Critical Buckling Examples With Varying Boundary Conditions

Thanks the Bardell equations implamentation, composipy is capable of simulating different boundary conditions and different combinations of load cases.

Importing composipy objects and creating properties

from composipy import OrthotropicMaterial, LaminateProperty
from composipy import PlateStructure
import matplotlib

#Ply Material Properties (MPa and mm)
E1 = 60800
E2 = 58250
v12 = 0.07
G12 = 4550
t = 0.21

# Plate Parameters (mm)
a = 360.
b = 360.
m = 10 # discretization in x direction
n = 10 # discretization in y direction


# Stacking sequence
stacking = [45,-45,0,90,45,-45,0,90,45,-45]
stacking += stacking[::-1] # symmetry

# Ply material and laminate property objects

ply_1 = OrthotropicMaterial(E1, E2, v12, G12, t)
l1 = LaminateProperty(stacking, ply_1)

Pinned Nxx

panel_SSSS = PlateStructure(l1, a, b, m=m, n=n, Nxx=-1,constraints='PINNED')

eigvals, eigvecs = panel_SSSS.buckling_analysis()

eigvals

array([ 97.04915682, 144.47730786, 246.83882036, 388.19669784,
       393.21258067])

panel_SSSS.plot_eigenvalue()

Clamped Nxy and Nyy

panel_CCCC = PlateStructure(l1, a, 1.5*b, m=m, n=n, Nxy=-1, Nyy=-1, constraints='CLAMPED')

panel_CCCC.buckling_analysis()

(array([138.79310181, 146.27293322, 214.40196835, 235.95368935,
        345.90300267]),
 array([[ 9.34248014e-16, -1.88156661e-14,  2.02134850e-14,
          2.34440133e-15,  1.61245714e-14],
        [-2.12462063e-14,  9.37191184e-14, -1.09651915e-13,
          1.22922751e-15, -8.64977457e-14],
        [-1.68030603e-14, -2.94928446e-15,  3.17565273e-15,
          6.43801745e-15,  2.49531496e-15],
        ...,
        [ 1.48429879e-13, -6.09319462e-02,  5.26382491e-01,
          6.94793823e-13,  8.03873977e-01],
        [ 1.74056918e-01,  1.50428248e-13,  1.23757124e-13,
         -1.99938292e-01,  1.44448141e-13],
        [ 1.19772248e-13, -4.03658981e-02,  4.21566452e-01,
          9.40855121e-13,  5.20345902e-01]]))

panel_CCCC.plot_eigenvalue()
%matplotlib inline

Free edge Nxx (custom boundary condition)

constraints={
                'x0': ['TX', 'TY', 'TZ'],
                'xa': ['TX', 'TY', 'TZ'],
                'y0': [],
                'yb': ['TX', 'TY', 'TZ'],
            }
panel_SSFS = PlateStructure(l1, 1.5*a, b, m=m, n=n, Nxx=-1, constraints=constraints)

panel_SSFS.buckling_analysis()

(array([ 20.12080055,  47.13886913,  92.5739614 , 156.53663617,
        185.19779529]),
 array([[-5.54254543e-15,  8.54682964e-15,  2.02336476e-15,
          2.14117401e-14,  2.25590066e-14],
        [ 2.70857705e-13, -3.87614772e-13,  1.33465332e-13,
         -2.01037659e-12, -4.41333984e-13],
        [-2.62755574e-14,  1.09823238e-13, -6.76289507e-15,
          1.36766074e-13,  1.13523615e-14],
        ...,
        [ 6.90309193e-03,  6.95127053e-05, -5.12419786e-03,
          3.38168226e-02, -1.43816796e-05],
        [ 9.66068997e-04, -2.79805029e-05,  4.46813288e-04,
         -2.74685452e-02, -3.51157619e-05],
        [ 3.64137204e-03,  3.67529764e-05, -2.79731072e-03,
          3.43269351e-02, -6.21653806e-06]]))

panel_SSFS.plot_eigenvalue()

Nxy Loading

panel_CCCC_nxy = PlateStructure(l1, a, b, m=m, n=n, Nxy=-1, constraints='CLAMPED')

panel_CCCC_nxy.buckling_analysis()

(array([338.84283307, 389.26571459, 776.82143839, 824.28455938,
        882.94931083]),
 array([[-9.85787017e-14,  5.49320863e-14, -5.53627846e-14,
         -5.47863549e-14, -1.63309599e-13],
        [-1.14383443e-13,  4.82531544e-14, -2.16269855e-14,
         -8.98291546e-14, -2.25169408e-13],
        [-8.24080163e-15,  5.29270154e-14, -4.71651923e-15,
         -9.11230373e-14, -1.89295317e-14],
        ...,
        [ 5.84301288e-01,  7.76122020e-13,  3.22800174e-01,
          3.29448845e-12,  2.20803287e-12],
        [-7.64092132e-13, -1.01135119e-01,  6.65989832e-12,
         -1.79699680e-01, -3.68197373e-01],
        [ 3.89453084e-01,  5.26513867e-13,  2.20302574e-01,
          1.92960329e-12, -5.54281896e-14]]))

panel_CCCC_nxy.plot_eigenvalue()