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#
[1]:
from composipy import OrthotropicMaterial, LaminateProperty
from composipy import PlateStructure
import matplotlib
[2]:
#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
[3]:
# Ply material and laminate property objects
ply_1 = OrthotropicMaterial(E1, E2, v12, G12, t)
l1 = LaminateProperty(stacking, ply_1)
Pinned Nxx#
[4]:
panel_SSSS = PlateStructure(l1, a, b, m=m, n=n, Nxx=-1,constraints='PINNED')
[5]:
eigvals, eigvecs = panel_SSSS.buckling_analysis()
[6]:
eigvals
[6]:
array([ 97.04915682, 144.47730786, 246.83882036, 388.19669784,
393.21258067])
[7]:
panel_SSSS.plot_eigenvalue()
Clamped Nxy and Nyy#
[8]:
panel_CCCC = PlateStructure(l1, a, 1.5*b, m=m, n=n, Nxy=-1, Nyy=-1, constraints='CLAMPED')
[9]:
panel_CCCC.buckling_analysis()
[9]:
(array([138.79310181, 146.27293322, 214.40196835, 235.95368935,
345.90300267]),
array([[-3.64618879e-13, 1.28381179e+00, -1.78192758e+00,
2.78515646e-13, -1.12734335e+00],
[ 4.78203748e+00, 1.76574015e-12, 1.88079163e-13,
-2.66381399e+00, -3.94121663e-13],
[ 2.24543959e-12, -5.23231059e+00, -2.78814793e+00,
6.82139456e-13, -4.26107290e+00],
[-3.49928726e+00, -1.43389214e-12, -7.46022132e-13,
-5.68459201e+00, -9.08892329e-13],
[-1.24845393e-12, 2.39465165e+00, 5.81817283e+00,
-6.30122968e-14, -2.06455886e+00],
[ 8.68863252e-01, 3.55224432e-13, 4.91127608e-13,
6.47556953e+00, 7.67885163e-13],
[ 4.57693801e-13, -4.09877859e-01, -2.89496525e+00,
-7.89172351e-13, 7.26371688e+00],
[-1.08720000e-01, -2.38328507e-14, -2.21405356e-13,
-2.48027907e+00, 3.91154650e-13],
[ 1.02073656e-13, 4.89715596e-02, 6.53499900e-01,
4.26646511e-13, -4.23172599e+00],
[ 3.27585142e-03, -1.60216893e-14, 1.31775514e-14,
5.12383379e-01, -2.17409335e-14],
[ 6.37061505e-01, 2.31937296e-13, -1.18953983e-13,
-9.65293487e-01, -3.55081383e-13],
[ 1.51781110e-12, -5.15291157e+00, 4.71274903e+00,
-4.16970120e-13, 1.73710091e+00],
[-8.23826420e+00, -3.19968351e-12, -8.44625729e-13,
1.80171685e-01, -3.41803590e-13],
[-2.92308314e-12, 4.95240914e+00, 1.15848693e+01,
-1.86255833e-12, 6.34967515e+00],
[ 1.87308489e+00, 8.95772552e-13, 9.22950790e-13,
1.38565754e+01, 1.75128945e-12],
[ 9.39208886e-13, -1.49786873e+00, -7.98676963e+00,
-1.19295462e-12, 1.44914159e+01],
[-3.32436556e-01, -1.61727351e-13, -3.84867913e-13,
-8.40961560e+00, 2.89596462e-13],
[-3.21245740e-13, 2.07956646e-01, 2.43960696e+00,
1.26155679e-12, -1.56227610e+01],
[ 9.12822935e-02, 6.92797586e-14, 6.77324522e-14,
2.19189810e+00, -9.02311573e-13],
[-1.12091909e-13, -3.67936422e-03, -4.85744880e-01,
-5.32213584e-13, 5.78430433e+00],
[ 7.64773050e-14, -2.78099067e-01, 3.92662495e-01,
-5.57178150e-14, 2.12274723e-01],
[-9.59237877e-01, -5.04410472e-13, 8.34733136e-14,
1.04600823e+00, -6.11447063e-13],
[-5.72496156e-13, 2.03710818e+00, -1.09774884e+00,
-4.07328541e-13, -7.18228555e-01],
[ 7.65757891e-01, 2.11875031e-13, 3.35405790e-13,
3.82815269e+00, 8.63447669e-13],
