Problem 4 and 6

README.md

@@ -111,3 +111,100 @@ end
 ```
 Most precise dart thrower: User 32
 - combined x & y STD of 3.4073
+
+#Problem 4
+###Part A
+```matlab
+function [mean_buckle_load,std_buckle_load]=buckle_monte_carlo(E,r_mean,r_std,L_mean,L_std);
+
+N=100;
+r_mean=0.01;
+r_std=.001;
+L_mean=5;
+L_std=L_mean*0.01;
+
+
+rrand=normrnd(r_mean,r_std,[N,1]);
+Lrand=normrnd(L_mean,L_std,[N,1]);
+E = 200*10^9;
+
+P_cr=(pi^3*E.*rrand.^4)./(16.*Lrand.^2);
+x1 = mean(P_cr)
+x2 = std(P_cr)
+P_test=1000*9.81/100;
+sum(P_cr<P_test)
+end
+```
+Output:
+- Mean_buckle_load = 164.4154 N
+- STD              = 63.6238 N
+
+###Part B
+```matlab
+function [mean_buckle_load,std_buckle_load]=buckle_monte_carlo_2(E,r_mean,r_std,P_cr);
+
+N=100;
+r_mean=0.01;
+r_std=.001;
+P_test=1000*9.81/100;
+sum(2.5<P_test)
+P_cr = 164.4154;
+rrand=normrnd(r_mean,r_std,[N,1]);
+E = 200*10^9;
+L = ((pi^3*E.*rrand.^4)./(16*P_cr)).^0.5;
+mean(L)
+end
+```
+Output:
+- L = 5.0108 m
+#Problem 5
+###Part A
+
+#Problem 6
+###Analytical
+```matlab
+fun = @(x) (1/6).*(x).^3+(1/2).*(x).^2+(x);
+q = integral(fun,2,3)
+```
+
+###Gauss Quadrature
+###1-point
+```matlab
+x = [0];
+c = [2];
+a = 2;
+b = 3;
+tildec = (b-a)/2*c;
+tildex = (b-a)/2*x + (b+a)/2;
+f = (1/6).*(tildex).^3+(1/2).*(tildex).^2+(tildex);
+value1 = sum(tildec.*f)
+```
+###2-point
+```matlab
+x = [-0.57735,0.57735];
+c = [1,1];
+a = 2;
+b = 3;
+tildec = (b-a)/2*c;
+tildex = (b-a)/2*x + (b+a)/2;
+f = (1/6).*(tildex).^3+(1/2).*(tildex).^2+(tildex);
+value2 = sum(tildec.*f)
+```
+###3-point
+```matlab
+%Three Point
+x = [-0.77459666,0,0.77459666];
+c = [0.5555555,0.88888888,0.55555555];
+a = 2;
+b = 3;
+tildec = (b-a)/2*c;
+tildex = (b-a)/2*x + (b+a)/2;
+f = (1/6).*(tildex).^3+(1/2).*(tildex).^2+(tildex);
+value3 = sum(tildec.*f)
+```
+
+|     Method     |   Value   |   Error   |
+|   Analytical   |   8.3750  |     0%    |
+| 1 Gauss Point  |   8.2292  |  1.74%    |
+| 2 Gauss Point  |   8.3750  |     0%    |
+| 3 Gauss Point  |   8.3750  |     0%    |