{VERSION 6 0 "Windows XP" "6.0" } {USTYLETAB {PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Ord ered List 5" -1 200 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 144 2 0 2 2 -1 1 }{PSTYLE "Ordered List 1" -1 201 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Lef t Justified Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Help" -1 10 1 {CSTYLE "" -1 -1 "Courier" 1 9 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Author" -1 19 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 8 8 2 0 2 0 2 2 -1 1 }{PSTYLE "Diagnostic" -1 9 1 {CSTYLE "" -1 -1 "Courier" 1 10 64 128 64 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Headi ng 2" -1 4 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 2 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 3" -1 202 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 72 2 0 2 2 -1 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Tim es" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Dash Item" -1 16 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Times " 1 12 0 0 0 1 1 1 2 2 2 2 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 } {PSTYLE "Ordered List 4" -1 203 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 108 2 0 2 2 -1 1 }{PSTYLE "Maple \+ Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Line Printed Output" -1 6 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "List Item" -1 14 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 0 2 0 2 2 -1 1 }{PSTYLE "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Error" -1 8 1 {CSTYLE "" -1 -1 "Courier" 1 10 255 0 255 1 2 2 2 2 2 1 1 0 0 1 }1 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Fixed Width" -1 17 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }3 1 0 0 0 0 2 0 2 0 2 2 -1 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 0 0 1 }1 1 0 0 8 4 2 0 2 0 2 2 -1 1 }{PSTYLE "Title " -1 18 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 1 2 2 2 1 0 0 1 }3 1 0 0 12 12 2 0 2 0 2 2 -1 1 }{PSTYLE "Ordered List 2" -1 204 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 0 0 1 }1 1 0 0 3 3 2 36 2 0 2 2 -1 1 }{CSTYLE "2D Math Italic Small201205" -1 200 "Times " 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Variable" -1 25 "Cour ier" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Text" -1 201 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Bold" -1 39 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Page Number" -1 33 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small" -1 202 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Nonterminal" -1 24 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Default" -1 38 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Comment" -1 21 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input " -1 0 "Courier" 1 12 255 0 0 1 2 1 2 2 1 2 0 0 0 1 }{CSTYLE "2D Math \+ Small" -1 7 "Times" 1 1 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Fix ed" -1 23 "Courier" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Popup" -1 31 "Times" 1 12 0 128 128 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "Plot Titl e" -1 27 "Times" 1 10 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Input" -1 19 "Times" 