def __main__():
# Define an isotropic material with E = 29,500 ksi and nu = 0.3
props = np.array(
[np.array([0, 29500, 29500, 0.3, 0.3, 29500 / (2 * (1 + 0.3))])])
# Define a lightly-meshed Cee shape
# (1 element per lip, 2 elements per flange, 3 elements on the web)
# Nodal location units are inches
nodes = np.array([[0, 5, 1, 1, 1, 1, 1, 0], [1, 5, 0, 1, 1, 1, 1, 0],
[2, 2.5, 0, 1, 1, 1, 1, 0], [3, 0, 0, 1, 1, 1, 1, 0],
[4, 0, 3, 1, 1, 1, 1, 0], [5, 0, 6, 1, 1, 1, 1, 0],
[6, 0, 9, 1, 1, 1, 1, 0], [7, 2.5, 9, 1, 1, 1, 1, 0],
[8, 5, 9, 1, 1, 1, 1, 0], [9, 5, 8, 1, 1, 1, 1, 0]])
thickness = 0.1
elements = [[0, 0, 1, thickness, 0], [1, 1, 2, thickness, 0],
[2, 2, 3, thickness, 0], [3, 3, 4, thickness, 0],
[4, 4, 5, thickness, 0], [5, 5, 6, thickness, 0],
[6, 6, 7, thickness, 0], [7, 7, 8, thickness, 0],
[8, 8, 9, thickness, 0]]
# These lengths will generally provide sufficient accuracy for
# local, distortional, and global buckling modes
# Length units are inches
lengths = [
0.5, 0.75, 1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75,
4, 4.25, 4.5, 4.75, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
19, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 52,
54, 56, 58, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 132, 144,
156, 168, 180, 204, 228, 252, 276, 300
]
# No special springs or constraints
springs = []
constraints = []
# Values here correspond to signature curve basis and orthogonal based upon geometry
gbt_con = {
'glob': [0],
'dist': [0],
'local': [0],
'other': [0],
'o_space': 1,
'couple': 1,
'orth': 2,
'norm': 0,
}
# Simply-supported boundary conditions
b_c = 'S-S'
# For signature curve analysis, only a single array of ones makes sense here
m_all = np.ones((len(lengths), 1))
# Solve for 10 eigenvalues
n_eigs = 10
# Set the section properties for this simple section
# Normally, these might be calculated by an external package
sect_props = {
'cx': 1.67,
'cy': 4.5,
'x0': -2.27,
'y0': 4.5,
'phi': 0,
'A': 2.06,
'Ixx': 28.303,
'Ixy': 0,
'Iyy': 7.019,
'I11': 28.303,
'I22': 7.019
}
# Generate the stress points assuming 50 ksi yield and pure compression
nodes_p = stress_gen(nodes=nodes,
forces={
'P': sect_props['A'] * 50,
'Mxx': 0,
'Myy': 0,
'M11': 0,
'M22': 0
},
sect_props=sect_props,
offset_basis=[-thickness / 2, -thickness / 2])
# Perform the Finite Strip Method analysis
signature, curve, shapes = strip(props=props,
nodes=nodes_p,
elements=elements,
lengths=lengths,
springs=springs,
constraints=constraints,
gbt_con=gbt_con,
b_c=b_c,
m_all=m_all,
n_eigs=n_eigs,
sect_props=sect_props)
# Return the important example results
# The signature curve is simply a matter of plotting the
# 'signature' values against the lengths
# (usually on a logarithmic axis)
return {
'X_values': lengths,
'Y_values': signature,
'Y_values_allmodes': curve,
'Orig_coords': nodes,
'Deformations': shapes
}
def __main__():
# Define an isotropic material with E = 203,000 MPa and nu = 0.3
props = [[0, 203000, 203000, 0.3, 0.3, 203000 / (2 * (1 + 0.3))]]
# Define a lightly-meshed Zed shape
# (1 element per lip, 2 elements per flange, 3 elements on the web)
# Nodal location units are millimetres
nodes = np.array([[0, 100, 25, 1, 1, 1, 1, 0], [1, 100, 0, 1, 1, 1, 1, 0],
