225
A P P E N D I X B
Samples of MATLAB
®
Programs
B.1 THE H-L METHOD FOR EXAMPLE 2.6
% The H-L method for Example 2.6
% The Limit State function: g(ka,kc,se,d,fa)
% Input the distribution parameters mx-mean,
% sz-standard deviation
clear, % Clear the memory
mx=[0.905,0.774,24.7,1.25,8.5]; % The means
sx=[0.0543,0.1262,2.14,0.0125,1.2]; % The standard
% deviations
n=5; % Total four random variables
beta=0; % Set beta=0
% Pick an initial design point x0(i)
for i=1:n-1
x0(i)=mx(i); %Use the means for the first n-1 variable
end
% Use surface of the limit state function to calclaue the
% value for the last random variable
x0(n)=x0(1)*x0(2)*x0(3)*(61.5*(x0(4))^2-15.279)/78.290;
% Initial point in standard normal distribution space
for i=1:n
z0(i)=(x0(i)-mx(i))/sx(i);
end
% Start iterative process
for j=1:1000
% Calculate the reliability beat0
% The Tylor series coefficent
G0(1)=sx(1)*x0(2)*x0(3);
G0(2)=sx(2)*x0(1)*x0(3);
G0(3)=sx(3)*x0(1)*x0(2);
226 B. SAMPLES OF MATLAB
®
PROGRAMS
G0(4)=sx(4)*78.290*x0(5)*61.5*2*x0(4)/(61.5*(x0(4))^2-15.279)^2;
G0(5)=sx(5)*(-78.290)/(61.5*(x0(4))^2-15.279);
g00=0;
z00=0;
for i=1:n
g00=g00+G0(i)^2;
z00=z00+(-1)*z0(i)*G0(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
% The values for the first n-1 random variable
for i=1:n-1
z1(i)=(-1)*beta0*G0(i)/Gi0;
x1(i)=sx(i)*z1(i)+mx(i);
end
% The value for the last random variable from the
% surface of the limit state function
x1(n)=x1(1)*x1(2)*x1(3)*(61.5*(x1(4))^2-15.279)/78.290;
z1(n)=(x1(n)-mx(n))/sx(n);
% Check the convengence condition
if ddp(j,n+2)<=0.0001;
break
end
% Use new design point to replace previous design point
for i=1:n
z0(i)=z1(i);
x0(i)=x1(i);
end
beta=beta0;
end
% Calculate and display reliability
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