1 12 255 0 0 1 2 2 2 2 1 2 0 0 0 1 }{CSTYLE "Copyright" -1 34 "Times" 1 10 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Maple Input P laceholder" -1 203 "Courier" 1 12 200 0 200 1 2 1 2 2 1 2 0 0 0 1 } {CSTYLE "2D Math Bold Small" -1 10 "Times" 1 1 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small202" -1 204 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Notes" -1 37 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined Bold" -1 41 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "Times" 1 12 0 128 128 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Math Symbol 2" -1 16 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Equation Label" -1 205 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small201204" -1 206 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Plot Text" -1 28 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small201" -1 207 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "He lp Italic" -1 42 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Ou tput Labels" -1 29 "Times" 1 8 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "H elp Heading" -1 26 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE " Help Normal" -1 30 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE " 2D Comment" -1 18 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "H elp Maple Name" -1 35 "Times" 1 12 104 64 92 1 2 1 2 2 2 2 0 0 0 1 } {CSTYLE "2D Output" -1 20 "Times" 1 12 0 0 255 1 2 2 2 2 2 2 0 0 0 1 } {CSTYLE "Dictionary Hyperlink" -1 45 "Times" 1 12 147 0 15 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Emphasized" -1 22 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Italic Bold" -1 40 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "LaTeX" -1 32 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 0 0 0 1 }{CSTYLE "Help Menus" -1 36 "Times" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic Small202204" -1 208 "Times" 1 1 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }{CSTYLE "Prompt" -1 1 "Courier" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined" -1 44 "Times" 1 12 0 0 0 1 2 2 1 2 2 2 0 0 0 1 }{CSTYLE "Help Underlined Italic" -1 43 "T imes" 1 12 0 0 0 1 1 2 1 2 2 2 0 0 0 1 }{CSTYLE "2D Math Bold" -1 5 "T imes" 1 12 0 0 0 1 2 1 2 2 2 2 0 0 0 1 }{CSTYLE "2D Math Italic" -1 3 "Times" 1 12 0 0 0 1 1 2 2 2 2 2 0 0 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "restart; # quadratic polynomial, C0 3 node line element (L3_C0)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(linalg):\n" }{MPLTEXT 1 0 62 "P:=matrix(1,3,[ 1,x,x^2]); # complete quadratic polynomial in x" }}{PARA 7 "" 1 "" {TEXT 209 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&\"\"#I\"xGF#6$F&F(*$)F,F+F&6$F&F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "# coordinate system, 0 <= x <= L fo r two identities in G below" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "G:=matrix(3,3,[[1, 0, 0],[1,L/2,L^2 /4],[1, L, L^2]]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"$F%E\\[l*6$F'F'*$)I\"LGF#\"\"#F &6$F-F',$*F&\"\"%F&F+F&F&6$F&F-\"\"!6$F'F&F&6$F&F'F46$F-F-,$*F&F-F &F,F&F&6$F'F-F,6$F&F&F&6$F-F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "G_inv:=evalm(inverse(G)); # exists for valid interpolations" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "N:=linalg[multiply](P,G_inv);" }} {PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"$F%E\\[l*6$F'F',$*&\"\" #F&)I\"LGF#F,!