# Contact stress problem

1. Apr 8, 2016

### Jesper Hellmann

Hi All

I am trying to validate a nylon (PA6 Guss) clamp which has a load of 166kN on a steel tube. I am only interested in validating the clamp.
My analytical (MatLab-Octave) calculations give me a peak Von Misses stress of about 145MPa

When comparing to FEM in ANSYS I only get about 30MPa
Can someone shed light on why there is such a big difference?

-Jesper Hemmlann
M.Sc. Applied Mechanics

2. Apr 8, 2016

### billy_joule

Who knows? Show your code and we might able to comment.

3. Apr 11, 2016

### Jesper Hellmann

%%%Contact stress
clear all
clc
close all
graphics_toolkit('gnuplot')

%%%Material parameters
%Youngs Modulus
E_1=2.62*10^9
E_2=213*10^9
%Poisson ratio
nu_1=0.34
nu_2=0.3

%OBS (R_2= infity for a flat plate)
%OBS (a cylindrical groove is a cylinder with a negative radius)
R_1=0.055275
R_2=0.055775
L=0.2

%Force
F=166000

%Contact area
b=sqrt(4*F*((1-nu_1^2)/E_1+(1-nu_2^2)/E_2)/(pi*L*(1/R_1+1/R_2)))

%maximum pressure
P_max=2*F/(pi*b*L)

%stresses
i=50
z=0.000000001:(b*3)/i:(b*3);

for n=1:i
sigma_1(n)=-2*nu_1*P_max*(sqrt(z(n)^2/b^2+1)-abs(z(n)/b));
sigma_2(n)=-P_max*((2-(z(n)^2/b^2+1)^-1)*sqrt(z(n)^2/b^2+1)-2*abs(z(n)/b));
sigma_3(n)=-P_max*(sqrt((z(n)^2/b^2)+1)^(-1));

tau_1(n)=abs((sigma_2(n)-sigma_3(n))/2);
tau_2(n)=abs((sigma_1(n)-sigma_3(n))/2);
tau_3(n)=abs((sigma_1(n)-sigma_2(n))/2);
sigma_vM(n)=sqrt(sigma_1(n)^2+sigma_2(n)^2+sigma_3(n)^2-sigma_1(n)*sigma_2(n)-sigma_2(n)*sigma_3(n)-sigma_3(n)*sigma_1(n)+3*(tau_1(n)^2+tau_2(n)^2+tau_3(n)^2));
end

figure
hold on

MPa=1/10^6;
plot(z,abs(sigma_1)*MPa,'-ko', "markersize", 3)
plot(z,abs(sigma_2)*MPa,'-m^', "markersize", 3)
plot(z,abs(sigma_3)*MPa,'-.r*', "markersize", 3)
plot(z,(tau_1)*MPa,'--yv', "markersize", 3)
plot(z,(tau_2)*MPa,':bs', "markersize", 3)
plot(z,(tau_3)*MPa,'-.go', "markersize", 3)
plot(z,sigma_vM*MPa,'-bv',"markersize", 3)

legend('\sigma_x', '\sigma_y', '\sigma_z', '\tau_1','\tau_2','\tau_3','\sigma_{vM}', "location",
"northeast");
xlabel('depth of surface [m]')
ylabel('Stress [MPa]')
title('Cylinder contact stress on clamp')
grid on

%Displacement in the center of the 2 cylinders
delta_c=2*F*(1-nu_1^2)/(pi*L*E_1)*(2/3+log(4*R_1/b)+log(4*R_2/b))*(1000)

4. Apr 13, 2016

### devecseri

I don't know ansys and have never actually done an fea but I know you can set one up in matlab so maybe try to do a simplified fea in matlab to see if your answers get closer? That would only confirm your ansys isnt setup right, though, if you know 30 isn't right