[ 9.82614146e-13, 5.03097166e-01, -4.97690420e+00,
4.35373822e-13, 3.21649332e+00],
[-5.34781480e-01, -3.41178520e-13, -1.12147781e-14,
-3.21205982e+00, 1.92493895e-12],
[-3.27983249e-13, 5.53787783e-01, 1.56690584e+00,
4.62279844e-13, -9.51521102e+00],
[-2.53539242e-01, -1.43056439e-13, -3.90564513e-13,
2.21911476e+00, 5.50473695e-13],
[-1.67885146e-14, 8.28018300e-02, -2.22744189e-01,
-3.43119058e-13, 7.04009153e+00],
[-9.18306018e-02, -1.67577817e-13, -1.76463504e-13,
-1.84614171e-01, 9.51903726e-13],
[-1.71250181e-01, -6.94863379e-14, -5.60642497e-15,
2.14303704e-01, 4.23258961e-14],
[-1.91152546e-13, 6.32515083e-01, -2.04969331e-01,
-1.60019944e-13, 1.23161395e-01],
[-4.29333199e-01, -7.96753238e-14, 1.22939338e-13,
1.17964111e+00, 2.63716592e-13],
[-6.18702609e-13, 1.22579313e+00, 9.68416274e-01,
-2.22271700e-13, 4.11753025e+00],
[ 2.71650646e-01, 3.27541365e-13, -9.63128704e-14,
2.38772537e+00, 2.81972898e-13],
[ 1.64068615e-13, 4.99865062e-01, -1.59546302e+00,
-1.93176545e-13, 1.24573564e+00],
[ 5.13117092e-01, 4.22488237e-13, -2.32577832e-13,
-1.34781426e+00, 3.24555659e-13],
[-1.05547190e-14, 3.43461974e-01, -6.74706919e-01,
-9.03540095e-13, -2.25040798e+00],
[ 3.52009640e-01, 2.34825150e-13, -1.81826877e-13,
-2.06152430e-02, -2.69164526e-13],
[-1.57143488e-16, 1.39451882e-01, -5.48286674e-01,
3.65083429e-13, -1.34260580e-01],
[ 3.64685582e-15, 5.22010092e-02, -9.62095563e-02,
-2.11001492e-15, -4.26791830e-02],
[ 2.71631997e-01, 1.04113120e-14, -4.14820412e-14,
-2.46025932e-01, 3.06609708e-13],
[ 4.08721704e-13, -6.57864195e-01, -2.69236443e-02,
1.84318330e-14, 1.75390128e-01],
[-8.25313846e-01, -6.55584420e-13, 5.95892303e-14,
-7.28018991e-01, 2.77578456e-12],
[-3.62093453e-13, 5.54832454e-01, 6.54091420e-01,
-5.17660892e-13, -1.62433589e+00],
[-4.75042739e-01, -6.20196336e-13, 2.40858478e-13,
1.14959905e+00, 1.23529412e-12],
[-2.55216132e-13, 3.52864362e-01, -2.95293195e-01,
1.05952132e-13, 1.46290210e-01],
[-5.38283562e-01, -5.07831398e-13, -2.59237859e-14,
3.62054482e-01, 1.63362821e-12],
[-1.84579634e-13, 2.04398066e-01, 3.27608890e-01,
5.13187095e-13, 6.79114100e-01],
[-2.60993571e-01, -3.42914780e-13, -2.11899266e-13,
4.12652410e-01, 7.66265348e-13],
[ 5.72377400e-03, 1.01226028e-14, 2.98651510e-14,
-7.76390617e-03, -5.96604688e-14],
[ 2.10658981e-13, -3.19007422e-03, 8.15955499e-02,
-1.08639471e-13, 1.15820937e-01],
[-1.11798609e-01, -4.28487689e-14, -9.50469549e-14,
2.15484565e-01, -1.03865915e-12],
[ 1.67166274e-13, 6.73699820e-01, -1.26248421e-02,
7.98421307e-15, 5.29795576e-02],
[ 6.12576956e-01, 4.19558217e-13, -6.84441660e-14,
1.47376074e+00, -9.41744074e-14],
[ 4.09823959e-13, 5.43059487e-01, -2.26363255e+00,
6.71821255e-13, 1.65103290e+00],
[ 8.60609626e-01, 5.54477758e-13, -3.61548479e-13,
-1.27263060e+00, -7.51650363e-13],
[-1.01273114e-14, 4.70844858e-01, -1.45244290e+00,
1.38550414e-12, -3.70123468e+00],
[ 6.46375422e-01, 4.76547362e-13, -3.57987407e-13,
