gtheler
/
pipe-linearized


			
							load "problem.ppl";
load "run/analytical.ppl"

ur1(x) = ur(0,x,0)
sigmal1(x) = sigmal(0,x,0)
sigmar1(x) = sigmar(0,x,0)
sigmatheta1(x) = sigmatheta(0,x,0)

delta = 0.05

set preamble "\usepackage{amsmath}"

set width 14*unit(cm)

set axis x arrow nomirrored
set axis y arrow nomirrored


set grid
set terminal pdf


set output "ur.pdf"
set xrange [a:b]
set yrange [*:*]
set key top right
set xlabel "$r$ [mm]"
set ylabel "$u_r(r)$ [mm]"
plot ur1(x)                        w l  lw 3  lt 1   color olivegreen   ti "Analytical solution $u_r(r)$",\
     "run/pipe-dist-1-3.dat" u 2:4 w l  lw 1  lt 2   color maroon       ti "",\
     "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",\
     "run/pipe-dist-1-6.dat" u 2:4 w l  lw 1  lt 4   color tan          ti "",\
     "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",\
     "run/pipe-dist-2-2.dat" u 2:4 w l  lw 2  lt 3   color cerulean     ti "",\
     "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"

set output "sigmatheta.pdf"
set xrange [a:b]
set yrange [*:*]
set key top right
set xlabel "$r$ [mm]"
set ylabel "$\sigma_\theta(r)$ [mm]"
plot sigmatheta1(x)                w l  lw 3  lt 1   color springgreen ti "Analytical solution $\sigma_\theta(r)$",\
     "run/pipe-dist-1-3.dat" u 2:5 w l  lw 1  lt 2   color melon       ti "",\
     "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",\
     "run/pipe-dist-1-6.dat" u 2:5 w l  lw 1  lt 2   color redorange   ti "",\
     "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",\
     "run/pipe-dist-2-2.dat" u 2:5 w l  lw 2  lt 3   color turquoise   ti "",\
     "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"

set output "sigmal.pdf"
set xrange [a:b]
set yrange [*:*]
set key top right
set xlabel "$r$ [mm]"
set ylabel "$\sigma_l(r)$ [mm]"
plot sigmal1(x)                    w l  lw 3  lt 1   color forestgreen    ti "Analytical solution $\sigma_l(r)$",\
     "run/pipe-dist-1-3.dat" u 2:6 w l  lw 1  lt 2   color peach          ti "",\
     "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",\
     "run/pipe-dist-1-6.dat" u 2:6 w l  lw 1  lt 2   color dandelion      ti "",\
     "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",\
     "run/pipe-dist-2-3.dat" u 2:6 w l  lw 2  lt 3   color periwinkle     ti "",\
     "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"

set output "sigmar.pdf"
set xrange [a:b]
set yrange [*:*]
set key top left
set xlabel "$r$ [mm]"
set ylabel "$\sigma_r(r)$ [mm]"
plot sigmar1(x)                    w l  lw 3  lt 1   color emerald      ti "Analytical solution $\sigma_r(r)$",\
     "run/pipe-dist-1-3.dat" u 2:7 w l  lw 1  lt 2   color bittersweet  ti "",\
     "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",\
     "run/pipe-dist-1-6.dat" u 2:7 w l  lw 1  lt 2   color orange       ti "",\
     "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",\
     "run/pipe-dist-2-3.dat" u 2:7 w l  lw 2  lt 3   color royalblue    ti "",\
     "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"


set output "M_tresca.pdf"
set key top right
set xrange [*:*]
set yrange [(1-delta)*M_tresca:(1+delta)*M_tresca]
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "$\text{M}_\\text{tresca}$ [MPa]"
plot M_tresca                      w l  lw 3 lt 1       color green    ti "Analytical solution",\
     "run/convergence-1.dat" u 1:2 w lp lw 2 lt 3 pt 2 ps 1.5 color brickred ti "First-order grid",\
     "run/convergence-2.dat" u 1:2 w lp lw 2 lt 2 pt 3 ps 1.5  color blue     ti "Second-order grid"

set output "M_vonmises.pdf"
set key top right
set yrange [(1-delta)*M_vonmises:(1+delta)*M_vonmises]
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "$\text{M}_\\text{vonmises}$ [MPa]"
plot M_vonmises                    w l  lw 3 lt 1       color green    ti "Analytical solution",\
     "run/convergence-1.dat" u 1:3 w lp lw 2 lt 3 pt 2 ps 1.5  color brickred ti "First-order grid",\
     "run/convergence-2.dat" u 1:3 w lp lw 2 lt 2 pt 3 ps 1.5  color blue     ti "Second-order grid"

set output "M_1.pdf"
set key top right
set yrange [(1-delta)*M_1:(1+delta)*M_1]
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "$\text{M}_1$ [MPa]"
plot M_1                           w l  lw 3 lt 1       color green    ti "Analytical solution",\
     "run/convergence-1.dat" u 1:4 w lp lw 2 lt 3 pt 2 ps 1.5  color brickred ti "First-order grid",\
     "run/convergence-2.dat" u 1:4 w lp lw 2 lt 2 pt 3 ps 1.5  color blue     ti "Second-order grid"

set output "M_2.pdf"
set key top right
set yrange [(1-delta)*M_2:(1+delta)*M_2]
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "$\text{M}_2$ [MPa]"
plot M_2                           w l  lw 3 lt 1       color green    ti "Analytical solution",\
     "run/convergence-1.dat" u 1:5 w lp lw 2 lt 3 pt 2 ps 1.5  color brickred ti "First-order grid",\
     "run/convergence-2.dat" u 1:5 w lp lw 2 lt 2 pt 3 ps 1.5  color blue     ti "Second-order grid"

