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pipe-linearized
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pipe-linearized/plot.ppl

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  1. load "problem.ppl";

  2. load "run/analytical.ppl"

  3. 

  4. ur1(x) = ur(0,x,0)

  5. sigmal1(x) = sigmal(0,x,0)

  6. sigmar1(x) = sigmar(0,x,0)

  7. sigmatheta1(x) = sigmatheta(0,x,0)

  8. 

  9. delta = 0.05

  10. 

  11. set preamble "\usepackage{amsmath}"

  12. 

  13. set width 14*unit(cm)

  14. 

  15. set axis x arrow nomirrored

  16. set axis y arrow nomirrored

  17. 

  18. 

  19. set grid

  20. set terminal pdf

  21. 

  22. 

  23. set output "ur.pdf"

  24. set xrange [a:b]

  25. set yrange [*:*]

  26. set key top right

  27. set xlabel "$r$ [mm]"

  28. set ylabel "$u_r(r)$ [mm]"

  29. plot ur1(x)                        w l  lw 3  lt 1   color olivegreen   ti "Analytical solution $u_r(r)$",\

  30.      "run/pipe-dist-1-3.dat" u 2:4 w l  lw 1  lt 2   color maroon       ti "",\

  31.      "run/pipe-dist-1-3.dat" u 2:4 w p  pt 18 ps 1.5 color maroon       every (100)/(1*3) ti "$n=3$ first order",\

  32.      "run/pipe-dist-1-6.dat" u 2:4 w l  lw 1  lt 4   color tan          ti "",\

  33.      "run/pipe-dist-1-6.dat" u 2:4 w p  pt 16 ps 1.5 color tan          every (100)/(1*6) ti "$n=6$ first order",\

  34.      "run/pipe-dist-2-2.dat" u 2:4 w l  lw 2  lt 3   color cerulean     ti "",\

  35.      "run/pipe-dist-2-2.dat" u 2:4 w p  pt 17 ps 1.5 color cerulean     every (100)/(2*2) ti "$n=2$ second order"

  36. 

  37. set output "sigmatheta.pdf"

  38. set xrange [a:b]

  39. set yrange [*:*]

  40. set key top right

  41. set xlabel "$r$ [mm]"

  42. set ylabel "$\sigma_\theta(r)$ [mm]"

  43. plot sigmatheta1(x)                w l  lw 3  lt 1   color springgreen ti "Analytical solution $\sigma_\theta(r)$",\

  44.      "run/pipe-dist-1-3.dat" u 2:5 w l  lw 1  lt 2   color melon       ti "",\

  45.      "run/pipe-dist-1-3.dat" u 2:5 w p  pt 18 ps 1.5 color melon       every (100)/(1*3) ti "$n=3$ first order",\

  46.      "run/pipe-dist-1-6.dat" u 2:5 w l  lw 1  lt 2   color redorange   ti "",\

  47.      "run/pipe-dist-1-6.dat" u 2:5 w p  pt 16 ps 1.5 color redorange   every (100)/(1*6) ti "$n=6$ first order",\

  48.      "run/pipe-dist-2-2.dat" u 2:5 w l  lw 2  lt 3   color turquoise   ti "",\

  49.      "run/pipe-dist-2-2.dat" u 2:5 w p  pt 17 ps 1.5 color turquoise   every (100)/(2*2) ti "$n=2$ second order"

  50. 

  51. set output "sigmal.pdf"

  52. set xrange [a:b]

  53. set yrange [*:*]

  54. set key top right

  55. set xlabel "$r$ [mm]"

  56. set ylabel "$\sigma_l(r)$ [mm]"

  57. plot sigmal1(x)                    w l  lw 3  lt 1   color forestgreen    ti "Analytical solution $\sigma_l(r)$",\

  58.      "run/pipe-dist-1-3.dat" u 2:6 w l  lw 1  lt 2   color peach          ti "",\

  59.      "run/pipe-dist-1-3.dat" u 2:6 w p  pt 18 ps 1.5 color peach          every (100)/(1*3) ti "$n=3$ first order",\

  60.      "run/pipe-dist-1-6.dat" u 2:6 w l  lw 1  lt 2   color dandelion      ti "",\

  61.      "run/pipe-dist-1-6.dat" u 2:6 w p  pt 16 ps 1.5 color dandelion      every (100)/(1*6) ti "$n=6$ first order",\

  62.      "run/pipe-dist-2-3.dat" u 2:6 w l  lw 2  lt 3   color periwinkle     ti "",\

  63.      "run/pipe-dist-2-3.dat" u 2:6 w p  pt 17 ps 1.5 color periwinkle     every (100)/(2*2) ti "$n=2$ second order"

  64. 