-2.93180066e-01, -9.93088394e-13],
[-4.43807020e-13, 2.30671654e-01, -1.06481924e+00,
1.12903587e-12, -3.14779260e-01],
[ 3.20103968e-14, -3.79582921e-03, 4.28921879e-03,
4.10808592e-14, -5.14772282e-03],
[-2.55393881e-02, 4.09211837e-15, 2.50607615e-13,
8.55398720e-05, -3.48884807e-14],
[ 7.44226636e-14, -2.62741137e-02, 4.66728024e-02,
1.37555533e-14, -1.48245403e-01],
[-2.95837146e-01, -2.94556579e-13, 4.56014618e-13,
8.55026029e-02, 1.71911510e-13],
[-6.24391094e-14, 2.02314153e-01, 4.28667106e-01,
1.89919041e-13, 4.03688695e-01],
[-4.40435206e-01, -5.25196335e-13, 4.97429940e-13,
5.81419517e-01, 7.40464258e-13],
[-2.88377556e-13, 2.22416426e-01, 3.48661900e-01,
4.27699143e-13, 1.09436818e-01],
[-5.05846692e-01, -6.19675091e-13, 2.71889909e-13,
4.62628735e-01, 1.74963368e-13],
[-2.18394110e-13, 1.46253643e-01, 3.78578015e-01,
5.10986822e-13, 5.89609479e-01],
[-3.11383993e-01, -4.50499862e-13, 2.17924492e-13,
3.67787998e-01, 1.67846120e-13],
[ 1.43010972e-03, -9.60938833e-15, 4.24038505e-15,
2.12519349e-03, -1.45477889e-14],
[-6.89197296e-14, 1.72063449e-02, -2.71308712e-02,
2.37103069e-13, -3.29891533e-03],
[ 5.23056519e-02, 4.07590609e-14, 1.78769554e-13,
3.30717675e-02, 2.69530403e-13],
[-1.12788264e-13, 1.14838699e-01, -2.45895165e-01,
3.63845323e-13, 8.55021318e-02],
[ 2.88692306e-01, 1.83782367e-13, 2.10478255e-13,
9.95167064e-02, -1.03123338e-13],
[-1.05781957e-16, 2.12875187e-01, -1.08972618e+00,
1.04575944e-12, -2.96894258e-01],
[ 5.52151264e-01, 2.77475777e-13, -6.06739728e-14,
-5.89707319e-01, -2.33444469e-13],
[-1.79301056e-13, 2.42806313e-01, -1.29871506e+00,
1.88858495e-12, -1.98688745e+00],
[ 4.78616465e-01, 2.58959224e-13, -2.50962085e-13,
-4.11699615e-01, -1.63932330e-13],
[-4.17363734e-13, 1.45667753e-01, -9.47644623e-01,
1.66603017e-12, -8.85913291e-01],
[ 3.88078890e-14, 1.62222238e-04, 8.36960997e-04,
1.89586640e-14, 3.56828489e-04],
[-6.25751168e-03, -4.86188978e-14, 1.71452822e-14,
2.57159237e-03, -3.57037740e-14],
[ 2.70099107e-14, 2.54063015e-03, 2.85575757e-02,
1.12368685e-13, 2.01239192e-02],
[-7.20936010e-02, -2.20680157e-13, 9.32277220e-14,
4.36644465e-02, 1.85513036e-13],
[ 2.99444096e-14, 6.75703754e-02, 1.61596696e-01,
1.08372906e-13, 7.84072851e-02],
[-1.56840424e-01, -3.96134347e-13, 2.57761715e-13,
2.75442157e-01, 2.33865445e-13],
[ 8.70520777e-15, 9.60832875e-02, 1.79686527e-01,
1.67854875e-13, 3.09842863e-01],
[-2.21640121e-01, -4.52704967e-13, 2.74221626e-13,
2.50734418e-01, -1.75118205e-13],
[-1.67773335e-14, 6.73353927e-02, 2.00215078e-01,
2.87874332e-13, 2.24252984e-01],
[-1.59649143e-01, -3.50198611e-13, 9.03987484e-14,
2.00790854e-01, -2.67528682e-13],
[ 5.83459434e-04, 1.42347592e-14, 4.70289052e-14,
-2.48950673e-04, 2.16301068e-14],
[ 4.80948226e-14, 1.45135402e-03, -8.58256149e-03,
6.90132800e-15, -4.42064439e-03],
[ 1.46557342e-02, 2.85344007e-14, 1.25008540e-13,
-5.84311023e-03, -5.92032750e-14],
[-7.82508867e-14, 1.40453094e-02, -8.79459170e-02,