[2, 50, 0, 1, 1, 1, 1, 0], [3, 0, 0, 1, 1, 1, 1, 0],
[4, 0, 100, 1, 1, 1, 1, 0], [5, 0, 200, 1, 1, 1, 1, 0],
[6, 0, 300, 1, 1, 1, 1, 0], [7, -50, 300, 1, 1, 1, 1, 0],
[8, -100, 300, 1, 1, 1, 1, 0],
[9, -100, 275, 1, 1, 1, 1, 0]])
elements = [[0, 0, 1, 2, 0], [1, 1, 2, 2, 0], [2, 2, 3, 2, 0],
[3, 3, 4, 2, 0], [4, 4, 5, 2, 0], [5, 5, 6, 2, 0],
[6, 6, 7, 2, 0], [7, 7, 8, 2, 0], [8, 8, 9, 2, 0]]
# These lengths will generally provide sufficient accuracy for
# local, distortional, and global buckling modes
# Length units are millimetres
lengths = [
10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160,
170, 180, 190, 200, 250, 300, 350, 400, 450, 500, 600, 700, 800, 900,
1000, 1100, 1200, 1300, 1400, 1500, 2000, 2500, 3000, 3500, 4000, 4500,
5000, 6000, 7000, 8000, 9000, 10000
]
# No special springs or constraints
springs = []
constraints = []
# Values here correspond to signature curve basis and orthogonal based upon geometry
gbt_con = {
'glob': [0],
'dist': [0],
'local': [0],
'other': [0],
'o_space': 1,
'couple': 1,
'orth': 2,
'norm': 0,
}
# Simply-supported boundary conditions
b_c = 'S-S'
# For signature curve analysis, only a single array of ones makes sense here
m_all = np.ones((len(lengths), 1))
# Solve for 10 eigenvalues
n_eigs = 10
# Set the section properties for this simple section
# Normally, these might be calculated by an external package
sect_props = {
'cx': 0,
'cy': 150,
'x0': 0,
'y0': 150,
'phi': 16.54,
'A': 1084,
'Ixx': 14921145,
'Ixy': -4151084,
'Iyy': 2177529,
'I11': 16154036,
'I22': 944639
}
# Generate the stress points assuming 500 MPa yield and X-axis bending
nodes_p = stress_gen(nodes=nodes,
forces={
'P': 0,
'Mxx': 500 * sect_props['Ixx'] / sect_props['cy'],
'Myy': 0,
'M11': 0,
'M22': 0
},
sect_props=sect_props)
# Perform the Finite Strip Method analysis
signature, curve, shapes = strip(props=props,
nodes=nodes_p,
elements=elements,
lengths=lengths,
springs=springs,
constraints=constraints,
gbt_con=gbt_con,
b_c=b_c,
m_all=m_all,
n_eigs=n_eigs,
sect_props=sect_props)
# Return the important example results
# The signature curve is simply a matter of plotting the
# 'signature' values against the lengths
# (usually on a logarithmic axis)
return {
'X_values': lengths,
'Y_values': signature,
'Y_values_allmodes': curve,
'Orig_coords': nodes,
'Deformations': shapes
}
'x0': 0,
'y0': 150,
'phi': 16.54,
'A': 1084,
'Ixx': 14921145,
'Ixy': -4151084,
'Iyy': 2177529,
'I11': 16154036,
'I22': 944639
}
# Generate the stress points assuming 500 MPa yield and X-axis bending
nodes_p = stress_gen(nodes=nodes,
forces={
'P': sect_props['A'] * 50,
'Mxx': 0,
'Myy': 0,
'M11': 0,
'M22': 0
},
sect_props=sect_props)
print(nodes_p)
#####CALL CROSS SECTION
#Flag = {node, elem, mat, stress, stresspic, coord, constraints, springs, origin, propaxis}
flag = np.array([1, 0, 0, 1, 1, 0, 0, 0, 0, 0])
crossect.crossect(nodes_p, elements, springs, constraints, flag)
plt.show()
# Perform the Finite Strip Method analysis
signature, curve, shapes = strip(props=props,
nodes=nodes_p,
elements=elements,
lengths=lengths,