  65. set output "sigmar.pdf"

  66. set xrange [a:b]

  67. set yrange [*:*]

  68. set key top left

  69. set xlabel "$r$ [mm]"

  70. set ylabel "$\sigma_r(r)$ [mm]"

  71. plot sigmar1(x)                    w l  lw 3  lt 1   color emerald      ti "Analytical solution $\sigma_r(r)$",\

  72.      "run/pipe-dist-1-3.dat" u 2:7 w l  lw 1  lt 2   color bittersweet  ti "",\

  73.      "run/pipe-dist-1-3.dat" u 2:7 w p  pt 18 ps 1.5 color bittersweet  every (100)/(1*3) ti "$n=3$ first order",\

  74.      "run/pipe-dist-1-6.dat" u 2:7 w l  lw 1  lt 2   color orange       ti "",\

  75.      "run/pipe-dist-1-6.dat" u 2:7 w p  pt 16 ps 1.5 color orange       every (100)/(1*6) ti "$n=6$ first order",\

  76.      "run/pipe-dist-2-3.dat" u 2:7 w l  lw 2  lt 3   color royalblue    ti "",\

  77.      "run/pipe-dist-2-3.dat" u 2:7 w p  pt 17 ps 1.5 color royalblue    every (100)/(2*2) ti "$n=2$ second order"

  78. 

  79. 

  80.      

  81. set output "M_tresca.pdf"

  82. set key top right

  83. set xrange [*:*]

  84. set yrange [(1-delta)*M_tresca:(1+delta)*M_tresca]

  85. set xlabel "Number $n$ of elements through the pipe thickness"

  86. set ylabel "$\text{M}_\\text{tresca}$ [MPa]"

  87. plot M_tresca                      w l  lw 3 lt 1       color green    ti "Analytical solution",\

  88.      "run/convergence-1.dat" u 1:2 w lp lw 2 lt 3 pt 2 ps 1.5 color brickred ti "First-order grid",\

  89.      "run/convergence-2.dat" u 1:2 w lp lw 2 lt 2 pt 3 ps 1.5  color blue     ti "Second-order grid"

  90. 

  91. set output "M_vonmises.pdf"

  92. set key top right

  93. set yrange [(1-delta)*M_vonmises:(1+delta)*M_vonmises]

  94. set xlabel "Number $n$ of elements through the pipe thickness"

  95. set ylabel "$\text{M}_\\text{vonmises}$ [MPa]"

  96. plot M_vonmises                    w l  lw 3 lt 1       color green    ti "Analytical solution",\

  97.      "run/convergence-1.dat" u 1:3 w lp lw 2 lt 3 pt 2 ps 1.5  color brickred ti "First-order grid",\

  98.      "run/convergence-2.dat" u 1:3 w lp lw 2 lt 2 pt 3 ps 1.5  color blue     ti "Second-order grid"

  99. 

  100. set output "M_1.pdf"

  101. set key top right

  102. set yrange [(1-delta)*M_1:(1+delta)*M_1]

  103. set xlabel "Number $n$ of elements through the pipe thickness"

  104. set ylabel "$\text{M}_1$ [MPa]"

  105. plot M_1                           w l  lw 3 lt 1       color green    ti "Analytical solution",\

  106.      "run/convergence-1.dat" u 1:4 w lp lw 2 lt 3 pt 2 ps 1.5  color brickred ti "First-order grid",\

  107.      "run/convergence-2.dat" u 1:4 w lp lw 2 lt 2 pt 3 ps 1.5  color blue     ti "Second-order grid"

  108. 

