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2 1 2 2 2 2 1 1 1 1 }1 1 0 0 3 3 1 0 1 0 2 2 15 2 }{PSTYLE "Heading 3" -1 267 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 1" -1 268 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 8 4 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 2 " -1 269 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 } 3 1 0 0 8 2 1 0 1 0 2 2 0 1 }{PSTYLE "Heading 3" -1 270 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 268 "" 0 "" {TEXT 284 15 "FINITE ELEMENTS" }} {PARA 269 "" 0 "" {TEXT -1 29 "SYMBOLIC PROGRAMMING IN MAPLE" }}{PARA 19 "" 0 "" {TEXT 285 16 "by Artur Portela" }{TEXT 286 0 "" }}{PARA 270 "" 0 "" {TEXT 283 20 "Elastics Example 2: " }{TEXT 287 30 "Bending of a Short Cantilever\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 " restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "libname := \"C: /mylib/fem\", libname;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(libnameG6 $Q-C:/mylib/fem6\"Q=C:\\Program~Files\\Maple~6/libF'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "interface(verboseproc=3):printlevel:=3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(Plotter);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7:%+draw_labelG%,draw_symbolG%*draw_textG%+d raw_titleG%)move_penG%*new_arrowG%)new_axesG%*new_colorG%.new_pen_styl eG%1new_plot_shadingG%/new_plot_styleG%.new_thicknessG%)pen_downG%'pen _upG%-plot_elementG%2show_2D_animationG%-show_2D_plotG%2show_3D_animat ionG%-show_3D_plotG%3start_2D_animationG%.start_2D_plotG%3start_3D_ani mationG%.start_3D_plotG%/upgrade_framesG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "with(Cst_fem); with(G_cst_fem);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$%(cst_femG%/read_save_dataG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*%/animate_3D_defG%/animate_3D_rotG%6animate_displacem entsG%3plot_contour_linesG%3plot_displacementsG%*plot_meshG%2plot_prob lem_dataG%.plot_stressesG" }}}{SECT 0 {PARA 20 "" 0 "" {TEXT 257 17 " \+ Data Preparation" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "The best way t o input data for " }{TEXT 266 7 "Cst_fem" }{TEXT -1 25 " is to use the procedure " }{TEXT 265 14 "read_save_data" }{TEXT -1 50 ", which read s a file with the following structure:" }}{PARA 0 "" 0 "" {TEXT 258 10 "*elements*" }{TEXT -1 127 " [element, node1, node2, node3, mate rial]\n1 1 2 4 1 \n2 4 3 \+ 1 1 \n" }}{PARA 0 "" 0 "" {TEXT 259 7 "*nodes*" }{TEXT -1 123 " [node, x, y]\n1 1 1 \n2 \+ 0 1\n3 1 0 \n4 0 0 \n" }} {PARA 0 "" 0 "" {TEXT 260 11 "*materials*" }{TEXT -1 132 " [materi al, Young modulus, Poisson coef, specific weight, thickness]\n1 \+ 210000000000. .28 -77000. 0.01\n" }}{PARA 0 "" 0 " " {TEXT 261 8 "*forces*" }{TEXT -1 62 " [node, fx, fy]\n1 \+ 0 10\n2 0 10\n" }}{PARA 0 "" 0 "" {TEXT 262 13 "*c onstraints*" }{TEXT -1 131 " [node, direction(x, y or angle measured from x), displacement]\n4 x 0\n4 y 0\n3 90 \+ 0\n2 0 0\n" }}{PARA 0 "" 0 "" {TEXT 263 10 "*control* " }{TEXT -1 127 " [title, plane stress/strain, point forces, self weight]\ntitle Plate Under Uniaxial Traction \nplane stress\npoint fo rces\n" }}{PARA 0 "" 0 "" {TEXT 264 5 "*end*" }{TEXT -1 1 "\n" }} {PARA 0 "" 0 "" {TEXT -1 83 "The data blocks, with the respective keyw ord on the top, can be given in any order." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 83 "Alternatively, data can be give n manually through the definition of the variables: " }{TEXT 267 5 "ti tle" }{TEXT -1 2 ", " }{TEXT 268 10 "plane_case" }{TEXT -1 2 ", " } {TEXT 269 7 "control" }{TEXT -1 2 ", " }{TEXT 270 4 "nods" }{TEXT -1 2 ", " }{TEXT 271 9 "mat_props" }{TEXT -1 2 ", " }{TEXT 272 5 "elems" }{TEXT -1 2 ", " }{TEXT 273 6 "forces" }{TEXT -1 5 " and " }{TEXT 274 9 "bdr_conds" }{TEXT -1 46 ". See bellow the structure of these variab les." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 20 "" 0 "" {TEXT 275 30 " Bending of a Short Cantilever" }{TEXT -1 0 " " }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "As another problem, consider t he case of a square catilever plate, with 1" }{TEXT 276 1 "m" }{TEXT -1 80 " of length, under the simultaneous action of the self weight a nd a load of 100" }{TEXT 277 3 "kN/" }{XPPEDIT 18 0 "m^2;" "6#*$%\"mG \"\"#" }{TEXT -1 62 ", uniformly distributed on the free end, perpendi cular to the " }{TEXT 278 1 "x" }{TEXT -1 75 " direction. The analysis of this short cantilever will be carried out for 1" }{TEXT 279 1 "m" }{TEXT -1 43 " of thickness. The material properties are " }{TEXT 280 2 "E=" }{TEXT -1 4 "206*" }{XPPEDIT 18 0 "10^6;" "6#*$\"#5\"\"'" } {TEXT -1 0 "" }{TEXT 282 3 "kN/" }{XPPEDIT 18 0 "m^2;" "6#*$%\"mG\"\"# " }{TEXT 281 4 ", " }{XPPEDIT 18 0 "nu=0.3;" "6#/%#nuG$\"\"$!\"\"" } {TEXT -1 9 " and " }{XPPEDIT 18 0 "rho=77 kN;" "6#/%$rhoG*&\"#x\" \"\"%#kNGF'" }{TEXT -1 2 "//" }{XPPEDIT 18 0 "m^3;" "6#*$%\"mG\"\"$" } {TEXT -1 168 ". For the sake of simplicity, consider the discretizatio n of the plate with 2 finite elements. Note that the distributed load \+ is replaced by the equivalent nodal loads." }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 17 "read_save_data();" }}}{EXCHG {PARA 0 "read data fro m a file (y/n) ? " 0 "" {MPLTEXT 1 0 2 "y;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"yG" }}}{EXCHG {PARA 0 "file name: " 0 "" {MPLTEXT 1 0 16 "\"dat_test5.txt\";" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q.dat_test 5.txt6\"" }}}{EXCHG {PARA 0 "save data into a file (y/n) ? " 0 "" {MPLTEXT 1 0 2 "n;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"nG" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "This is the finite element data:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "tcase;plane_case;control; nods;mat_props;elems;forces;bdr_conds;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q@~Plate~Under~Uniaxial~Traction~6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#Q-plane~stress6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7# Q-point~forces6\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&7$\"\"\"F%7$\" \"!F%7$F%F'7$F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7#7&$\"-+++++@\" \"!$\"#G!\"#$!&+q(F'$\"\"\"F*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$7& \"\"\"\"\"#\"\"%F%7&F'\"\"$F%F%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$7 %\"\"\"\"\"!\"#57%\"\"#F&F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&7%\" \"%%\"xG\"\"!7%F%%\"yGF'7%\"\"$\"#!*F'7%\"\"#F'F'" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 10 "Check data" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "plot_problem_data();plot_mesh();" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 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