Elastic properties of CSM¶

This case study applies the principles from Elastic properties of woven plies and the case study On transverse isotropy.

Details are left for an exercise. Basic code without further description:

import numpy as np

Ef, vf = 70000.0, 0.22
Em, vm =  3000.0, 0.40
Gf=Ef/(2+2*vf)
Gm=Em/(2+2*vm)

Vf=0.15

import compositelib
E1= compositelib.micmec_E1(  Vf=Vf, E1f=Ef, Em=Em )
E2= compositelib.micmec_E2c( Vf=Vf, E2f=Ef, Em=Em, xi1=1)
v12=compositelib.micmec_v12( Vf=Vf, v12f=vf, vm=vm)
G12=compositelib.micmec_G12c(Vf=Vf, G12f=Gf, Gm=Gm,xi2=1)

print('E1=',round(E1,0))
print('E2=',round(E2,0))
print('v12=',round(v12,3))
print('G12=',round(G12,0))

E1= 13050.0
E2= 3958.0
v12= 0.373
G12= 1418.0

E3=E2
v13=v12
v23=0.45
G13=G12
G23=E2/(2+2*v23)

m_UD3 = {'E1':E1,    'E2':E2,   'E3':E3,
        'v12':v12, 'v13':v13, 'v23':v23, 
        'G12':G12, 'G13':G13, 'G23':G23}

C0 =compositelib.C3D(m_UD3)
C60p=compositelib.C3Dtz(C0,60)
C60n=compositelib.C3Dtz(C0,-60)

Cav=(C0+C60p+C60n)/3.0
Sav=np.linalg.inv(Cav)

m_csm = {'E1':  1/Sav[0,0],
         'E2':  1/Sav[1,1],
         'E3':  1/Sav[2,2],
         'G23': 1/Sav[3,3],
         'G13': 1/Sav[4,4],
         'G12': 1/Sav[5,5],
         'v23': -Sav[1,2]*(1/Sav[1,1]),
         'v13': -Sav[0,2]*(1/Sav[0,0]),
         'v12': -Sav[0,1]*(1/Sav[0,0]) }


display(m_csm)

{'E1': 6839.339171464384,
 'E2': 6839.339171464382,
 'E3': 4275.092699815866,
 'G23': 1391.3711015436477,
 'G13': 1391.3711015436481,
 'G12': 2545.099462842836,
 'v23': 0.35396673814801105,
 'v13': 0.3539667381480113,
 'v12': 0.34362905483956036}

Disclaimer:This site is designed for educational purposes only. There are most likely errors, mistakes, typos, and poorly crafted statements that are not detected yet... www.ntnu.edu/employees/nils.p.vedvik