Composite Module (compmech.composite)

The compmech.composite module includes functions used to calculate laminate properties based on input data of stacking sequence and lamina properties.

The most convenient usage is probably using the compmech.composite.laminate.read_stack() function:

from compmech.composite.laminate import read_stack

laminaprop = (E11, E22, nu12, G12, G13, G23)
plyt = ply_thickness
stack = [0, 90, +45, -45]
lam = read_stack(stack, plyt=plyt, laminaprop=laminaprop)

Where the laminate stiffness matrix, the often called ABD matrix, with shape=(6, 6), can be accessed using:

>>> lam.ABD

and when shear stiffnesses are required, the ABDE matrix, with shape=(8, 8):

>>> lam.ABDE

Composite Laminate Module (compmech.composite.laminate)

class compmech.composite.laminate.Laminate

attribute	description
plies	list of plies
t	total thickness of the laminate
offset	offset at the normal direction
e1	equivalent laminate modulus in 1 direction
e2	equivalent laminate modulus in 2 direction
g12	equivalent laminate shear modulus in 12 direction
nu12	equivalent laminate Poisson ratio in 12 direction
nu21	equivalent laminate Poisson ratio in 21 direction
xiA	laminate parameters for extensional matrix A
xiB	laminate parameters for extension-bending matrix B
xiD	laminate parameters for bending matrix D
A	laminate extension matrix
B	laminate extension-bending matrix
D	laminate bending matrix
E	laminate transferse shear matrix
ABD	laminate ABD matrix
ABDE	laminate ABD matrix with transverse shear terms

Methods

calc_ABDE_from_lamination_parameters()	Use the ABDE matrix based on lamination parameters.
calc_constitutive_matrix()	Calculates the laminate constitutive matrix
calc_equivalent_modulus()	Calculates the equivalent laminate properties.
calc_lamination_parameters()	Calculate the lamination parameters.
force_balanced_LP()	Force balanced lamination parameters
force_orthotropic()	Force an orthotropic laminate
force_symmetric()	Force a symmetric laminate
force_symmetric_LP()	Force symmetric lamination parameters

rebuild

calc_ABDE_from_lamination_parameters()

Use the ABDE matrix based on lamination parameters.

Given the lamination parameters xiA, xiB, xiC and xiD, the ABD matrix is calculated.

calc_constitutive_matrix()

Calculates the laminate constitutive matrix

This is the commonly called ABD matrix with shape=(6, 6) when the classical laminated plate theory is used, or the ABDE matrix when the first-order shear deformation theory is used, containing the transverse shear terms.

calc_equivalent_modulus()

Calculates the equivalent laminate properties.

The following attributes are calculated:

e1, e2, g12, nu12, nu21

calc_lamination_parameters()

Calculate the lamination parameters.

The following attributes are calculated:

xiA, xiB, xiD, xiE

force_balanced_LP()

Force balanced lamination parameters

The lamination parameters \(\xi_{A2}\) and \(\xi_{A4}\) are set to null to force a balanced laminate.

force_orthotropic()

Force an orthotropic laminate

The terms \(A_{13}\), \(A_{23}\), \(A_{31}\), \(A_{32}\), \(B_{13}\), \(B_{23}\), \(B_{31}\), \(B_{32}\), \(D_{13}\), \(D_{23}\), \(D_{31}\), \(D_{32}\) are set to zero to force an orthotropic laminate.

force_symmetric()

Force a symmetric laminate

The \(B\) terms of the constitutive matrix are set to zero.

force_symmetric_LP()

Force symmetric lamination parameters

The lamination parameters \(\xi_{Bi}\) are set to null to force a symmetric laminate.

compmech.composite.laminate.read_lamination_parameters(thickness, laminaprop, xiA1, xiA2, xiA3, xiA4, xiB1, xiB2, xiB3, xiB4, xiD1, xiD2, xiD3, xiD4, xiE1, xiE2, xiE3, xiE4)

Calculates a laminate based on the lamination parameters.

The lamination parameters: \(\xi_{A1} \cdots \xi_{A4}\), \(\xi_{B1} \cdots \xi_{B4}\), \(\xi_{C1} \cdots \xi_{C4}\), \(\xi_{D1} \cdots \xi_{D4}\), \(\xi_{E1} \cdots \xi_{E4}\)

are used to calculate the laminate constitutive matrix.

Parameters:

thicknessfloat

The total thickness of the laminate

laminaproptuple

The laminaprop tuple used to define the laminate material.

xiA1 to xiD4float

The 16 lamination parameters used to define the laminate.