8.86462095e-14, -5.86418355e-02],
[ 7.79000793e-02, 5.06120908e-14, 1.44866674e-13,
-4.07790241e-02, -1.48026968e-13],
[-1.91417022e-13, 4.21641599e-02, -3.38861607e-01,
4.62977200e-13, -2.41315537e-01],
[ 1.77460607e-01, 1.32305176e-13, 1.17057839e-13,
-2.16000171e-01, -4.08427848e-13],
[-2.80768464e-13, 6.09319462e-02, -5.26382491e-01,
8.69261507e-13, -8.03873977e-01],
[ 1.74056918e-01, 1.37181180e-13, 1.03596710e-13,
-1.99938292e-01, -2.71172638e-13],
[-2.57485006e-13, 4.03658981e-02, -4.21566452e-01,
8.23747372e-13, -5.20345902e-01]]))
[10]:
panel_CCCC.plot_eigenvalue()
%matplotlib inline
Free edge Nxx (custom boundary condition)#
[11]:
constraints={
'x0': 'pinned',
'xa': 'pinned',
'y0': 'free',
'yb': 'pinned',
}
panel_SSFS = PlateStructure(l1, 1.5*a, b, m=m, n=n, Nxx=-1, constraints=constraints)
[12]:
panel_SSFS.buckling_analysis()
[12]:
(array([ 20.12080055, 47.13886913, 92.5739614 , 156.53663617,
185.19779529]),
array([[-6.64602782e-01, -4.40741305e-01, -3.21998989e-01,
-2.53957602e-01, 2.36558996e-01],
[ 7.67084690e-01, 7.01790021e-01, 6.96072097e-01,
7.09349881e-01, -8.79759269e-01],
[ 7.06516166e-01, 4.81372557e-01, 3.44176719e-01,
2.61557308e-01, 7.50390811e-01],
[-1.38971756e-01, -2.87840954e-01, -3.92644459e-01,
-4.73238641e-01, -4.20905413e-01],
[ 4.42080854e-02, 1.62392960e-01, 2.94645688e-01,
4.15458025e-01, -4.60977406e-01],
[-1.50662709e-02, -7.48610571e-02, -1.80504923e-01,
-3.04263494e-01, 2.23427086e-01],
[ 1.36890276e-03, 2.55831272e-02, 8.89360034e-02,
1.84715624e-01, -2.88094706e-02],
[-4.00849530e-03, -1.01944714e-02, -4.16728395e-02,
-1.04747498e-01, 9.08923185e-03],
[-2.04950319e-04, 2.13396987e-03, 1.53261755e-02,
4.82541723e-02, -7.05409677e-03],
[-1.73703950e-03, -1.58651565e-03, -7.40562178e-03,
-2.55315434e-02, 1.41614950e-03],
[ 6.65261548e-01, -4.40590939e-01, 3.22410876e-01,
-2.55128132e-01, 2.37442376e-01],
[-7.61520276e-01, 6.97561763e-01, -6.93514499e-01,
7.10214241e-01, -8.76968730e-01],
[-7.16788714e-01, 4.85898572e-01, -3.46292317e-01,
2.60147868e-01, 7.61795661e-01],
[ 1.28118925e-01, -2.78567219e-01, 3.83618541e-01,
-4.64257140e-01, -4.17393290e-01],
[-4.61761610e-02, 1.61764841e-01, -2.93063615e-01,
4.14438742e-01, -4.54135260e-01],
[ 4.50466132e-03, -6.63810636e-02, 1.72028421e-01,
-2.97578561e-01, 2.23998675e-01],
[-2.78630481e-03, 2.48304217e-02, -8.68335846e-02,
1.81913149e-01, -2.01927442e-02],
[-3.37487931e-03, -4.70825907e-03, 3.55134316e-02,
-9.93447393e-02, 9.21704319e-03],
[-3.14255834e-04, 1.65678626e-03, -1.41652640e-02,
4.65522941e-02, -2.97960015e-03],
[-1.72946902e-03, 7.59919972e-04, 4.56816500e-03,
-2.31145915e-02, 1.11050144e-03],
[-3.58822112e-01, -2.67456742e-05, 6.96702705e-01,
-7.94618304e-04, 1.43946968e-04],
[ 4.12439101e-01, -7.37230816e-03, -1.50309187e+00,
-2.09948654e-03, 7.48787137e-03],
[ 3.83996692e-01, 8.42658087e-03, -7.46463185e-01,
5.11567948e-04, 1.33865392e-02],
[-7.20942978e-02, 1.05470433e-02, 8.40146156e-01,
