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{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "P:= matrix(1,4,[1,x,x^2,x^3]);  # c
ubic polynomial" }}{PARA 206 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"F&;F&\"
\"%E\\[l%6$F&\"\"$*$)I\"xGF#\"\"#F&6$F&F&F&6$F&F/F.6$F&F(*$)F.F+F&" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "dP:=matrix(1,4,[0,1,2*x,3*x
^2]); # local derivative" }}{PARA 207 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"
\"F&;F&\"\"%E\\[l%6$F&\"\"$,$*&\"\"#F&I\"xGF#F&F&6$F&F&\"\"!6$F&F.F&6$
F&F(,$*&F+F&)F/F.F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "d2
P:=matrix(1,4,[0,0,2,6*x]):    # local 2nd derivative" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "x_i:=[0,L]:                      # \+
local nodes" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "G:=matrix(4,4,[[1,0,  0,  0],[0, 1,
   0,     0],\n" }{MPLTEXT 1 0 67 "               [1,L,L^2,L^3],[0, 1,
 2*L, 3*L^2]]):\n               " }{MPLTEXT 1 0 38 "# P(x_i) and dP_dx
(x_i) identity pairs" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "G_i
nv:=linalg[inverse](G):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "
N:=linalg[multiply](P,G_inv);     # beam deflection, 4x1" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 2 "\n" }}{PARA 208 "" 1 "" {XPPMATH 20 "=6\"6$;\"
\"\"F&;F&\"\"%E\\[l%6$F&\"\"$,&*(F+F&)I\"xGF#\"\"#F&)I\"LGF#F0!\"\"F&*
(F0F&)F/F+F&)F2F+F3F36$F&F&,(F&F&F-F3F4F&6$F&F0,(F/F&*(F0F&F.F&F2F3F3*
&F5F&F1F3F&6$F&F(,&*&F.F&F2F3F3F<F&" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 60 "Constant_Load := map(int,evalm(transpose(N) * W), x=0
..L);\n" }{MPLTEXT 1 0 77 "# trapezoidal load from w_1 to w_2 interpol
ated. Supply data then integrate\n" }{MPLTEXT 1 0 71 "We   := vector(2
,[w_1, w_2]);              # vector of nodal loads, 2x1" }{MPLTEXT 1 
0 148 "\nNw   := matrix(1,2,[(1 - x/L), (x/L)]);    # linear interploa
tion, 1x2\nWx   := linalg[multiply](Nw, We);          # interpolation \+
of loads, 1x1\n" }{MPLTEXT 1 0 2 "\n" }}{PARA 209 "" 1 "" {XPPMATH 20 
"=6\"6$;\"\"\"\"\"%;F&F&E\\[l%6$F'F&,$*(#F&\"#7F&I\"WGF#F&)I\"LGF#\"\"
#F&!\"\"6$F&F&,$*(#F&F2F&F/F&F1F&F&6$\"\"$F&F56$F2F&,$F,F&" }}{PARA 
210 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"\"\"\"#E\\[l#F&I$w_1GF#F'I$w_2GF#"
 }}{PARA 211 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"F&;F&\"\"#E\\[l#6$F&F&,
&F&F&*&I\"xGF#F&I\"LGF#!\"\"F/6$F&F(F," }}{PARA 212 "" 1 "" {XPPMATH 
20 "=6\"6#;\"\"\"F&E\\[l\"F&,&*&,&F&F&*&I\"xGF#F&I\"LGF#!\"\"F.F&I$w_1
GF#F&F&*(F,F&F-F.I$w_2GF#F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 70 "N_Wx := evalm(transpose(N) &* Wx);        # vector times scalar,
 4x1\n" }{MPLTEXT 1 0 71 "Nt_Nw:= map(int,evalm(transpose(N) &* Nw), x
=0..L);            #  4x2\n" }{MPLTEXT 1 0 107 "Trapezoidal_Load := ma
p(int, evalm(transpose(N) &* Wx), x=0..L):\nTrapezoidal_Load_2 := eval
m(Nt_Nw &* We);" }}{PARA 213 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"\"\"\"%E
\\[l%F&*&,(F&F&*(\"\"$F&)I\"xGF#\"\"#F&)I\"LGF#F/!\"\"F2*(F/F&)F.F,F&)
F1F,F2F&F&,&*&,&F&F&*&F.F&F1F2F2F&I$w_1GF#F&F&*(F.F&F1F2I$w_2GF#F&F&F&
F/*&,(F.F&*(F/F&F-F&F1F2F2*&F4F&F0F2F&F&F6F&F,*&,&F+F&F3F2F&F6F&F'*&,&
*&F-F&F1F2F2F@F&F&F6F&" }}{PARA 214 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"
\"\"%;F&\"\"#E\\[l)6$\"\"$F),$*&#\"\"(\"#?F&I\"LGF#F&F&6$F'F&,$*&#F&\"
#IF&)F2F)F&!\"\"6$F&F&F-6$F'F),$*&#F&F1F&F8F&F96$F,F&,$*&#F,F1F&F2F&F&
6$F&F)F@6$F)F),$F5F&6$F)F&,$F=F&" }}{PARA 215 "" 1 "" {XPPMATH 20 "=6
\"6#;\"\"\"\"\"%E\\[l%F&,&*(#\"\"(\"#?F&I\"LGF#F&I$w_1GF#F&F&*(#\"\"$F
-F&F.F&I$w_2GF#F&F&\"\"#,&*(#F&F-F&F/F&)F.F4F&F&*(#F&\"#IF&F8F&F3F&F&F
2,&*(F1F&F.F&F/F&F&*(F+F&F.F&F3F&F&F',&*(F:F&F/F&F8F&!\"\"*(F7F&F8F&F3
F&FA" }}}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "" "%#%?G" }}}}
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