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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "restart;   # linear \+
polynomial for C0 2 node line element (L2_C0)" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 15 "with(linalg):\n" }{MPLTEXT 1 0 62 "P:=matrix(1,2
,[1,x]); # complete linear polynomial in x, u=P*C" }}{PARA 7 "" 1 "" 
{TEXT 211 79 "Warning, the protected names norm and trace have been re
defined and unprotected" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"
F&;F&\"\"#E\\[l#6$F&F&F&6$F&F(I\"xGF#" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 62 "# coordinate system, 0 <= x <= L for two identities i
n G below" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "G:=matrix(2,2,
[[1, 0],[1, L]]):        # u(x_i) == Ue = G(P(x_i))*C:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "G_inv:=evalm(inverse(G)): # exists \+
for valid interpolations" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "N:=lina
lg[multiply](P,G_inv);           # u = P*G_inv*Ue == N * Ue" }}{PARA 
11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"F&;F&\"\"#E\\[l#6$F&F&,&F&F&*&I\"
xGF#F&I\"LGF#!\"\"F/6$F&F(F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 53 "Constant_Load := map(w * int,transpose(N), x = 0..L);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"#;F&F&E\\[l#6$F&F&,$*(#F&F'F&
-I\"wGF#6$,&F&F&*&I\"xGF#F&I\"LGF#!\"\"F5/F3;\"\"!F4F&F4F&F&6$F'F&,$*(
F-F&-F/6$F2F6F&F4F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "# \+
trapezoidal load from w_1 to w_2 interpolated. Supply data then integr
ate\n" }{MPLTEXT 1 0 65 "We := vector(2,[w_1, w_2]);             # vec
tor of nodal loads\n" }{MPLTEXT 1 0 78 "Wx := linalg[multiply](N, We);
          # \"iso\" interpolation, dot product\n" }{MPLTEXT 1 0 63 "N_
Wx := evalm(transpose(N) &* Wx);      # vector times scalar\n" }
{MPLTEXT 1 0 64 "Trapezoidal_Load := map(int, evalm(transpose(N) &* Wx
), x=0..L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"\"\"\"#E\\[l#F
&I$w_1GF#F'I$w_2GF#" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"\"F&E
\\[l\"F&,&*&,&F&F&*&I\"xGF#F&I\"LGF#!\"\"F.F&I$w_1GF#F&F&*(F,F&F-F.I$w
_2GF#F&F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"\"\"\"#E\\[l#F&*
&,&F&F&*&I\"xGF#F&I\"LGF#!\"\"F.F&,&*&F*F&I$w_1GF#F&F&*(F,F&F-F.I$w_2G
F#F&F&F&F'*(F,F&F-F.F/F&" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"
\"\"\"#E\\[l#F&,(*(#F&\"\"$F&)I\"LGF#F'F&,&*&F.!\"\"I$w_1GF#F&F1*&F.F1
I$w_2GF#F&F&F&F1*(#F&F'F&,&*(F'F&F.F1F2F&F1F3F&F&F-F&F&*&F2F&F.F&F&F',
&F*F&*(F6F&F2F&F.F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "# \+
trapezoidal load option 2. Integrate first, then supply data\n" }
{MPLTEXT 1 0 76 "Nt_N:= map(int,evalm(transpose(N) &* N), x=0..L): # a
 \"mass\" type matrix\n" }{MPLTEXT 1 0 49 "Trapezoidal_Load_2 := linal
g[multiply](Nt_N, We);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6#;\"\"\"
\"\"#E\\[l#F&,&*(#F&\"\"$F&I$w_1GF#F&I\"LGF#F&F&*(#F&\"\"'F&F.F&I$w_2G
F#F&F&F',&*(F0F&F-F&F.F&F&*(F+F&F.F&F2F&F&" }}}{EXCHG {PARA 0 "> " 0 "
" {XPPEDIT 19 1 "" "%#%?G" }}}}
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