\"\"F&6$F,F',$*$F.F/F/6$F&F,\"\"!6$F'F&F*6$F&F'F46$F,F,, $*&\"\"%F&F.F/F&6$F'F,,$*&F:F&F-F/F/6$F&F&F&6$F,F&,$*&F'F&F.F/F/" }} {PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"F&;F&\"\"$E\\[l$6$F&\"\"#,& *(\"\"%F&I\"xGF#F&I\"LGF#!\"\"F&*(F.F&)F/F+F&)F0F+F1F16$F&F(,&*&F/F&F0 F1F1*(F+F&F3F&F4F1F&6$F&F&,(F&F&*(F(F&F/F&F0F1F1F8F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "Load := map(int,transpose(N), x = 0..L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\"\"\"\"$;F&F&E\\[l$6$F'F&,$*F&\"\"'F&I\"LGF#F &F&6$F&F&F+6$\"\"#F&,$*F2F'F&F/F&F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "B:= map (diff,N,x); # B is dN/dx" }}{PARA 11 "" 1 "" {XPPMATH 20 "=6\"6$;\"\" \"F&;F&\"\"$E\\[l$6$F&\"\"#,&*&\"\"%F&I\"LGF#!\"\"F&*(\"\")F&I\"xGF#F& )F/F+F0F06$F&F(,&*$F/F0F0*(F.F&F3F&F4F0F&6$F&F&,&*&F(F&F/F0F0F8F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "L:=1 : plot(\{seq(N[1,j],j=1 ..3)\},x=0..1,color=[red,blue,green],\n" }{MPLTEXT 1 0 12 "thickness=2 ," }{MPLTEXT 1 0 41 "title=\"Quadratic C^0 Shape Functions\");" }} {PARA 13 "" 1 "" {TEXT 210 0 "" }{GLPLOT2D 400 400 400 {PLOTDATA 2 "6) -%+AXESLABELSG6$Q\"x6\"Q!F'-%'CURVESG6$7S7$$\"\"!F/F.7$$\"3emmm;arz@!# >$!3kzNrIAp%3#F37$$\"3[LL$e9ui2%F3$!3nZNfFR&Ru$F37$$\"3nmmm\"z_\"4iF3$ !3[F9'QA\"3QaF37$$\"3[mmmT&phN)F3$!3k7^[`\"e'fpF37$$\"3CLLe*=)H\\5!#=$ !3q6w]9&G4H)F37$$\"3gmm\"z/3uC\"FH$!3AH@:.o-i$*F37$$\"3%)***\\7LRDX\"F H$!3]gV[H_cI5FH7$$\"3]mm\"zR'ok;FH$!3H8\\BP-X56FH7$$\"3w***\\i5`h(=FH$ !3?&pJ1,j@<\"FH7$$\"3WLLL3En$4#FH$!3rsi:5'zp@\"FH7$$\"3qmm;/RE&G#FH$!3 _^#H=ox2C\"FH7$$\"3\")*****\\K]4]#FH$!3')ykP>)***\\7FH7$$\"3$******\\P Avr#FH$!3wr[F.o`S7FH7$$\"3)******\\nHi#HFH$!3$*y)HGllO@\"FH7$$\"3jmm\" z*ev:JFH$!3!y;O[$*oT<\"FH7$$\"3?LLL347TLFH$!3q,H^BJ]36FH7$$\"3,LLLLY.K NFH$!3g1,7.4)p.\"FH7$$\"3w***\\7o7Tv$FH$!3YreXlFSa$*F37$$\"3'GLLLQ*o]R FH$!3M5z;E1+\"H)F37$$\"3A++D\"=lj;%FH$!3E1`VlTXYpF37$$\"31++vV&R
*zz>K-J\\!#@7$$\"3&em;zRQb@&FH$
\"3IH'>6e(H[AF37$$\"3\\***\\(=>Y2aFH$\"31bG'zhpmS%F37$$\"39mm;zXu9cFH$
\"3umi*oenK!pF37$$\"3l******\\y))GeFH$\"3-V_vN'))Hm*F37$$\"3'*)***\\i_
QQgFH$\"3#oVvJ0MSD\"FH7$$\"3@***\\7y%3TiFH$\"3kq+5oI9\\:FH7$$\"35****
\\P![hY'FH$\"3s=I2^g1'*=FH7$$\"3kKLL$Qx$omFH$\"3qnp(>+u]A#FH7$$\"3!)**
***\\P+V)oFH$\"3_F]kbzT%f#FH7$$\"3?mm\"zpe*zqFH$\"3'\\]C\\L/_%HFH7$$\"
3%)*****\\#\\'QH(FH$\"3u\\!HQ=GiM$FH7$$\"3GKLe9S8&\\(FH$\"3ny%HZws-u$F
H7$$\"3R***\\i?=bq(FH$\"3mT+7fR[pTFH7$$\"3\"HLL$3s?6zFH$\"3HCPI!pKig%F
H7$$\"3a***\\7`Wl7)FH$\"31byUs1g\"3&FH7$$\"3#pmmm'*RRL)FH$\"3?LT$p5rpb
&FH7$$\"3Qmm;a<.Y&)FH$\"3]J$yW****31'FH7$$\"3=LLe9tOc()FH$\"3GMt*\\RE%
ylFH7$$\"3u******\\Qk\\*)FH$\"3/j&o$e6epqFH7$$\"3CLL$3dg6<*FH$\"3=k#oB
nw3l(FH7$$\"3ImmmmxGp$*FH$\"3Aj_D%)GU(=)FH7$$\"3A++D\"oK0e*FH$\"3yj)
\\+h)yw()FH7$$\"3A++v=5s#y*FH$\"3U2')Q(30wN*FH7$$\"\"\"F/Fiz-%&COLORG6
&%$RGBG$\"#5!\"\"$F/Fa[lFb[l-F*6$7S7$F.Fiz7$F1$\"3i3`f$p(eb$*FH7$F7$\"
3BzR2y(\\.\"))FH7$F<$\"3FC0G>8O9#)FH7$FA$\"3sb\"=jF+Gj(FH7$FF$\"3_rDQp
2JsqFH7$FL$\"3Wa9&QA\")*olFH7$FQ$\"3]Sc,3hNkgFH7$FV$\"3c`<$p'p