cannot solve for unknown variable

I am trying to solve for unknown variable P in the following code. I determined value of P= 2.945e-5 manually. However, I am not getting that value with the code. As a matter of fact, if I change the constant (1.9664e+08) in the sigma equation, the result is not changing.

Can anyone help in this?

%Constants
L= 300e-6;             
O= 5e-6;                                  
theta= atan(2*O/L);
E= 188e9;                       
w= 1.57e-6;                      
h= 2.5e-6;                       
I= (h*w^3)/12;
L_0 = (L/2)*(tan(theta))^2;

%Calculations
syms P real
k= sqrt(P/(E*I));
G= tan((k*L)/4);
L_p= ((tan(theta))^2/(4*k))*( 2*G + k*L + k*L*G^2 + sin(k*L) - 2*G*cos(k*L) - G^2*sin(k*L));
delta_L = L_p - L_0;

sigma = (E/L)*(delta_L + ((P*L)/(E*w*h))) -1.9664e+08==0;

F = vpasolve(sigma, P)

Answer 1

[Walter Roberson]

vpasolve(sigma, [0 .5e-4])

There is a discontinuity before 1e-4 so if you do not confine the search range the discontinuity can cause search failures

[Md Shariful Islam]

Thanks a lot!

It is working. However, I am not clear about the problem you mentioned, as I am a new matlab user. I will search online on that, btw. Thanks again.

[Walter Roberson]

fplot(lhs(sigma), [0 1e-4])

Notice how the plot goes up to about 1e11 in the middle

[Md Shariful Islam]

I see!

Thanks for your help.