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Copy pathReliability_Stiffened_Plate.m
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Reliability_Stiffened_Plate.m
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clc;
clear all;
clf;
%% Random variables
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
n_random_var = 2; % number of random variables
x = zeros(n_random_var,1); % random variables (cirticle displacment,
% stiffness [N/mm^2], force [N])
mu = zeros(n_random_var,1); % expected values
sigma = zeros(n_random_var,1); % standard deviation
%% Input
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Criticle displacement
u0 = 14;
Emodule=1092000; % Young elastic modulus
Load=1; % Uniform load
% Stiffness
mu(1) = 1092000;
sigma(1) = 109200;
% Forces
mu(2) = 1;
sigma(2) = 0.1;
%% Finding design point using FORM Method 2
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%
% Variable declaration
eps = 0.001; % stopping creterium for the fix point iteration
alpha = zeros(n_random_var,1);
dg = zeros(n_random_var,1);
dx = 0.001*sigma;
dbeta = 100;
% step 2
x = mu;
% step 3
y = (x-mu)./sigma;
beta = 9999;
step=0;
while (abs(dbeta) > 0.001)
step=step+1
% step 4 and 5
tmp_u1 = cal_SP(x(1), x(2));
tmp_u2 = cal_SP(x(1)+dx(1), x(2));
dg(1) = (tmp_u2 - tmp_u1)/dx(1) * sigma(1);
tmp_u2 = cal_SP(x(1), x(2)+dx(2));
dg(2) = (tmp_u2 - tmp_u1)/dx(2) * sigma(2);
% step 6
g = -u0 + tmp_u1;
y = 1./(dg'*dg)*(dg'*y - g)*dg;
% step 7
tmp = beta;
beta = sqrt(y'*y)
dbeta = beta - tmp;
% step 8
x = mu + sigma.*y;
end
pf = 1 - normcdf(beta);
sprintf('Probability of failure: %g\n', pf)
pf;
% % % % % % % % % % % % % % % % % % % %
% u0=10
% step = 1
% beta = 1.299989776988072
% step = 2
% beta = 1.424389879545184
% step = 3
% beta = 1.424228404569439
% ans = Probability of failure: 0.0771902
% % % % % % % % % % % % % % % % % % %
% u0=11
% step = 1
% beta = 0.722846633012398
% step = 2
% beta = 0.760648877360251
% step = 3
% beta = 0.760640830412670
% ans = Probability of failure: 0.223436
% % % % % % % % % % % % % % % % % % % % %
% u0=12
% step = 1
% beta = 0.145703489036724
% step = 2
% beta = 0.147204861176776
% step = 3
% beta = 0.147204858905609
% ans = Probability of failure: 0.441485
% % % % % % % % % % % % % % % % % % % % %
% u0=12.5
% step = 1
% beta = 0.142868082951114
% step = 2
% beta = 0.141425152878370
% step = 3
% beta = 0.141425151032474
% ans = Probability of failure: 0.443767
% % % % % % % % % % % % % % % % % %
%
% u0=13.5
% step = 1
% beta = 0.720011226926788
% step = 2
% beta = 0.684301082594260
% step = 3
% beta = 0.684294433686579
% ans = Probability of failure: 0.246895
% % % % % % % % % % % % % % % % % %
% u0=14
% step = 1
% beta = 1.008582798914625
% step = 2
% beta = 0.939353129088658
% step = 3
% beta = 0.939318500388323
% ans =Probability of failure: 0.173784
% % % % % % % % % % % % % % % % % % %