Question

15. In the solution of elasticity pfa normal point load applied to the surface of a half plane that was solved by Boussinesq in 1878, the stresses Op and σ, are given by: 2TR where v is Poisson's ratio. For P 2,000 lb and v0.3, plot the stress components (each in a sep- arate figure) as a function of r and z in the domain 0 < θ < 90° and 0.02 R < 0, 1 in. Plot the coordinates r and z in the horizontal plane and the stresses in the vertical direction. O:

Answer 1

MATLAB CODE:

clear
clf
P=2000;
v=.3;
th=0:.1:90;
R=linspace(.02,.1,length(th));
[z,r]=meshgrid(R.*cosd(th),R.*sind(th));
stressz=(-3*P.*z.^3)./(2*pi*R.^5);
stressr=(P/(2*pi)).*((1-2*v)./(R.*(R+z))-(3.*r.^2.*z./(R.^5)));
plot3(r,z,stressz)
zlabel('\sigma_z')
xlabel('r')
ylabel('z')
figure
plot3(r,z,stressr)
zlabel('\sigma_r')
xlabel('r')
ylabel('z')

PLOTS:

* 107 0.06 0.04 0.02 002 00400 0