B.2. THE R-F METHOD FOR EXAMPLE 2.7 227
format short e
disp('reliability')
R=normcdf(beta0)
% Displaye iterative process and write it to Excel file
disp(ddp)
xlswrite('example2_6',ddp); % Write the iterative process
% into a Excel file
B.2 THE R-F METHOD FOR EXAMPLE 2.7
% The R-F method for Example 2.7
% The Limit State function: g(M,ka,se, kf, d)
clear; % Clean memory
% Input the distribution parameters dp1 and dp2
% Means or the first distribution parameter
dp1=[0.315,0.905,24.7,1.562,1.250];
% Standard deviation or the second distribution parameter
dp2=[0.142,0.0543,2.14,0.1250,0.00125];
kb=0.8507; % Size mofification factor
r=1; %Number of non-normal distribution
n=5; % Total five random variables
% Calculate the mean of lognorm M and the initial
% point x0(i)
x0(1)=exp(dp1(1)+dp2(1)^2/2);
for i=2:n-1
x0(i)=dp1(i);
end
% Use the surface of the limit state function
% to calculate x0(n)
x0(5)=(x0(4)*32*x0(1)/pi/(x0(2)*kb*x0(3)))^(1/3);
beta=0; %Set the beta =0
% Iterative process starting
for j=1:1000
%Calculate the equivalent mean and standard deviation
zteq=norminv(logncdf(x0(1),dp1(1),dp2(1)));
steq=normpdf(zteq)/lognpdf(x0(1),dp1(1),dp2(1));
mteq=x0(1)-zteq*steq;
% Mean and standard deviation matrix
meq(1)=mteq;
228 B. SAMPLES OF MATLAB
®
PROGRAMS
seq(1)=steq;
for i=2:n
meq(i)=dp1(i);
seq(i)=dp2(i);
end
% Calculate z0(i) in standrad normal distribution space
for i=1:n
z0(i)=(x0(i)-meq(i))/seq(i);
end
% Calculate the Taylor Series Coefficient
Gi(1)=seq(1)*(-x0(4))*32/pi()/(x0(5))^3;
Gi(2)=seq(2)*kb*x0(3);
Gi(3)=seq(3)*x0(2)*kb;
Gi(4)=seq(4)*(-32)*x0(1)/pi()/(x0(5))^3;
Gi(5)=seq(5)*x0(4)*96*x0(1)/pi()/(x0(5))^4;
g00=0;
z00=0;
for i=1:n
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:n
ddp(j,i)=x0(i);
end
ddp(j,n+1)=beta0;
ddp(j,n+2)=abs(beta0-beta);
% New design proint
for i=1:n-1
z1(i)=(-1)*beta0*Gi(i)/Gi0;
x1(i)=seq(i)*z1(i)+meq(i);
end
% Use the surface of the limit state function to
% calculate x1(n)
x1(5)=(x1(4)*32*x1(1)/pi/(x1(2)*kb*x1(3)))^(1/3);
z1(5)=(x1(5)-meq(5))/seq(5);
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