> | 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): |
> | p:=subs(r=sqrt(B*(R_o)^2+A),H): |
> | x0:=simplify((sigma_r-sigma_theta)/r): |
> | y0:=simplify(sigma_z*r): |
> | 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): |
> | solve({Eq1=p_o-p_i,Eq2=F_a},{A,B}); |
> | ![%?]()
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