  109. set output "M_2.pdf"

  110. set key top right

  111. set yrange [(1-delta)*M_2:(1+delta)*M_2]

  112. set xlabel "Number $n$ of elements through the pipe thickness"

  113. set ylabel "$\text{M}_2$ [MPa]"

  114. plot M_2                           w l  lw 3 lt 1       color green    ti "Analytical solution",\

  115.      "run/convergence-1.dat" u 1:5 w lp lw 2 lt 3 pt 2 ps 1.5  color brickred ti "First-order grid",\

  116.      "run/convergence-2.dat" u 1:5 w lp lw 2 lt 2 pt 3 ps 1.5  color blue     ti "Second-order grid"

  117. 

  118. set output "M_3.pdf"

  119. set key top right

  120. set yrange [(1+delta)*M_3:(1-delta)*M_3]

  121. set xlabel "Number $n$ of elements through the pipe thickness"

  122. set ylabel "$\text{M}_3$ [MPa]"

  123. plot M_3                           w l  lw 3 lt 1       color green    ti "Analytical solution",\

  124.      "run/convergence-1.dat" u 1:6 w lp lw 2 lt 3 pt 2 ps 1.5  color brickred ti "First-order grid",\

  125.      "run/convergence-2.dat" u 1:6 w lp lw 2 lt 2 pt 3 ps 1.5  color blue     ti "Second-order grid"

  126. 

  127.      

  128.      

  129. 

  130.      

  131. 

  132. set output "MB_tresca.pdf"

  133. set key top right

  134. set yrange [(1-delta)*MB_tresca:(1+delta)*MB_tresca]

  135. set xlabel "Number $n$ of elements through the pipe thickness"

  136. set ylabel "$\text{MB}_\\text{tresca}$ [MPa]"

  137. plot MB_tresca                      w l  lw 3 lt 1              color limegreen  ti "Analytical solution",\

  138.      "run/convergence-1.dat" u 1:7 w lp lw 2 lt 3 pt 16 ps 1.5  color salmon    ti "First-order grid",\

  139.      "run/convergence-2.dat" u 1:7 w lp lw 2 lt 2 pt 17 ps 1.5  color cadetblue ti "Second-order grid"

  140. 

  141. set output "MB_vonmises.pdf"

  142. set key top right

  143. set yrange [(1-delta)*MB_vonmises:(1+delta)*MB_vonmises]

  144. set xlabel "Number $n$ of elements through the pipe thickness"

  145. set ylabel "$\text{MB}_\\text{vonmises}$ [MPa]"

  146. plot MB_vonmises                    w l  lw 3 lt 1              color limegreen  ti "Analytical solution",\

  147.      "run/convergence-1.dat" u 1:8 w lp lw 2 lt 3 pt 16 ps 1.5  color salmon    ti "First-order grid",\

  148.      "run/convergence-2.dat" u 1:8 w lp lw 2 lt 2 pt 17 ps 1.5  color cadetblue ti "Second-order grid"

  149. 

  150. set output "MB_1.pdf"

  151. set key top right

  152. set yrange [(1-delta)*MB_1:(1+delta)*MB_1]

  153. set xlabel "Number $n$ of elements through the pipe thickness"

  154. set ylabel "$\text{MB}_1$ [MPa]"

  155. plot MB_1                           w l  lw 3 lt 1              color limegreen  ti "Analytical solution",\

  156.      "run/convergence-1.dat" u 1:9 w lp lw 2 lt 3 pt 16 ps 1.5  color salmon    ti "First-order grid",\

  157.      "run/convergence-2.dat" u 1:9 w lp lw 2 lt 2 pt 17 ps 1.5  color cadetblue ti "Second-order grid"

  158. 

  159. set output "MB_2.pdf"

  160. set key top right

  161. set yrange [(1-delta)*MB_2:(1+delta)*MB_2]

  162. set xlabel "Number $n$ of elements through the pipe thickness"

  163. set ylabel "$\text{MB}_2$ [MPa]"

  164. plot MB_2                           w l  lw 3 lt 1               color limegreen  ti "Analytical solution",\

  165.      "run/convergence-1.dat" u 1:10 w lp lw 2 lt 3 pt 16 ps 1.5  color salmon    ti "First-order grid",\

  166.      "run/convergence-2.dat" u 1:10 w lp lw 2 lt 2 pt 17 ps 1.5  color cadetblue ti "Second-order grid"

  167. 

