Load Factor
Solution
cyl2car.m
function [xc,yc]=cyl2car(r,thet) %function 6: conversion of coordinates
xc=r*cos(thet);
yc=r*sin(thet);
end
loadf1.m
function lf1=loadf1(estress,ystress) %function 4: Load Factor I
lf1=estress/ystress;
end
loadf2.m
function lf2=loadf2(mstress,c,ftough) %function 5: Load Factor II
lf2=mstress*sqrt(c)/ftough;
end
loadfactor.m
%Declaration of parameters and other constants
clear all
clc
opengl software
a=6; %outer radius
b=3; %inner radius
c=0.1; %diameter of circular crack
P=10E3; %internal pressure
T=2E6; %torque
sigax=10E3; %applied axial stress
M1=-1E5; %bending moment along Y axis
M2=1E6; %bending moment along X axis
ystress=68200; %yield stress
ftough=7.252; %fracture toughness
%mainroutine: calculates and plots the contours for the load factors
r=a:(b-a)/1000:b; %radial coordinate array
thet=0:(2*pi)/1000:2*pi; %angular coordinate array
[sr1,sr2]=size(r);
[st1,st2]=size(thet);
xxm=zeros(sr2,st2);
yym=zeros(sr2,st2);
LF1m=zeros(sr2,st2);
LF2m=zeros(sr2,st2);
for j=1:1:sr2
for k=1:1:st2
[xx(j,k),yy(j,k)]=cyl2car(r(j),thet(k));
[sigrad,sigtan]=pstress(P,a,b,r(j));
[sigx,sigy,sigapp]=nstress(M1,M2,xx(j,k),yy(j,k),M1+M2,sigax);
tt=tstress(T,r(j),M1+M2);
LF1(j,k)=loadf1((sigrad^2)+(sigtan^2),ystress);
LF2(j,k)=loadf2(max([sigx,sigy,sigapp,tt]),c,ftough);
end
end
figure(1) %start of source code
axes(‘FontSize’,18)
hold on
colormap(jet)
axis square
pcolor(xx,yy,LF1)
numcount=5;
contourf(xx,yy,LF1),xlabel(‘x position (in)’),ylabel(‘y position (in)’),title(‘LF1’)
colorbar(‘southoutside’)
hold off
figure(2)
axes(‘FontSize’,18)
hold on
colormap(jet)
axis square
pcolor(xx,yy,LF2)
numcount=5;
contourf(xx,yy,LF2),xlabel(‘x position (in)’),ylabel(‘y position (in)’),title(‘LF2’)
colorbar(‘southoutside’)
hold off %end of source code
nstress.m
function [sigxsigysigapp]=nstress(M1,M2,x,y,I,sigax) %function 2:stresses due to applied axial stress, and bending moments
sigx=(M1*x/I);
sigy=(M2*y/I);
sigapp=sigax;
end
pstress.m
function [sigrad,sigtan]=pstress(P,a,b,r) %function 1: stresses due to pressure
sigrad=-P*(b^2)*((a^2)-(r^2))/((r^2)*((a^2)-(b^2))); %Stress due to pressure in radial direction
sigtan=P*(b^2)*((a^2)+(r^2))/((r^2)*((a^2)-(b^2))); %Stress due to pressure in tangential direction
end
tstress.m
functiontt=tstress(T,r,J) %function 3: stress due to torque
tt=(T*r/J);
end