# Now let's make all of the laminate objects we will need for the box beam. In
# this case it's 4:
n_i_Lay1 = [6]
m_i_Lay1 = [2]
th_Lay1 = [0.]
lam1_Lay1 = Laminate(n_i_Lay1, m_i_Lay1, matLib, th=th_Lay1)
lam2_Lay1 = Laminate(n_i_Lay1, m_i_Lay1, matLib, th=th_Lay1)
lam3_Lay1 = Laminate(n_i_Lay1, m_i_Lay1, matLib, th=th_Lay1)
lam4_Lay1 = Laminate(n_i_Lay1, m_i_Lay1, matLib, th=th_Lay1)
# Assemble the laminates into an array.
laminates_Lay1 = [lam1_Lay1,lam2_Lay1,lam3_Lay1,lam4_Lay1]
# Create the cross-section vector:
xsect_Lay1 = XSect(2,af2,xdim2,laminates_Lay1,matLib,typeXSect='rectBox',\
meshSize=2)
# Create the cross-section object.
xsect_Lay1.xSectionAnalysis()
# Having created the cross-section, we can now generate a superbeam. A
# superbeam is just a collection of beam elements. In other words, a superbeam
# is just there to fascilitate beam meshing and other pre/post processing
# benefits. In order to make a superbeam, we need to initialize a few things.
# First, let's initialize the starting and stopping location of the beam:
x1 = np.array([0,0,0])
x2 = np.array([0,0,4])
# Initialize a superbeam ID
SBID = 1
# Next we need to initialize the number of elements the superbeam should mesh:
noe = 20
# Now let's make the superbeam
sbeam1 = SuperBeam(SBID,x1,x2,xsect_Lay1,noe)
# In order to analyze this beam, we'll need to add it to a finite element
# model. First let's make a finite element model!
n_i_3 = [8] m_i_3 = [1] th_3 = [-10] lam3 = Laminate(n_i_3, m_i_3, matLib, th=th_3) n_i_4 = [1, 1, 1, 1] m_i_4 = [1, 1, 1, 1] th_4 = [45, -45, 45, -45] lam4 = Laminate(n_i_4, m_i_4, matLib, th=th_4) # Organize the laminates into an array laminates_Lay3 = [lam1, lam2, lam3, lam4] # Create the cross-section object and mesh it xsect_Lay3 = XSect(4, af3, xdim3, laminates_Lay3, matLib, typeXSect="box", meshSize=4) # Run the cross-sectional analysis. Since this is an airfoil and for this, # symmetric airfoils the AC is at the 1/c chord, we will put the reference axis # here xsect_Lay3.xSectionAnalysis() # ref_ax=[0.25*c3,0.]) K_tmp = xsect_Lay3.K F_tmp = xsect_Lay3.F xs_tmp = xsect_Lay3.xs ys_tmp = xsect_Lay3.ys # Let's see what the rigid cross-section looks like: xsect_Lay3.plotRigid() # Print the stiffness matrix xsect_Lay3.printSummary(stiffMat=True) x1 = np.array([0, 0, 0]) x2 = np.array([0, 0, 160.5337]) # Initialize a superbeam ID SBID = 1 # Next we need to initialize the number of elements the superbeam should mesh: noe = 40
elem1 = CQUADX9(1, nodes, 3, matLib)
N1 = Node(1, [0., 0., 0.])
N2 = Node(2, [1., 0., 0.])
N3 = Node(3, [1., 1., 0.])
N4 = Node(4, [0., 1., 0.])
nodes1 = [N1, N2, N3, N4]
elem2 = CQUADX(2, nodes1, 3, matLib)
b = 1
h = 1
elemX = 24
elemY = elemX
xsect1 = XSect(1,None,[b,h],None,matLib,elemX=elemX,elemY=elemY,typeXSect='solidBox',\
MID=3,elemOrder=1)
xsect1.xSectionAnalysis()
xsect2 = XSect(1,None,[b,h],None,matLib,elemX=elemX,elemY=elemY,typeXSect='solidBox',\
MID=3,elemOrder=2)
xsect2.xSectionAnalysis()
E = 71.7e9
nu = .33
G = E / (2 * (1 + nu))
A = 1
k = 5. / 6
I = b * h**3 / 12.
Ktrue = np.array([[G*A*k,0,0,0,0,0],[0,G*A*k,0,0,0,0],[0,0,E*A,0,0,0],\
[0,0,0,E*I,0,0],[0,0,0,0,E*I,0],[0,0,0,0,0,G*2.25*(b/2.)**4]])
Kapprox1 = xsect1.K
Kapprox2 = xsect2.K
elem1 = CQUADX9(1,nodes,3,matLib)
N1 = Node(1,[0.,0.,0.])
N2 = Node(2,[1.,0.,0.])
N3 = Node(3,[1.,1.,0.])