  168. set output "MB_3.pdf"

  169. set key top right

  170. set yrange [(1+delta)*MB_3:(1-delta)*MB_3]

  171. set xlabel "Number $n$ of elements through the pipe thickness"

  172. set ylabel "$\text{MB}_3$ [MPa]"

  173. plot MB_3                           w l  lw 3 lt 1               color limegreen  ti "Analytical solution",\

  174.      "run/convergence-1.dat" u 1:11 w lp lw 2 lt 3 pt 16 ps 1.5  color salmon    ti "First-order grid",\

  175.      "run/convergence-2.dat" u 1:11 w lp lw 2 lt 2 pt 17 ps 1.5  color cadetblue ti "Second-order grid"

  176. 

  177. 

  178. 

  179. set output "nodes-vs-n.pdf"

  180. set key bottom right

  181. set yrange [*:*]

  182. set logscale y

  183. set xlabel "Number $n$ of elements through the pipe thickness"

  184. set ylabel "Number of nodes"

  185. plot "run/convergence-1.dat" u 1:12  w lp lw 2 lt 3 pt 16  color melon ti "First-order grid",\

  186.      "run/convergence-2.dat" u 1:12  w lp lw 3 lt 4 pt 17  color violet  ti "Second-order grid"

  187.      

  188. 

  189. set output "elements-vs-n.pdf"

  190. set key bottom right

  191. set yrange [*:*]

  192. set logscale y

  193. set xlabel "Number $n$ of elements through the pipe thickness"

  194. set ylabel "Number of elements"

  195. plot "run/convergence-1.dat" u 1:13  w lp lw 2 lt 3 pt 16 ps 1.5 color apricot     ti "First-order grid",\

  196.      "run/convergence-2.dat" u 1:13  w lp lw 3 lt 4 pt 17 ps 1   color plum        ti "Second-order grid"

  197. 

  198. set output "cpu-vs-n.pdf"

  199. set key bottom right

  200. set yrange [*:*]

  201. set logscale y

  202. set xlabel "Number $n$ of elements through the pipe thickness"

  203. set ylabel "CPU time [sec]"

  204. plot "run/convergence-1.dat" u 1:14  w lp lw 2 lt 3 pt 16 ps 1.75 color melon       ti "First-order grid",\

  205.      "run/convergence-2.dat" u 1:14  w lp lw 3 lt 4 pt 17 ps 1.25 color plum        ti "Second-order grid"

  206. 

  207. set output "memory-vs-n.pdf"

  208. set key bottom right

  209. set yrange [*:*]

  210. set logscale y

  211. set xlabel "Number $n$ of elements through the pipe thickness"

  212. set ylabel "Memory [Mb]"

  213. plot "run/convergence-1.dat" u 1:15 w lp lw 2 lt 3 pt 16  color bittersweet ti "First-order grid",\

  214.      "run/convergence-2.dat" u 1:15 w lp lw 3 lt 4 pt 17  color violet      ti "Second-order grid"

  215. 

  216. 

  217. set output "error-M-vs-cpu.pdf"

  218. set key top right

  219. set yrange [*:*]

  220. set logscale y

  221. set logscale x

  222. set xlabel "CPU time [sec]"

  223. set ylabel "$|\text{M}_\\text{vonmises} - \text{analytical solution}|$ [MPa]"

  224. plot "run/convergence-1.dat" u 14:(abs($3-M_vonmises)) w lp lw 2 lt 3 pt 16  color orangered ti "First-order grid",\

  225.      "run/convergence-2.dat" u 14:(abs($3-M_vonmises)) w lp lw 3 lt 4 pt 17  color cadetblue ti "Second-order grid"

  226. 

  227. set output "error-MB-vs-cpu.pdf"

  228. set key top right

  229. set yrange [*:*]

  230. set logscale y

  231. set logscale x

  232. set xlabel "CPU time [sec]"

  233. set ylabel "$|\text{MB}_\\text{vonmises} - \text{analytical solution}|$ [MPa]"

  234. plot "run/convergence-1.dat" u 14:(abs($8-MB_vonmises)) w lp lw 2 lt 3 pt 16  color salmon   ti "First-order grid",\

  235.      "run/convergence-2.dat" u 14:(abs($8-MB_vonmises)) w lp lw 3 lt 4 pt 17  color navyblue ti "Second-order grid"

  236.