<jupyter_start><jupyter_text>Definition of rotation matrix $A$<jupyter_code>A = Matrix([[m**2, n**2, 2*m*n], [n**2, m**2, -2*m*n], [-m*n, m*n,m**2-n**2]])
At = simplify(A.inv())

At, simplify(A)
# The inverse of the rotation matrix in voigt notation is not the transpose
simplify(A.subs(theta,0))<jupyter_output><empty_output><jupyter_text>Definition of the Reuter Matrix $R$<jupyter_code>R = Matrix([[1, 0, 0], [0, 1, 0], [0, 0,2]])
Rt = Matrix([[1, 0, 0], [0, 1, 0], [0, 0,0.5]])
R<jupyter_output><empty_output><jupyter_text>transversely isotropic stiffness tensor $C$$C' = A^{-1}CRAR^{-1}$<jupyter_code>C = Matrix( symarray('C', (3,3)) )
C
gamma = symbols('\gamma')
C[2,0] = 0
C[2,1] = 0
C[0,2] = 0
C[1,2] = 0
C[1,1] = C[0,0]
C[1,0] = C[0,1]
C[2,2] = 0.5 *(C[0,0] - C[1,0])
#C[2,2] = gamma
C
CTrue = simplify(At*C*R*A*Rt)
CTrue
CTrue[2,2]
CPrime = simplify(At*C*A)
CPrime[2,2]
print(ccode(Assignment(x,CTrue[2,2])))
CTrue[2,2].subs(theta,0)
simplify(CTrue[2,2].subs(theta,pi/2))
simplify(CTrue[2,2].subs(theta,pi/4))
(R*A*Rt).subs(theta,0)
C
A
R*A*Rt
CTrue.subs(theta,pi/2)
v1 = Matrix([4,5,6])
v1
C[0,0] = 1
C[1,1] = 3
C[0,1] = 2
C[1,0] = 2
C[2,2] = 13
CTrue = simplify(At*C*R*A*Rt)
(CTrue*v1).subs(theta, pi/4)
-9/2
x, n, delta = symbols('x n \delta')

Weight = (1 - 2*abs(x))
Weight
plot(Weight, (x, -0.5, .5), ylim=[0,1])
Weight = ((n+1.0)/(n-1.0))*(1.0 - n * (abs(2.0 * x))**( n - 1.0) + (n - 1.0) * (abs(2.0*x))**(n))
Weight
plot(Weight.subs(n,100), (x, -0.5, .5),ylim=[0,2])<jupyter_output><empty_output>
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