1.00239307e-02, 5.81763214e-03],
[ 2.43324993e-02, -9.50005687e-04, -6.36463467e-01,
-1.96632182e-03, 8.08588405e-03],
[-5.30645181e-03, 1.05192777e-02, 3.82425790e-01,
8.68803611e-03, 1.74807321e-04],
[ 1.07372680e-03, -9.31183122e-04, -1.91201414e-01,
-3.58492898e-03, 1.07840861e-02],
[-1.85596992e-04, 6.79713380e-03, 8.46446862e-02,
6.75153516e-03, 1.74281636e-04],
[ 5.34156295e-06, -5.87720851e-04, -3.26262941e-02,
-2.13012239e-03, 5.05477031e-03],
[-6.61185160e-06, 2.91403254e-03, 1.36117154e-02,
3.00790505e-03, -3.81180987e-04],
[-9.33474752e-05, 8.01732688e-01, -8.32047405e-04,
-5.52552585e-01, -4.31193247e-01],
[ 3.65965036e-03, -1.27299984e+00, 1.28679677e-02,
1.55129249e+00, 1.59808868e+00],
[-7.20317338e-03, -8.79887402e-01, -9.99347663e-03,
5.65539414e-01, -1.37551166e+00],
[-1.42779923e-02, 5.15315231e-01, -1.28192216e-02,
-1.03056079e+00, 7.62664522e-01],
[-3.86515638e-03, -2.94894016e-01, 4.40846687e-03,
9.15651236e-01, 8.32586533e-01],
[-1.67074176e-02, 1.28570413e-01, -1.49695128e-02,
-6.72554392e-01, -4.06961642e-01],
[-2.55975964e-03, -4.58793384e-02, 3.72724209e-03,
4.14808823e-01, 4.46835949e-02],
[-1.24233107e-02, 1.36322851e-02, -1.04546917e-02,
-2.40460976e-01, -1.66093119e-02],
[-9.12148381e-04, -3.46299468e-03, 1.94612293e-03,
1.14042882e-01, 9.18692502e-03],
[-5.91801504e-03, 7.93274651e-04, -4.82511142e-03,
-6.40535429e-02, -2.28009864e-03],
[ 2.70407464e-02, -3.10081279e-04, -1.17922548e+00,
2.36655654e-03, 1.64807037e-03],
[-3.10875355e-02, -5.36988183e-04, 2.52488865e+00,
-2.06026787e-02, -1.98525854e-03],
[-2.89735591e-02, 2.54745525e-03, 1.26434463e+00,
1.30817135e-02, 8.44712958e-04],
[ 5.39938273e-03, 9.99186435e-03, -1.39903865e+00,
1.24451605e-02, 7.25812782e-03],
[-1.90100148e-03, 1.23065700e-03, 1.04986375e+00,
-1.01883031e-02, 1.86645368e-02],
[ 3.64095132e-04, 1.36535589e-02, -6.14111234e-01,
1.79891509e-02, 5.32852341e-03],
[-1.46481044e-04, -3.60783058e-04, 2.93457749e-01,
-7.36738804e-03, 1.42411242e-02],
[-6.93828246e-06, 1.04468001e-02, -1.12426627e-01,
1.16215187e-02, 7.62310331e-04],
[-3.53802105e-05, -7.59688264e-04, 3.60792577e-02,
-3.64568753e-03, 8.10476144e-03],
[-5.99499392e-06, 4.75813991e-03, -5.84625933e-03,
4.97461723e-03, -5.98191859e-04],
[ 6.88757372e-05, -1.51790981e-01, 9.23606797e-04,
1.47335222e+00, 8.16397490e-02],
[ 3.17771009e-03, 2.40969384e-01, -4.26935897e-03,
-4.01921816e+00, -3.02532290e-01],
[-7.35935632e-03, 1.66605082e-01, 9.55661172e-04,
-1.51588578e+00, 2.60450877e-01],
[-1.33969219e-02, -9.74927862e-02, -6.42041241e-03,
2.60314836e+00, -1.44355988e-01],
[-5.19876749e-03, 5.58003423e-02, -1.21326076e-03,
-2.27577075e+00, -1.57513827e-01],
[-1.91473112e-02, -2.42445317e-02, -1.23195114e-02,
1.57832183e+00, 7.71076218e-02],
[-3.84058843e-03, 8.65597830e-03, 1.21755808e-03,
-9.18270514e-01, -8.34752025e-03],
[-1.60429310e-02, -2.49533809e-03, -1.16501818e-02,
4.30569623e-01, 3.18506278e-03],
