A.2. THE R-F METHOD FOR EXAMPLE 3.13 243
disp(ddp)
xlswrite('example3.11',ddp)
A.2 THE R-F METHOD FOR EXAMPLE 3.13
% The R-F method for example 3.13
% The Limit State function: g(T, d, Ssy)=Ssy*pi/10*d^3-T
% Input the distribution parameters dp1 and dp2
clear
mx=[34, 2.125, 31]; %The mean or the first distribution
%parameter
sx=[3,0.002,2.4]; %The standard deviation or the second
% distribution
%parameter
% Calculate the mean of T (Weibull) and the initial
% point x0(i)
x0(1)=mx(1)*gamma(1/sx(1)+1);
x0(2)=mx(2);
% The value of the last variable is determined by the
% limit state function
x0(3)=16*x0(1)/pi/x0(2)^3; % Equation (3.71) or (d)
beta=0; %set the beta =0
% Iterative process starting
for j=1:1000
% Calculate the equivalent mean and standard deviation
zteq=norminv(wblcdf(x0(1),mx(1),sx(1)));
steq=normpdf(zteq)/wblpdf(x0(1),mx(1),sx(1));
mteq=x0(1)-zteq*steq;
% Mean and standard deviation matrix
meq(1)=mteq;
seq(1)=steq;
for i=2:3
meq(i)=mx(i);
seq(i)=sx(i);
end
% Calculate z0(i)in the standrad normal distribution space
for i=1:3
z0(i)=(x0(i)-meq(i))/seq(i);
end
244 A. SAMPLES OF MATLAB
®
PROGRAMS
% Calculate the Taylor Series Coefficient, Equation (g)
Gi(1)=-seq(1);
Gi(2)=seq(2)*x0(1)*3*pi*(x0(2))^2/16;
Gi(3)=seq(3)*pi*x0(2)^3/16;
g00=0;
z00=0;
for i=1:3
g00=g00+Gi(i)^2;
z00=z00+(-1)*z0(i)*Gi(i);
end
Gi0=g00^0.5;
% Calculate the reliability index beta0
beta0=z00/Gi0;
% Data of iterative process
for i=1:3
ddp(j,i)=x0(i);
end
ddp(j,3+1)=beta0;
ddp(j,3+2)=abs(beta0-beta);
% new design point
for i=1:3-1
z1(i)=(-1)*beta0*Gi(i)/Gi0;
x1(i)=seq(i)*z1(i)+meq(i);
end
x1(3)=16*x1(1)/pi/x1(2)^3;
z1(3)=(x1(3)-meq(3))/seq(3);
% Check the convengence condition
if ddp(j,3+2)<=0.0001;
break
end
% use new design point to replace previous design point
for i=1:3
x0(i)=x1(i);
end
beta=beta0;
end
% calculate and display reliability
format short e
disp('reliability')
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