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1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 271 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 269 "" 0 "" {TEXT 258 15 "FINITE ELEMENTS" }} {PARA 270 "" 0 "" {TEXT -1 29 "SYMBOLIC PROGRAMMING IN MAPLE" }}{PARA 19 "" 0 "" {TEXT 259 16 "by Artur Portela" }{TEXT 260 0 "" }}{PARA 271 "" 0 "" {TEXT 256 26 "Potential-Flow Example 1: " }{TEXT 261 37 "U niform Flow in a Rectangular Domain\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "restart:interface(verboseproc=3):printlevel:=3:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "libname := \"C:/mylib/fem\", libname:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(Plotter): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(Cgt_fem):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "with(G_cgt_fem):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 1 {PARA 20 "" 0 "" {TEXT 263 17 " Data Preparation" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "The b est way to input data for " }{TEXT 265 7 "Cgt_fem" }{TEXT -1 25 " is t o use the procedure " }{TEXT 264 14 "read_save_data" }{TEXT -1 50 ", w hich reads a file with the following structure:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1 "*" }{TEXT 269 7 "control" }{TEXT -1 169 "* [title,point sources,element sources,boun dary velocities]\ntitle Potential Flow in a Rectangular Domain\npoint \+ sources\nelement sources\nboundary velocities\n\n*" }{TEXT 270 9 "mate rials" }{TEXT -1 104 "* [material,x-permeability,y-permeabil ity,angle of the local x-direction]\n1 2 2 45\n2 8 8 45\n\n*" }{TEXT 271 5 "nodes" }{TEXT -1 180 "* [node,x,y]\n1 0 0\n2 \+ 0 1 \n3 0 2 \n4 1 0 \n5 1 1 \n6 1 2\n7 2 0 \n8 2 1 \n9 2 2\n10 3 0 \n11 3 1 \n12 3 2\n13 4 0 \n14 4 1 \n15 4 2 \n\n*" }{TEXT 272 8 "elements" }{TEXT -1 399 "* \+ [element,node1,node2,node3,material]\n1 1 4 5 1 \n2 1 \+ 5 2 1 \n3 2 5 3 1 \n4 3 5 6 1 \n5 4 7 8 1 \n6 5 4 8 1\n7 5 8 6 1 \n8 6 8 9 \+ 1\n9 7 10 11 1 \n10 7 11 8 1 \n11 8 11 9 \+ 1\n12 11 12 9 1 \n13 10 13 14 1\n14 10 14 11 \+ 1 \n15 11 14 12 1\n16 12 14 15 1 \n\n*" }{TEXT 273 11 "constraints" }{TEXT -1 59 "* [node,potential]\n1 10\n2 10 \n3 10\n13 0\n14 0\n15 0\n\n*" }{TEXT 274 19 "boundary velocities" } {TEXT -1 52 "* [node1,node2,normal velocity]\n1 2 0\n2 3 0\n5 4 0\n\n* " }{TEXT 275 13 "point sources" }{TEXT -1 25 "* [node,Q]\n1 -50 \n\n*" }{TEXT 276 15 "element sources" }{TEXT -1 25 "* [element,q] \n2 30\n\n*" }{TEXT 277 3 "end" }{TEXT -1 1 "*" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 85 "The data blocks, with the respective keyword on the top, can be defined in any order." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "Alternatively, \+ data can be given manually through the definition of the variables: " }{TEXT 278 5 "tcase" }{TEXT -1 2 ", " }{TEXT 279 7 "control" }{TEXT -1 2 ", " }{TEXT 280 4 "nods" }{TEXT -1 2 ", " }{TEXT 281 5 "elems" } {TEXT -1 2 ", " }{TEXT 282 9 "mat_props" }{TEXT -1 2 ", " }{TEXT 283 9 "bdr_conds" }{TEXT -1 2 ", " }{TEXT 284 7 "b_velts" }{TEXT -1 2 ", \+ " }{TEXT 285 6 "p_srcs" }{TEXT -1 5 " and " }{TEXT 286 6 "e_srcs" } {TEXT -1 46 ". See bellow the structure of these variables." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 20 "" 0 " " {TEXT 262 37 " Uniform Flow in a Rectangular Domain" }{TEXT -1 0 "" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 84 "As the first problem, consider t he case of a uniform flow in a rectangular domain, 4" }{TEXT 266 1 "m " }{TEXT -1 11 " long and 2" }{TEXT 267 1 "m" }{TEXT -1 101 " wide. De fine flow potentials, uniformly distributed on the two opposite sides, perpendicular to the " }{TEXT 268 1 "x" }{TEXT -1 61 " direction. Con sider the hydraulic conductivity specified as " }{TEXT 287 2 "Kx" } {TEXT -1 1 "=" }{TEXT 288 2 "Ky" }{TEXT -1 2 "=2" }{TEXT 289 3 "m/h" } {TEXT -1 40 ", in the first half of the domain, and " }{TEXT 290 2 "K x" }{TEXT -1 1 "=" }{TEXT 291 2 "Ky" }{TEXT -1 2 "=8" }{TEXT 292 3 "m/ h" }{TEXT -1 50 " in the second half, with the angle of the local " } {TEXT 293 1 "x" }{TEXT -1 37 "-direction, measured from the global " } {TEXT 294 1 "x" }{TEXT -1 32 "-direction, equal to 45 degrees." }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "read_save_data();" }}} {EXCHG {PARA 0 "read data from a file (y/n) ? " 0 "" {MPLTEXT 1 0 2 "y ;" }}}{EXCHG {PARA 0 "file name: " 0 "" {MPLTEXT 1 0 16 "\"dat_test1.t xt\";" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q**control*6\"" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#Q,*materials*6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q(*nodes*6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q+*elements*6\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q.*constraints*6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q6*boundary~velocities*6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q0*point~sources*6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #Q2*element~sources*6\"" }}}{EXCHG {PARA 0 "save data into a file (y/n ) ? 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