[-1.39020447e-03, 6.36715869e-04, 1.59526469e-03,
-1.80178646e-01, -1.67611542e-03],
[-8.03434067e-03, -1.04290996e-04, -6.12894119e-03,
4.57611467e-02, 4.50866766e-04],
[-6.95015627e-04, -7.89844744e-05, 3.68113305e-01,
-1.98780524e-03, -2.18913155e-03],
[ 7.96110391e-04, -1.92979151e-03, -8.04393366e-01,
1.35892286e-02, 9.42809049e-03],
[ 7.16560792e-04, 3.87516057e-03, -3.93960174e-01,
-5.96123256e-03, 8.08078413e-03],
[-1.68319537e-04, 7.35287104e-03, 4.55977530e-01,
-5.49647715e-04, -2.20759955e-03],
[-5.96674743e-06, 1.52593248e-03, -3.50721831e-01,
4.35732164e-03, 1.89906034e-02],
[-4.56836269e-05, 1.19242836e-02, 2.19173328e-01,
4.71838594e-03, 1.74602036e-04],
[-5.86808776e-05, 1.94243590e-04, -1.16519235e-01,
4.27975899e-04, 1.74422428e-02],
[-2.22354138e-05, 1.02226157e-02, 6.00657867e-02,
6.68377183e-03, -6.67394338e-04],
[-3.57370630e-05, -5.86995764e-04, -2.67422938e-02,
-1.08129369e-03, 9.05168353e-03],
[-6.55159673e-06, 4.92130020e-03, 1.54327445e-02,
3.76189624e-03, -1.06110532e-03],
[ 3.69877000e-05, 1.15208566e-02, -7.49478624e-05,
-6.58832869e-01, -6.19679997e-03],
[ 1.94060298e-03, -1.83482600e-02, 2.57034188e-03,
1.87039289e+00, 2.29726919e-02],
[-5.34582025e-03, -1.26311399e-02, -3.46410195e-03,
6.73335230e-01, -1.97173268e-02],
[-9.27562109e-03, 7.48200758e-03, -5.72628986e-03,
-1.25341683e+00, 1.09721912e-02],
[-4.77172354e-03, -4.29388530e-03, -1.67133702e-04,
1.12096987e+00, 1.20467693e-02],
[-1.47693158e-02, 1.95393354e-03, -1.05541972e-02,
-8.37154203e-01, -5.81249213e-03],
[-4.01835568e-03, -7.10089465e-04, 1.06518922e-03,
5.26227162e-01, 7.37111425e-04],
[-1.37450919e-02, 2.87699293e-04, -1.02976944e-02,
-3.18646300e-01, -2.07499001e-04],
[-1.53475476e-03, -7.72739790e-05, 1.21765402e-03,
1.55478555e-01, 1.87229319e-04],
[-7.25095095e-03, 5.87505647e-05, -5.51474880e-03,
-9.36138905e-02, -1.60154289e-05],
[ 8.80983318e-06, -4.39378514e-05, -4.93647890e-02,
4.71479055e-04, 8.70651692e-04],
[-1.01817155e-05, -5.57398627e-04, 9.30240628e-02,
-4.42920686e-03, -1.29679038e-03],
[-2.35437570e-05, 1.85534716e-03, 5.34442484e-02,
3.23811454e-03, 1.76690828e-03],
[-1.46547683e-05, 3.32286058e-03, -4.38703872e-02,
3.46484773e-03, 3.27789646e-03],
[-2.66520240e-05, 1.31444600e-03, 2.63873678e-02,
-1.46816581e-03, 5.54350100e-03],
[-2.16481949e-05, 5.95801613e-03, -5.67556826e-03,
6.02421184e-03, 3.04659652e-03],
[-3.31646112e-05, 4.76870012e-04, -5.58084538e-03,
-2.02339605e-03, 7.71942674e-03],
[-1.38277652e-05, 5.61504910e-03, 1.20676164e-02,
5.33574075e-03, 7.65891976e-04],
[-2.07920090e-05, -2.40439703e-04, -8.78579193e-03,
-1.25341317e-03, 4.58024764e-03],
[-3.61208390e-06, 2.75515687e-03, 8.20847610e-03,
2.43412765e-03, -5.20962318e-04],
[ 2.26076416e-05, -4.70777107e-04, 5.32764440e-05,
1.29832656e-01, 2.53830045e-04],
[ 6.56677613e-04, 6.91495954e-04, 2.25861501e-04,
-3.05942448e-01, -9.17536279e-04],
[-2.58794221e-03, 5.24296435e-04, -1.19448600e-03,
