Solving system of 3 nonlinear Equations

Hello. I am having trouble finding the solutions to system of 3 Equations...

fun1 = EPS0*(E1*A1 + E2*A2) - (1/RO)*(E1*A1*e_y1 + E2*A2*e_y2) == 0
fun2 = E1*EPS0*A1*e_z1 + E2*EPS0*A2*e_z2 - (E1/RO)*(I_y1z1 + e_y1*e_z1*A1) - (E2/RO)*(I_y2z2 + e_y2*e_z2*A2) == -M*sin(alfa)
fun3 = E1*EPS0*A1*e_y1 + E2*EPS0*A2*e_y2 - (E1/RO)*(I_z1 + (e_y1^2)*A1) - (E2/RO)*(I_z2 + (e_y2^2)*A2) == M*cos(alfa)

S = vpasolve(fun1==0,fun2==-M*sin(alfa),fun3==M*cos(alfa))

S.RO
S.alfa
S.EPS0

alfa is "hidden" in I_yz and e_yz components of the equation, for example:

I_z1 = (((a^3)*b + a*b^3)/384) + (((a^3)*b - a*b^3)/384)*cos2a

How can I solve those 3 equations, since I am certain there is something wrong with results I get...

Answer 1

[Stephan]

syms EPS0 E1 A1 E2 A2 RO e_y1 e_y2 e_z1 e_z2 I_y1z1 I_y2z2 M I_z1 I_z2 alfa 

fun1 = EPS0*(E1*A1 + E2*A2) - (1/RO)*(E1*A1*e_y1 + E2*A2*e_y2) == 0
fun2 = E1*EPS0*A1*e_z1 + E2*EPS0*A2*e_z2 - (E1/RO)*(I_y1z1 + e_y1*e_z1*A1) - (E2/RO)*(I_y2z2 + e_y2*e_z2*A2) == -M*sin(alfa)
fun3 = E1*EPS0*A1*e_y1 + E2*EPS0*A2*e_y2 - (E1/RO)*(I_z1 + (e_y1^2)*A1) - (E2/RO)*(I_z2 + (e_y2^2)*A2) == M*cos(alfa)

S.RO = isolate(fun1, RO);
S.EPS0 = isolate(subs(fun2,RO,rhs(S.RO)),EPS0);
S.alfa = isolate(subs(subs(fun3,RO,rhs(S.RO)),EPS0,rhs(S.EPS0)),alfa);

S.RO
S.EPS0
S.alfa

Using this results you can first calculate alfa to get EPS0, then use EPS0 to calculate RO.