.plt.show()

Total running time of the script: (0 minutes 0.147 seconds)

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