Returns:

lamLaminate

laminate with the ABD and ABDE matrices already calculated

compmech.composite.laminate.read_stack(stack, plyt=None, laminaprop=None, plyts=[], laminaprops=[], offset=0.0)

Read a laminate stacking sequence data.

An Laminate object is returned based on the inputs given.

Parameters:

stacklist

Angles of the stacking sequence in degrees.

plytfloat, optional

When all plies have the same thickness, plyt can be supplied.

laminaproptuple, optional

When all plies have the same material properties, laminaprop can be supplied.

plytslist, optional

A list of floats with the thickness of each ply.

laminapropslist, optional

A list of tuples with a laminaprop for each ply.

offsetfloat, optional

Offset along the normal axis about the mid-surface, which influences the laminate properties.

Notes

plyt or plyts must be supplied laminaprop or laminaprops must be supplied

For orthotropic plies, the laminaprop should be:

laminaprop = (E11, E22, nu12, G12, G13, G23)

For isotropic pliey, the laminaprop should be:

laminaprop = (E, E, nu)

Composite Lamina Module (compmech.composite.lamina)

class compmech.composite.lamina.Lamina

attribute	description
plyid	id of the composite lamina
matobj	a pointer to a MatLamina object
t	ply thickness
theta	ply angle in degrees
L	transformation matrix for displacements to laminate csys
R	transformation matrix for stresses to laminate csys
T	transformation matrix for stresses to lamina csys
QL	constitutive matrix for plane-stress in laminate csys
laminates	laminates that contain this lamina

Methods

rebuild

Composite Matlamina Module (compmech.composite.matlamina)

class compmech.composite.matlamina.MatLamina

Orthotropic material lamina

attributes	description
e1	Young Modulus in direction 1
e2	Young Modulus in direction 2
g12	in-plane shear modulus
g13	transverse shear modulus for plane 1-Z
g23	transverse shear modulus for plane 2-Z
nu12	Poisson’s ratio 12
nu13	Poisson’s ratio 13
nu23	Poisson’s ratio 23
nu21	Poisson’s ratio 21: use formula nu12/e1 = nu21/e2
nu31	Poisson’s ratio 31: use formula nu31/e3 = nu13/e1
nu32	Poisson’s ratio 32: use formula nu23/e2 = nu32/e3
rho	especific mass (mass / volume)
a1	thermal expansion coeffiecient in direction 1
a2	thermal expansion coeffiecient in direction 2
a3	thermal expansion coeffiecient in direction 3
tref	reference temperature
st1,st2	allowable tensile stresses for directions 1 and 2
sc1,sc2	allowable compressive stresses for directions 1 and 2
ss12	allowable in-plane stress for shear
strn	allowable strain for direction 1
q11	lamina constitutive constant 11
q12	lamina constitutive constant 12
q13	lamina constitutive constant 13
q21	lamina constitutive constant 21
q22	lamina constitutive constant 22
q23	lamina constitutive constant 23
q31	lamina constitutive constant 31
q32	lamina constitutive constant 32
q33	lamina constitutive constant 33
q44	lamina constitutive constant 44
q55	lamina constitutive constant 55
q66	lamina constitutive constant 66
u	matrix with lamina invariants
c	matrix with lamina stiffness coefficients

Notes

For isotropic materials when the user defines \(\nu\) and \(E\), \(G\) will be recaculated based on equation: \(G = E/(2 \times (1+\nu))\); in a lower priority if the user defines \(\nu\) and \(G\), \(E\) will be recaculated based on equation: \(E = 2 \times (1+\nu) \times G\).

Methods

read_inputs
rebuild

compmech.composite.matlamina.read_laminaprop(laminaprop=None)

Returns a MatLamina object based on an input laminaprop tuple

Parameters:

laminaproplist or tuple

Tuple containing the folliwing entries:

(e1, e2, nu12, g12, g13, g23, e3, nu13, nu23)

for othotropic materials the user can only supply:

(e1, e2, nu12, g12, g13, g23)

for isotropic materials the user can only supply:

(e1, e2, nu12)

symbol	value
e1	Young Module in direction 1
e2	Young Module in direction 2
nu12	12 Poisson’s ratio
g12	12 Shear Modulus
g13	13 Shear Modulus
g23	13 Shear Modulus
e3	Young Module in direction 3
nu13	13 Poisson’s ratio
nu23	23 Poisson’s ratio

Returns:

matlamMatLamina

A MatLamina object.