N4 = Node(4,[0.,1.,0.])
nodes1 = [N1,N2,N3,N4]
elem2 = CQUADX(2,nodes1,3,matLib)
b = 1
h = 1
elemX = 24
elemY = elemX
xsect1 = XSect(1,None,[b,h],None,matLib,elemX=elemX,elemY=elemY,typeXSect='solidBox',\
MID=3,elemOrder=1)
xsect1.xSectionAnalysis()
xsect2 = XSect(1,None,[b,h],None,matLib,elemX=elemX,elemY=elemY,typeXSect='solidBox',\
MID=3,elemOrder=2)
xsect2.xSectionAnalysis()
E = 71.7e9
nu = .33
G = E/(2*(1+nu))
A = 1
k = 5./6
I = b*h**3/12.
Ktrue = np.array([[G*A*k,0,0,0,0,0],[0,G*A*k,0,0,0,0],[0,0,E*A,0,0,0],\
[0,0,0,E*I,0,0],[0,0,0,0,E*I,0],[0,0,0,0,0,G*2.25*(b/2.)**4]])
Kapprox1 = xsect1.K
Kapprox2 = xsect2.K
th_4 = [45, -45, 45, -45]
lam4 = Laminate(n_i_4, m_i_4, matLib, th=th_4)
# Organize the laminates into an array
laminates_Lay3 = [lam1, lam2, lam3, lam4]
# Create the cross-section object and mesh it
xsect_Lay3 = XSect(4,
af3,
xdim3,
laminates_Lay3,
matLib,
typeXSect='box',
meshSize=4)
# Run the cross-sectional analysis. Since this is an airfoil and for this,
# symmetric airfoils the AC is at the 1/c chord, we will put the reference axis
# here
xsect_Lay3.xSectionAnalysis() #ref_ax=[0.25*c3,0.])
K_tmp = xsect_Lay3.K
F_tmp = xsect_Lay3.F
xs_tmp = xsect_Lay3.xs
ys_tmp = xsect_Lay3.ys
# Let's see what the rigid cross-section looks like:
xsect_Lay3.plotRigid()
# Print the stiffness matrix
xsect_Lay3.printSummary(stiffMat=True)
x1 = np.array([0, 0, 0])
x2 = np.array([0, 0, 160.5337])
# Initialize a superbeam ID
SBID = 1
# Next we need to initialize the number of elements the superbeam should mesh:
noe = 40
lam1 = Laminate(n_1, m_1, matLib, th=th_1, sym=True)
# In order to make a cross-section, we must add all of the laminates to be used
# to an array:
laminates1 = [lam1]
# We now have all the information necessary to make a laminate beam cross-
# section:
xsect1 = XSect(1,
af1,
xdim1,
laminates1,
matLib,
typeXSect='laminate',
meshSize=2)
# With the cross-section object initialized, let's run the cross-sectional
# analysis to get cross-section stiffnesses, etc.
xsect1.xSectionAnalysis()
# Let's see what our rigid cross-section looks like when plotted in 3D:
xsect1.plotRigid(mesh=True)
# Note that while it might look like the cross-section is made of triangular
# elements, it's actually made of quadrilaterals. This is an artifact of how
# the visualizer mayavi works. Let's get a summary of the cross-section's
# stiffnesses, ect.
xsect1.printSummary(stiffMat=True)
# Notice that from the command line output, all of the important cross-
# sectional geometric properties are located at the origin. By observing the
# cross-section stiffness matrix, it can be seen by the 1,3 entry that there
# is shear-axial coupling. From the non-zero 4,6 entry, we can also tell that
# the cross-section has bending-torsion coupling.
# We can apply a force to the face of this cross-section at the reference axis
# (which in this case is at x,y = 0,0) and see what the stresses look like. In
# this case we'll apply [Fx,Fy,Fz,Mx,My,Mz]=[0.,0.,0.,100.,0.,0.] as if the
th_1 = [0,45,90] n_1 = [2,1,3] m_1 = [1,1,1] # Notice how the orientations are stored in the 'th_1' array, the subscripts are # stored in the 'n_1' array, and the material information is held in 'm_1'. # Create the laminate object: lam1 = Laminate(n_1,m_1,matLib,th=th_1,sym=True) # In order to make a cross-section, we must add all of the laminates to be used # to an array: laminates1 = [lam1] # We now have all the information necessary to make a laminate beam cross- # section: xsect1 = XSect(1,af1,xdim1,laminates1,matLib,typeXSect='laminate',meshSize=2) # With the cross-section object initialized, let's run the cross-sectional # analysis to get cross-section stiffnesses, etc. xsect1.xSectionAnalysis() # Let's see what our rigid cross-section looks like when plotted in 3D: xsect1.plotRigid(mesh=True) # Note that while it might look like the cross-section is made of triangular # elements, it's actually made of quadrilaterals. This is an artifact of how # the visualizer mayavi works. Let's get a summary of the cross-section's # stiffnesses, ect. xsect1.printSummary(stiffMat=True) # Notice that from the command line output, all of the important cross- # sectional geometric properties are located at the origin. By observing the # cross-section stiffness matrix, it can be seen by the 1,3 entry that there # is shear-axial coupling. From the non-zero 4,6 entry, we can also tell that # the cross-section has bending-torsion coupling. # We can apply a force to the face of this cross-section at the reference axis # (which in this case is at x,y = 0,0) and see what the stresses look like. In # this case we'll apply [Fx,Fy,Fz,Mx,My,Mz]=[0.,0.,0.,100.,0.,0.] as if the