-1.35985084e-01, 8.21395373e-04],
[-4.17783270e-03, -2.31616006e-04, -2.26443024e-03,
1.72262710e-01, -4.53181954e-04],
[-2.77485370e-03, 1.06916945e-04, -8.38634477e-04,
-1.33143317e-01, -4.30007347e-04],
[-7.02761962e-03, 1.98671853e-05, -4.62696128e-03,
5.83842351e-02, 2.36841942e-04],
[-2.50412515e-03, -3.24256190e-05, 4.86973701e-06,
-9.29556437e-03, 4.38277596e-05],
[-6.90309193e-03, 6.95126786e-05, -5.12419776e-03,
-3.38168232e-02, 1.43814665e-05],
[-9.66068998e-04, -2.79805088e-05, 4.46813274e-04,
2.74685453e-02, 3.51159464e-05],
[-3.64137204e-03, 3.67529610e-05, -2.79731066e-03,
-3.43269355e-02, 6.21642142e-06]]))
[13]:
panel_SSFS.plot_eigenvalue()
Nxy Loading#
[14]:
panel_CCCC_nxy = PlateStructure(l1, a, b, m=m, n=n, Nxy=-1, constraints='CLAMPED')
[15]:
panel_CCCC_nxy.buckling_analysis()
[15]:
(array([338.84283307, 389.26571459, 776.82143839, 824.28455938,
882.94931083]),
array([[-1.47728432e+00, 3.34644952e-13, -8.43249877e-01,
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-1.30314642e+00, 9.81823952e-01],
[ 9.95721068e-01, -1.19028836e-13, 1.11385518e-01,
6.46266870e-13, -1.34946433e-13],
[ 1.21927510e-13, 6.80148527e-01, -6.10393128e-13,
6.51084994e-02, -1.46811101e+00],
[-3.01802434e-01, -6.50998956e-14, 3.24308478e-01,
5.03416636e-14, -3.12802218e-13],
[-1.26137100e-13, -1.33387414e-01, 2.46430131e-14,
1.90512102e-01, 6.91947740e-01],
[ 1.26145071e-02, 4.64762416e-14, -2.07071433e-01,
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-8.01887995e-02, -1.30219392e-01],
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-2.65481591e-14, 3.98700408e-14],
[ 4.17507020e-14, -2.35155548e-04, 4.74419292e-14,
1.39117543e-02, 2.21385083e-02],
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-1.31530631e+00, -9.66102602e-01],
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3.02615270e-12, -1.77822561e-12],
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3.52006133e-12, -2.70428896e-12],
[-1.02070773e-13, -1.15297228e+00, -2.87635342e-12,
3.75221134e+00, 5.45255010e+00],
[ 3.62393749e-01, -3.55608825e-14, -2.90060377e+00,
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3.46689486e-01, 4.43599484e-01],
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-1.44324697e-13, 7.69726779e-13],
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-1.06444975e-02, 5.88300002e+00],
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1.00440128e-11, -3.28355201e-12],
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1.30652178e+01, 1.09523048e+01],
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-9.17425677e-12, 2.32986659e-12],
[ 3.11615052e-16, 9.52805183e-01, 5.87189036e-12,
-6.77007884e+00, -6.06616545e+00],
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2.20992954e-12, 5.60397385e-13],
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2.11038983e+00, 2.65059027e+00],
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[ 1.12600133e-13, 6.77554992e-01, 2.21200853e-13,