set output "M_3.pdf"
set key top right
set yrange [(1+delta)*M_3:(1-delta)*M_3]
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "$\text{M}_3$ [MPa]"
plot M_3                           w l  lw 3 lt 1       color green    ti "Analytical solution",\
     "run/convergence-1.dat" u 1:6 w lp lw 2 lt 3 pt 2 ps 1.5  color brickred ti "First-order grid",\
     "run/convergence-2.dat" u 1:6 w lp lw 2 lt 2 pt 3 ps 1.5  color blue     ti "Second-order grid"

     
set output "MB_tresca.pdf"
set key top right
set yrange [(1-delta)*MB_tresca:(1+delta)*MB_tresca]
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "$\text{MB}_\\text{tresca}$ [MPa]"
plot MB_tresca                      w l  lw 3 lt 1              color limegreen  ti "Analytical solution",\
     "run/convergence-1.dat" u 1:7 w lp lw 2 lt 3 pt 16 ps 1.5  color salmon    ti "First-order grid",\
     "run/convergence-2.dat" u 1:7 w lp lw 2 lt 2 pt 17 ps 1.5  color cadetblue ti "Second-order grid"

set output "MB_vonmises.pdf"
set key top right
set yrange [(1-delta)*MB_vonmises:(1+delta)*MB_vonmises]
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "$\text{MB}_\\text{vonmises}$ [MPa]"
plot MB_vonmises                    w l  lw 3 lt 1              color limegreen  ti "Analytical solution",\
     "run/convergence-1.dat" u 1:8 w lp lw 2 lt 3 pt 16 ps 1.5  color salmon    ti "First-order grid",\
     "run/convergence-2.dat" u 1:8 w lp lw 2 lt 2 pt 17 ps 1.5  color cadetblue ti "Second-order grid"

set output "MB_1.pdf"
set key top right
set yrange [(1-delta)*MB_1:(1+delta)*MB_1]
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "$\text{MB}_1$ [MPa]"
plot MB_1                           w l  lw 3 lt 1              color limegreen  ti "Analytical solution",\
     "run/convergence-1.dat" u 1:9 w lp lw 2 lt 3 pt 16 ps 1.5  color salmon    ti "First-order grid",\
     "run/convergence-2.dat" u 1:9 w lp lw 2 lt 2 pt 17 ps 1.5  color cadetblue ti "Second-order grid"

set output "MB_2.pdf"
set key top right
set yrange [(1-delta)*MB_2:(1+delta)*MB_2]
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "$\text{MB}_2$ [MPa]"
plot MB_2                           w l  lw 3 lt 1               color limegreen  ti "Analytical solution",\
     "run/convergence-1.dat" u 1:10 w lp lw 2 lt 3 pt 16 ps 1.5  color salmon    ti "First-order grid",\
     "run/convergence-2.dat" u 1:10 w lp lw 2 lt 2 pt 17 ps 1.5  color cadetblue ti "Second-order grid"

set output "MB_3.pdf"
set key top right
set yrange [(1+delta)*MB_3:(1-delta)*MB_3]
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "$\text{MB}_3$ [MPa]"
plot MB_3                           w l  lw 3 lt 1               color limegreen  ti "Analytical solution",\
     "run/convergence-1.dat" u 1:11 w lp lw 2 lt 3 pt 16 ps 1.5  color salmon    ti "First-order grid",\
     "run/convergence-2.dat" u 1:11 w lp lw 2 lt 2 pt 17 ps 1.5  color cadetblue ti "Second-order grid"


set output "nodes-vs-n.pdf"
set key bottom right
set yrange [*:*]
set logscale y
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "Number of nodes"
plot "run/convergence-1.dat" u 1:12  w lp lw 2 lt 3 pt 16  color melon ti "First-order grid",\
     "run/convergence-2.dat" u 1:12  w lp lw 3 lt 4 pt 17  color violet  ti "Second-order grid"
     

set output "elements-vs-n.pdf"
set key bottom right
set yrange [*:*]
set logscale y
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "Number of elements"
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",\
     "run/convergence-2.dat" u 1:13  w lp lw 3 lt 4 pt 17 ps 1   color plum        ti "Second-order grid"

set output "cpu-vs-n.pdf"
set key bottom right
set yrange [*:*]
set logscale y
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "CPU time [sec]"
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",\
     "run/convergence-2.dat" u 1:14  w lp lw 3 lt 4 pt 17 ps 1.25 color plum        ti "Second-order grid"

set output "memory-vs-n.pdf"
set key bottom right
set yrange [*:*]
set logscale y
set xlabel "Number $n$ of elements through the pipe thickness"
set ylabel "Memory [Mb]"
plot "run/convergence-1.dat" u 1:15 w lp lw 2 lt 3 pt 16  color bittersweet ti "First-order grid",\
     "run/convergence-2.dat" u 1:15 w lp lw 3 lt 4 pt 17  color violet      ti "Second-order grid"


set output "error-M-vs-cpu.pdf"
set key top right
set yrange [*:*]
set logscale y
set logscale x
set xlabel "CPU time [sec]"
set ylabel "$|\text{M}_\\text{vonmises} - \text{analytical solution}|$ [MPa]"
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",\
     "run/convergence-2.dat" u 14:(abs($3-M_vonmises)) w lp lw 3 lt 4 pt 17  color cadetblue ti "Second-order grid"

set output "error-MB-vs-cpu.pdf"
set key top right
set yrange [*:*]
set logscale y
set logscale x
set xlabel "CPU time [sec]"
set ylabel "$|\text{MB}_\\text{vonmises} - \text{analytical solution}|$ [MPa]"
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",\
     "run/convergence-2.dat" u 14:(abs($8-MB_vonmises)) w lp lw 3 lt 4 pt 17  color navyblue ti "Second-order grid"