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HW7Solutions

# HW7Solutions - matlab code to plot parts c and d plot(x,u'k...

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Unformatted text preview: % matlab code to plot parts c and d plot(x,u,'k') hold on plot(x,u1,'b') plot(x,u3,'r') hold off legend('exact','1st and 2nd order','3rd order') xlabel('x/L') ylabel('u/u_m_a_x') figure(2) plot(x,F,'k') hold on plot(x,F1,'b') plot(x,F3,'r') hold off legend('exact','1st and 2nd order','3rd order') xlabel('x/L') ylabel('F/F_m_a_x') 1.4 exact 1st and 2nd order 3rd order 1.2 1 0.8 u/umax 0.6 0.4 0.2 0 0 0.1 0.2 0.3 0.4 0.5 x/L 0.6 0.7 0.8 0.9 1 Mathematica for part D In[41]:= u= Lqx 2 AE − q x2 2 AE ; In[42]:= Out[42]= F = [email protected] ∂x uD u1 = 1 q HL − 2 xL 2 AE 4 L2 q [email protected] π3 AE πx L In[43]:= In[44]:= u3 = In[45]:= Out[45]= F1 = AE ∂x u1 In[46]:= Out[46]= F3 = [email protected] ∂x u3D SimplifyA 1− 2x L SimplifyA 8 [email protected] π2 πx L 4 L q [email protected] πLx D π2 4 L q H9 [email protected] 4 L2 q [email protected] π3 πx L D ; 4 L2 q [email protected] 27 AE 3πx L π3 D + D ; πx L 2 In[47]:= π D + [email protected] 3 L x DL 2 9π Lq Out[47]= FE 2 Lq In[48]:= Out[48]= In[50]:= Out[50]= FullSimplifyA 8 H9 [email protected] πx L D F1E 2 Lq F3E D + [email protected] 9 π2 3πx L DL 1 exact 1st and 2nd order 3rd order 0.8 0.6 0.4 0.2 F/Fmax 0 -0.2 -0.4 -0.6 -0.8 -1 0 0.1 0.2 0.3 0.4 0.5 x/L 0.6 0.7 0.8 0.9 1 ...
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