8.72197601e-02, 1.46034319e+00],
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7.93256655e-12, -8.02488486e-12],
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4.13490435e+00, 2.51675218e+00],
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3.51280996e-12, 1.58653128e-11],
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2.75170798e+00, -2.24702976e+00],
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[ 5.83812953e-13, -1.79966458e-01, -6.90426074e-12,
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[ 1.26123352e-02, 2.44084968e-14, -2.02982003e-01,
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5.24698976e-12, 2.14222995e-13],
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4.10379381e+00, -2.58954482e+00],
[ 1.81623703e-01, -1.65773011e-12, -2.26149779e+00,
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6.13346626e-14, 9.54669381e-13],
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[ 6.41976347e-13, -1.75135194e-01, -5.62570118e-12,
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[-5.85063947e-01, -1.97822009e-12, -3.23821435e-01,
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[ 5.02685501e-04, -4.27358547e-14, 3.76076536e-02,
2.12195931e-13, 1.86214763e-14],
[-1.97585246e-14, -2.82017125e-02, -3.99473700e-13,
3.39077401e-01, -4.46381875e-01],
[ 5.98434989e-02, -3.70676000e-13, -6.03990818e-01,
-2.18255082e-12, 3.02484360e-14],
[-7.97592715e-14, -8.00524109e-02, 2.04969375e-12,
-6.97135379e-01, 9.68898825e-01],
[ 1.95378881e-01, -6.21081609e-13, -2.48017445e-02,
-1.00916326e-12, 3.56801650e-12],
[-2.45713583e-13, -1.77896818e-01, -1.18933415e-12,
-2.84166592e-01, -6.35965163e-01],
[ 3.61794354e-01, -5.29152455e-13, -1.39333986e-02,
4.24284724e-12, 1.38909337e-11],
[-3.61975481e-13, -1.73037941e-01, -2.73256246e-12,
-3.42693138e-01, -3.03684193e-01],
[ 2.98763780e-01, 1.15622176e-12, 5.60037295e-02,
1.95700330e-12, 1.40933794e-11],
[-4.66952848e-13, -9.99083671e-02, -1.37514796e-12,
-1.85035462e-01, -3.65634746e-01],
[-6.50791295e-15, -2.41384131e-04, -2.56849801e-14,
1.34706549e-02, -2.20906061e-02],
[-1.68169457e-02, -2.00872864e-14, -1.23220736e-01,
-2.52212702e-13, 2.58106177e-12],
[ 1.20829797e-13, 7.80172589e-03, -2.33018899e-13,
-3.09555384e-01, 3.88889256e-01],
[-1.72259028e-01, -4.61403315e-13, 6.30644792e-02,
9.90159346e-13, 8.74759936e-12],
[ 3.39036263e-13, -6.53641280e-02, -3.03325637e-12,
-6.54325237e-02, 1.38241252e-01],
[-4.44246872e-01, -1.50104334e-12, -3.54260927e-01,
-2.90848938e-12, 2.11755972e-11],
[ 2.71420256e-13, -1.25014313e-01, -5.38420698e-12,
-3.15395343e-01, 4.86929497e-01],
[-5.84301288e-01, -2.20988505e-12, -3.22800174e-01,
-1.40853215e-11, 2.21721046e-11],
[ 3.82826746e-13, -1.01135119e-01, -4.27173574e-12,
-1.79699680e-01, 3.68197373e-01],
[-3.89453084e-01, -1.49754705e-12, -2.20302574e-01,
-8.61348878e-12, 1.88082258e-11]]))
[16]:
panel_CCCC_nxy.plot_eigenvalue()
[ ]: