Question: How I can solve these equations

how I can solve these equations?

Fung.mws

 

restart:

with(LinearAlgebra):

with(VectorCalculus):

Q:=a_11*(E_r)^2+a_22*(E_theta)^2+a_33*(E_z)^2+2*a_12*E_r*E_theta+2*a_13*E_r*E_z+2*a_23*E_theta*E_z:

psi:=0.5*c*(Q+0.5*Q^2):

F:=matrix([[B*R/r,0,0],[0,r/R,0],[0,0,1/B]]):

#b:=matrix([[B^2*R^2/r^2,0,0],[0,r^2/R^2,0],[0,0,1/B^2]]):

b:=matrix([[B*(r^2-A)/r^2,0,0],[0,B*r^2/(r^2-A),0],[0,0,1/B^2]]):

sigma_r:=-p+diff(psi,E_r)*b[1,1]:

sigma_theta:=-p+diff(psi,E_theta)*b[2,2]:

sigma_z:=-p+diff(psi,E_z)*b[3,3]:

#H:=p_o+subs(r=r_o,diff(psi,E_r)*b[1,1]):

H:=p_o+subs(r=sqrt(B*(R_o)^2+A),diff(psi,E_r)*b[1,1]):

E_r:=0.5*(((B*r^2-B*A)/r^2)-1):

E_theta:=0.5*((B*r^2/(r^2-A))-1):

E_z:=0.5*((1/B^2)-1):

H:

p:=subs(r=sqrt(B*(R_o)^2+A),H):

x0:=simplify((sigma_r-sigma_theta)/r):

y0:=simplify(sigma_z*r):

x1:=int(x0,r):

y1:=2*Pi*int(y0,r):

Digits:=50:

p_i:=1.858e3:

p_o:=0:

R_i:=1:

R_o:=10:

a_11:=165.857:

a_22:=47.028:

a_33:=145.448:

a_12:=46.747:

a_13:=0.799:

a_23:=14.587:

c:=0.0004e6:

F_a:=0:

x2:=subs(r=sqrt(B*R^2+A),x1):

y2:=subs(r=sqrt(B*R^2+A),y1):

eq1:=subs(R=R_o,x2)-subs(R=R_i,x2):

eq2:=subs(R=R_o,y2)-subs(R=R_i,y2):

Eq1:=simplify(eq1):

Eq2:=simplify(eq2):

solve({Eq1=p_o-p_i,Eq2=F_a},{A,B});

 

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