Intro to FEA 

Assignment# 6 

 

 

 

 

 

 

 

 

 

 

 

 

‐ Abhijith Madabhushi  

                                                       623002955 

 

Solution) Input file: 1a) Triangular mesh 0 1 0 0 ITYPE, IGRAD, ITEM, NEIGN 0 3 1 0 IELTYP, NPE, MESH, NPRNT 4 8 NX, NY 0.5 0.125 0.125 0.125 0.125 X0,DX(I) 0.0 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 Y0,DY(I) 17 NSPV,ISPV(I,J),VSPV(I) 1 1 2 1 3 1 4 1 5 1 10 1 15 1 20 1 25 1 30 1 35 1 40 1 41 1 42 1 43 1 44 1 45 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.9239 0.7071 0.3827 0.0 0 NSSV 1.0 0.0 0.0 A10, A1X, A1Y 1.0 0.0 0.0 A20, A2X, A2Y 0.0 A00 0 ICONV 0.0 0.0 0.0 F0, FX, FY

Similarly 1b) Rectangular Mesh 0 1 0 0 ITYPE, IGRAD, ITEM, NEIGN 1 4 1 0 IELTYP, NPE, MESH, NPRNT 4 8 NX, NY 0.5 0.125 0.125 0.125 0.125 X0,DX(I) 0.0 0.125 0.125 0.125 0.125 0.125 0.125 0.125 0.125 Y0,DY(I) 17 NSPV,ISPV(I,J),VSPV(I) 1 1 2 1 3 1 4 1 5 1 10 1 15 1 20 1 25 1 30 1 35 1 40 1 41 1 42 1 43 1 44 1 45 1 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1.0 0.9239 0.7071 0.3827 0.0 0 NSSV 1.0 0.0 0.0 A10, A1X, A1Y 1.0 0.0 0.0 A20, A2X, A2Y 0.0 A00 0 ICONV 0.0 0.0 0.0 F0, FX, FY Post-processing Results: Triangular mesh: Node x-coord. y-coord. Primary DOF _________________________________________________________________ 1 0.50000E+00 0.00000E+00 0.00000E+00 2 0.62500E+00 0.00000E+00 0.00000E+00 3 0.75000E+00 0.00000E+00 0.00000E+00 4 0.87500E+00 0.00000E+00 0.00000E+00 5 0.10000E+01 0.00000E+00 0.00000E+00 6 0.50000E+00 0.12500E+00 0.35819E-01 7 0.62500E+00 0.12500E+00 0.33093E-01

8 0.75000E+00 0.12500E+00 0.25328E-01 9 0.87500E+00 0.12500E+00 0.13708E-01 10 0.10000E+01 0.12500E+00 0.00000E+00 11 0.50000E+00 0.25000E+00 0.77092E-01 12 0.62500E+00 0.25000E+00 0.71224E-01 13 0.75000E+00 0.25000E+00 0.54512E-01 14 0.87500E+00 0.25000E+00 0.29502E-01 15 0.10000E+01 0.25000E+00 0.00000E+00 16 0.50000E+00 0.37500E+00 0.13010E+00 17 0.62500E+00 0.37500E+00 0.12020E+00 18 0.75000E+00 0.37500E+00 0.91996E-01 19 0.87500E+00 0.37500E+00 0.49788E-01 20 0.10000E+01 0.37500E+00 0.00000E+00 21 0.50000E+00 0.50000E+00 0.20292E+00 22 0.62500E+00 0.50000E+00 0.18747E+00 23 0.75000E+00 0.50000E+00 0.14348E+00 24 0.87500E+00 0.50000E+00 0.77653E-01 25 0.10000E+01 0.50000E+00 0.00000E+00 26 0.50000E+00 0.62500E+00 0.30663E+00 27 0.62500E+00 0.62500E+00 0.28329E+00 28 0.75000E+00 0.62500E+00 0.21682E+00 29 0.87500E+00 0.62500E+00 0.11734E+00 30 0.10000E+01 0.62500E+00 0.00000E+00 31 0.50000E+00 0.75000E+00 0.45701E+00 32 0.62500E+00 0.75000E+00 0.42223E+00 33 0.75000E+00 0.75000E+00 0.32316E+00 34 0.87500E+00 0.75000E+00 0.17489E+00 35 0.10000E+01 0.75000E+00 0.00000E+00 36 0.50000E+00 0.87500E+00 0.67698E+00 37 0.62500E+00 0.87500E+00 0.62545E+00 38 0.75000E+00 0.87500E+00 0.47869E+00 39 0.87500E+00 0.87500E+00 0.25907E+00 40 0.10000E+01 0.87500E+00 0.00000E+00 41 0.50000E+00 0.10000E+01 0.10000E+01 42 0.62500E+00 0.10000E+01 0.92390E+00 43 0.75000E+00 0.10000E+01 0.70710E+00 44 0.87500E+00 0.10000E+01 0.38270E+00 45 0.10000E+01 0.10000E+01 0.00000E+00

Rectangular mesh: Node x-coord. y-coord. Primary DOF _________________________________________________________________ 1 0.50000E+00 0.00000E+00 0.00000E+00 2 0.62500E+00 0.00000E+00 0.00000E+00 3 0.75000E+00 0.00000E+00 0.00000E+00 4 0.87500E+00 0.00000E+00 0.00000E+00 5 0.10000E+01 0.00000E+00 0.00000E+00 6 0.50000E+00 0.12500E+00 0.33934E-01 7 0.62500E+00 0.12500E+00 0.31351E-01 8 0.75000E+00 0.12500E+00 0.23995E-01 9 0.87500E+00 0.12500E+00 0.12986E-01 10 0.10000E+01 0.12500E+00 0.00000E+00 11 0.50000E+00 0.25000E+00 0.73311E-01 12 0.62500E+00 0.25000E+00 0.67730E-01 13 0.75000E+00 0.25000E+00 0.51838E-01 14 0.87500E+00 0.25000E+00 0.28055E-01 15 0.10000E+01 0.25000E+00 0.00000E+00 16 0.50000E+00 0.37500E+00 0.12444E+00 17 0.62500E+00 0.37500E+00 0.11497E+00 18 0.75000E+00 0.37500E+00 0.87996E-01 19 0.87500E+00 0.37500E+00 0.47623E-01 20 0.10000E+01 0.37500E+00 0.00000E+00 21 0.50000E+00 0.50000E+00 0.19554E+00 22 0.62500E+00 0.50000E+00 0.18065E+00 23 0.75000E+00 0.50000E+00 0.13827E+00 24 0.87500E+00 0.50000E+00 0.74829E-01 25 0.10000E+01 0.50000E+00 0.00000E+00 26 0.50000E+00 0.62500E+00 0.29799E+00 27 0.62500E+00 0.62500E+00 0.27531E+00 28 0.75000E+00 0.62500E+00 0.21071E+00 29 0.87500E+00 0.62500E+00 0.11404E+00 30 0.10000E+01 0.62500E+00 0.00000E+00 31 0.50000E+00 0.75000E+00 0.44823E+00 32 0.62500E+00 0.75000E+00 0.41411E+00 33 0.75000E+00 0.75000E+00 0.31695E+00 34 0.87500E+00 0.75000E+00 0.17153E+00 35 0.10000E+01 0.75000E+00 0.00000E+00

36 0.50000E+00 0.87500E+00 0.67037E+00 37 0.62500E+00 0.87500E+00 0.61934E+00 38 0.75000E+00 0.87500E+00 0.47402E+00 39 0.87500E+00 0.87500E+00 0.25654E+00 40 0.10000E+01 0.87500E+00 0.00000E+00 41 0.50000E+00 0.10000E+01 0.10000E+01 42 0.62500E+00 0.10000E+01 0.92390E+00 43 0.75000E+00 0.10000E+01 0.70710E+00 44 0.87500E+00 0.10000E+01 0.38270E+00 45 0.10000E+01 0.10000E+01 0.00000E+00 Table

node  x  y  tri  rect  Ex 

1  5.00E‐01  0.00E+00  0.00E+00  0.00E+00  0.00E+00 

6  5.00E‐01  1.25E‐01  3.58E‐02  3.39E‐02  3.49E‐02 

11  5.00E‐01  2.50E‐01  7.71E‐02  7.33E‐02  7.52E‐02 

16  5.00E‐01  3.75E‐01  1.30E‐01  1.24E‐01  1.27E‐01 

21  5.00E‐01  5.00E‐01  2.03E‐01  1.96E‐01  1.99E‐01 

26  5.00E‐01  6.25E‐01  3.07E‐01  2.98E‐01  0.302363 

31  5.00E‐01  7.50E‐01  4.57E‐01  4.48E‐01  0.452688 

36  5.00E‐01  8.75E‐01  6.77E‐01  6.70E‐01  6.74E‐01 

Graph:

Hence the solution is obtained.

Solution: Input file: 2a) Linear Rectangular element 0 0 2 1 ITYPE,IGRAD,ITEM,NEIGN 81 0 NVALU,NVCTR 1 4 1 0 IELTYP,NPE,MESH,NPRNT 8 8 NX,NY 0.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 X0,DX(I) 0.0 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 Y0,DY(I) 32 NSPV 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 18 1 19 1 27 1 28 1 36 1 37 1 45 1 46 1 54 1 55 1 63 1 64 1 72 1 73 1 74 1 75 1 76 1 77 1 78 1 79 1 80 1 81 1 12.5 0.0 0.0 A10, A1X, A1Y 12.5 0.0 0.0 A20, A2X, A2Y 0.0 A00 0 ICONV 2.5 0.0 0.0 C0, CX, CY 2b) Triangular element 0 0 2 1 ITYPE,IGRAD,ITEM,NEIGN

81 0 NVALU,NVCTR 0 3 1 0 IELTYP,NPE,MESH,NPRNT 8 8 NX,NY 0.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 X0,DX(I) 0.0 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 Y0,DY(I) 32 NSPV 1 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 18 1 19 1 27 1 28 1 36 1 37 1 45 1 46 1 54 1 55 1 63 1 64 1 72 1 73 1 74 1 75 1 76 1 77 1 78 1 79 1 80 1 81 1 12.5 0.0 0.0 A10, A1X, A1Y 12.5 0.0 0.0 A20, A2X, A2Y 0.0 A00 0 ICONV 2.5 0.0 0.0 C0, CX, CY Post-processing:

Rectangular elements: Eigenvalue( 1) = 0.107268E+04 Frequency = 0.32752E+02 Eigenvalue( 2) = 0.101659E+04 Frequency = 0.31884E+02 Eigenvalue( 3) = 0.960731E+03 Frequency = 0.30996E+02 Eigenvalue( 4) = 0.889230E+03 Frequency = 0.29820E+02 Eigenvalue( 5) = 0.871123E+03 Frequency = 0.29515E+02 Eigenvalue( 6) = 0.918140E+03 Frequency = 0.30301E+02 Eigenvalue( 7) = 0.736372E+03 Frequency = 0.27136E+02 Eigenvalue( 8) = 0.792226E+03 Frequency = 0.28147E+02 Eigenvalue( 9) = 0.861264E+03 Frequency = 0.29347E+02 Eigenvalue( 10) = 0.848316E+03 Frequency = 0.29126E+02

Eigenvalue( 11) = 0.646764E+03 Frequency = 0.25432E+02 Eigenvalue( 12) = 0.636905E+03 Frequency = 0.25237E+02 Eigenvalue( 13) = 0.693781E+03 Frequency = 0.26340E+02 Eigenvalue( 14) = 0.568809E+03 Frequency = 0.23850E+02 Eigenvalue( 15) = 0.664871E+03 Frequency = 0.25785E+02 Eigenvalue( 16) = 0.423347E+03 Frequency = 0.20575E+02 Eigenvalue( 17) = 0.512955E+03 Frequency = 0.22649E+02 Eigenvalue( 18) = 0.470364E+03 Frequency = 0.21688E+02 Eigenvalue( 19) = 0.624899E+03 Frequency = 0.24998E+02 Eigenvalue( 20) = 0.441454E+03 Frequency = 0.21011E+02 Eigenvalue( 21) = 0.342591E+03 Frequency = 0.18509E+02 Eigenvalue( 22) = 0.398445E+03 Frequency = 0.19961E+02 Eigenvalue( 23) = 0.454535E+03 Frequency = 0.21320E+02 Eigenvalue( 24) = 0.413488E+03 Frequency = 0.20334E+02 Eigenvalue( 25) = 0.300000E+03 Frequency = 0.17321E+02 Eigenvalue( 26) = 0.282806E+03 Frequency = 0.16817E+02 Eigenvalue( 27) = 0.338896E+03 Frequency = 0.18409E+02 Eigenvalue( 28) = 0.266468E+03 Frequency = 0.16324E+02 Eigenvalue( 29) = 0.243124E+03 Frequency = 0.15592E+02 Eigenvalue( 30) = 0.252983E+03 Frequency = 0.15905E+02 Eigenvalue( 31) = 0.184361E+03 Frequency = 0.13578E+02

Eigenvalue( 32) = 0.227031E+03 Frequency = 0.15068E+02 Eigenvalue( 33) = 0.271090E+03 Frequency = 0.16465E+02 Eigenvalue( 34) = 0.226952E+03 Frequency = 0.15065E+02 Eigenvalue( 35) = 0.155451E+03 Frequency = 0.12468E+02 Eigenvalue( 36) = 0.724964E+02 Frequency = 0.85145E+01 Eigenvalue( 37) = 0.137344E+03 Frequency = 0.11719E+02 Eigenvalue( 38) = 0.210378E+03 Frequency = 0.14504E+02 Eigenvalue( 39) = 0.170942E+03 Frequency = 0.13074E+02 Eigenvalue( 40) = 0.111933E+03 Frequency = 0.10580E+02 Eigenvalue( 41) = 0.154524E+03 Frequency = 0.12431E+02 Eigenvalue( 42) = 0.127485E+03 Frequency = 0.11291E+02 Eigenvalue( 43) = 0.830234E+02 Frequency = 0.91117E+01 Eigenvalue( 44) = 0.550573E+02 Frequency = 0.74201E+01 Eigenvalue( 45) = 0.115087E+03 Frequency = 0.10728E+02 Eigenvalue( 46) = 0.435865E+02 Frequency = 0.66020E+01 Eigenvalue( 47) = 0.254797E+02 Frequency = 0.50477E+01 Eigenvalue( 48) = 0.156204E+02 Frequency = 0.39523E+01 Eigenvalue( 49) = 0.649165E+02 Frequency = 0.80571E+01

Triangular elements: Eigenvalue( 1) = 0.120405E+04 Frequency = 0.34699E+02

Eigenvalue( 2) = 0.120382E+04 Frequency = 0.34696E+02 Eigenvalue( 3) = 0.115079E+04 Frequency = 0.33923E+02 Eigenvalue( 4) = 0.110861E+04 Frequency = 0.33296E+02 Eigenvalue( 5) = 0.104302E+04 Frequency = 0.32296E+02 Eigenvalue( 6) = 0.104109E+04 Frequency = 0.32266E+02 Eigenvalue( 7) = 0.997967E+03 Frequency = 0.31591E+02 Eigenvalue( 8) = 0.969839E+03 Frequency = 0.31142E+02 Eigenvalue( 9) = 0.921211E+03 Frequency = 0.30351E+02 Eigenvalue( 10) = 0.898812E+03 Frequency = 0.29980E+02 Eigenvalue( 11) = 0.874583E+03 Frequency = 0.29573E+02 Eigenvalue( 12) = 0.842767E+03 Frequency = 0.29030E+02 Eigenvalue( 13) = 0.819391E+03 Frequency = 0.28625E+02 Eigenvalue( 14) = 0.765729E+03 Frequency = 0.27672E+02 Eigenvalue( 15) = 0.734098E+03 Frequency = 0.27094E+02 Eigenvalue( 16) = 0.688204E+03 Frequency = 0.26234E+02 Eigenvalue( 17) = 0.674225E+03 Frequency = 0.25966E+02 Eigenvalue( 18) = 0.654697E+03 Frequency = 0.25587E+02 Eigenvalue( 19) = 0.614672E+03 Frequency = 0.24793E+02 Eigenvalue( 20) = 0.590747E+03 Frequency = 0.24305E+02 Eigenvalue( 21) = 0.529099E+03 Frequency = 0.23002E+02

Eigenvalue( 22) = 0.502568E+03 Frequency = 0.22418E+02 Eigenvalue( 23) = 0.488740E+03 Frequency = 0.22107E+02 Eigenvalue( 24) = 0.459952E+03 Frequency = 0.21446E+02 Eigenvalue( 25) = 0.427161E+03 Frequency = 0.20668E+02 Eigenvalue( 26) = 0.404940E+03 Frequency = 0.20123E+02 Eigenvalue( 27) = 0.403490E+03 Frequency = 0.20087E+02 Eigenvalue( 28) = 0.341846E+03 Frequency = 0.18489E+02 Eigenvalue( 29) = 0.331239E+03 Frequency = 0.18200E+02 Eigenvalue( 30) = 0.323389E+03 Frequency = 0.17983E+02 Eigenvalue( 31) = 0.278971E+03 Frequency = 0.16702E+02 Eigenvalue( 32) = 0.268904E+03 Frequency = 0.16398E+02 Eigenvalue( 33) = 0.252880E+03 Frequency = 0.15902E+02 Eigenvalue( 34) = 0.244804E+03 Frequency = 0.15646E+02 Eigenvalue( 35) = 0.244266E+03 Frequency = 0.15629E+02 Eigenvalue( 36) = 0.201091E+03 Frequency = 0.14181E+02 Eigenvalue( 37) = 0.190034E+03 Frequency = 0.13785E+02 Eigenvalue( 38) = 0.181017E+03 Frequency = 0.13454E+02 Eigenvalue( 39) = 0.152115E+03 Frequency = 0.12333E+02 Eigenvalue( 40) = 0.141539E+03 Frequency = 0.11897E+02 Eigenvalue( 41) = 0.130933E+03 Frequency = 0.11443E+02 Eigenvalue( 42) = 0.123635E+03 Frequency = 0.11119E+02

Eigenvalue( 43) = 0.985646E+02 Frequency = 0.99280E+01 Eigenvalue( 44) = 0.789532E+02 Frequency = 0.88856E+01 Eigenvalue( 45) = 0.715131E+02 Frequency = 0.84565E+01 Eigenvalue( 46) = 0.566568E+02 Frequency = 0.75271E+01 Eigenvalue( 47) = 0.473184E+02 Frequency = 0.68788E+01 Eigenvalue( 48) = 0.271108E+02 Frequency = 0.52068E+01 Eigenvalue( 49) = 0.160199E+02 Frequency = 0.40025E+01 From the exact solution, the frequencies can be given

3.92699081698724 7.24101328411896 10.6825699570654 14.1589667489237 17.6496285770943 21.1474927455801 24.6494933201894 4.96729413289805 7.85398163397448 11.1072073453959 14.4820265682379 17.9098336964754 21.3651399141307 24.8364706644903 6.33208242835053 8.78101841380091 11.7809724509617 15.0050108430434 18.3353047400938 21.7230398523569 25.1450100804272 7.85398163397448 9.93458826579610 12.6641648567011 15.7079632679490 18.9148925331203

22.2144146907918 25.5707115969065 9.45744626656014 11.2451903669505 13.7163892441038 16.5679924072079 19.6349540849362 22.8306478758824 26.1078446822068 11.1072073453959 12.6641648567011 14.9018823986942 17.5620368276018 20.4806783834496 23.5619449019234 26.7496975511683 12.7853557984533 14.1589667489237 16.1913979292690 18.6687012246023 21.4371979261685 24.3979612968113

27.4889357189107 

Solution: Input file: For alpha=0.5: 0 0 1 0 ITYPE,IGRAD,ITEM,NEIGN 0 3 1 0 IELTYP,NPE,MESH,NPRNT 4 4 NX,NY 0.0 0.25 0.25 0.25 0.25 X0,DX(I) 0.0 0.25 0.25 0.25 0.25 Y0,DY(I) 9 NSPV 5 1 10 1 15 1 20 1 21 1 22 1 23 1 24 1 25 1 ISPV 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 VSPV 0 NSSV 1.0 0.0 0.0 A10, A1X, A1Y 1.0 0.0 0.0 A20, A2X, A2Y 0.0 A00 0 ICONV 1.0 0.0 0.0 F0, FX, FY 1.0 0.0 0.0 C0, CX, CY 100 101 1 0 NTIME,NSTP,INTVL,INTIAL 0.01 0.5 0.5 1.0E-3 DT,ALFA,GAMA,EPSLN For alpha=0 0 0 1 0 ITYPE,IGRAD,ITEM,NEIGN 0 3 1 0 IELTYP,NPE,MESH,NPRNT 4 4 NX,NY 0.0 0.25 0.25 0.25 0.25 X0,DX(I) 0.0 0.25 0.25 0.25 0.25 Y0,DY(I) 9 NSPV 5 1 10 1 15 1 20 1 21 1 22 1 23 1 24 1 25 1 ISPV 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 VSPV 0 NSSV 1.0 0.0 0.0 A10, A1X, A1Y 1.0 0.0 0.0 A20, A2X, A2Y 0.0 A00 0 ICONV 1.0 0.0 0.0 F0, FX, FY 1.0 0.0 0.0 C0, CX, CY 100 101 1 0 NTIME,NSTP,INTVL,INTIAL 0.01 0.0 0.5 1.0E-3 DT,ALFA,GAMA,EPSLN

For alpha=0, DT= 0.005 0 0 1 0 ITYPE,IGRAD,ITEM,NEIGN 0 3 1 0 IELTYP,NPE,MESH,NPRNT 4 4 NX,NY 0.0 0.25 0.25 0.25 0.25 X0,DX(I) 0.0 0.25 0.25 0.25 0.25 Y0,DY(I) 9 NSPV 5 1 10 1 15 1 20 1 21 1 22 1 23 1 24 1 25 1 ISPV 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 VSPV 0 NSSV 1.0 0.0 0.0 A10, A1X, A1Y 1.0 0.0 0.0 A20, A2X, A2Y 0.0 A00 0 ICONV 1.0 0.0 0.0 F0, FX, FY 1.0 0.0 0.0 C0, CX, CY 100 101 1 0 NTIME,NSTP,INTVL,INTIAL 0.005 0.0 0.5 1.0E-3 DT,ALFA,GAMA,EPSLN Post-processing results:

Graph: 1) Stability of the transient solution of heat conduction problem:

Graph 2: Variation of temperature as a function of t

Graph 3) Variation of temperature wrt t

 

Solution) Input File: 0 1 0 0 ITYPE, IGRAD, ITEM, NEIGN 1 4 1 2 IELTYP, NPE, MESH, NPRNT 8 8 NX, NY 0.0 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 DX(I) 0.0 1 1 1 1 1 1 1 1 DY(I) 0 NSPV 1 NSSV 63 1 ISSV(1,1),ISSV(1,2) 125 VSSV(1) 10 0.0 0.0 A10, A1X, A1Y 15 0.0 0.0 A20, A2X, A2Y 0.0 A00 1 ICONV 8 NBE 57 4 3 5.0 -5.0 58 4 3 5.0 -5.0 59 4 3 5.0 -5.0 60 4 3 5.0 -5.0 61 4 3 5.0 -5.0 62 4 3 5.0 -5.0 63 4 3 5.0 -5.0 64 4 3 5.0 -5.0 IBN, INODE, BETA, TINF 0.0 0.0 0.0 F0, FX, FY

Post-processing: The primary degree of freedom at nodes are:

nodes  x  y  T 

1  0.00E+00  0.00E+00  1.58E+01 

2  2.50E‐01  0.00E+00  1.58E+01 

3  5.00E‐01  0.00E+00  1.58E+01 

4  7.50E‐01  0.00E+00  1.58E+01 

5  1.00E+00  0.00E+00  1.58E+01 

6  1.25E+00  0.00E+00  1.58E+01 

7  1.50E+00  0.00E+00  1.58E+01 

8  1.75E+00  0.00E+00  1.58E+01 

9  2.00E+00  0.00E+00  1.58E+01 

10  0.00E+00  1.00E+00  1.58E+01 

11  2.50E‐01  1.00E+00  1.58E+01 

12  5.00E‐01  1.00E+00  1.58E+01 

13  7.50E‐01  1.00E+00  1.58E+01 

14  1.00E+00  1.00E+00  1.58E+01 

15  1.25E+00  1.00E+00  1.58E+01 

16  1.50E+00  1.00E+00  1.58E+01 

17  1.75E+00  1.00E+00  1.58E+01 

18  2.00E+00  1.00E+00  1.58E+01 

19  0.00E+00  2.00E+00  1.58E+01 

20  2.50E‐01  2.00E+00  1.58E+01 

21  5.00E‐01  2.00E+00  1.58E+01 

22  7.50E‐01  2.00E+00  1.58E+01 

23  1.00E+00  2.00E+00  1.58E+01 

24  1.25E+00  2.00E+00  1.58E+01 

25  1.50E+00  2.00E+00  1.58E+01 

26  1.75E+00  2.00E+00  1.58E+01 

27  2.00E+00  2.00E+00  1.59E+01 

28  0.00E+00  3.00E+00  1.58E+01 

29  2.50E‐01  3.00E+00  1.58E+01 

30  5.00E‐01  3.00E+00  1.58E+01 

31  7.50E‐01  3.00E+00  1.58E+01 

32  1.00E+00  3.00E+00  1.58E+01 

33  1.25E+00  3.00E+00  1.59E+01 

34  1.50E+00  3.00E+00  1.59E+01 

35  1.75E+00  3.00E+00  1.59E+01 

36  2.00E+00  3.00E+00  1.59E+01 

37  0.00E+00  4.00E+00  1.56E+01 

38  2.50E‐01  4.00E+00  1.57E+01 

39  5.00E‐01  4.00E+00  1.57E+01 

40  7.50E‐01  4.00E+00  1.58E+01 

41  1.00E+00  4.00E+00  1.58E+01 

42  1.25E+00  4.00E+00  1.59E+01 

43  1.50E+00  4.00E+00  1.59E+01 

44  1.75E+00  4.00E+00  1.60E+01 

45  2.00E+00  4.00E+00  1.61E+01 

46  0.00E+00  5.00E+00  1.51E+01 

47  2.50E‐01  5.00E+00  1.51E+01 

48  5.00E‐01  5.00E+00  1.53E+01 

49  7.50E‐01  5.00E+00  1.55E+01 

50  1.00E+00  5.00E+00  1.58E+01 

51  1.25E+00  5.00E+00  1.62E+01 

52  1.50E+00  5.00E+00  1.65E+01 

53  1.75E+00  5.00E+00  1.67E+01 

54  2.00E+00  5.00E+00  1.60E+01 

55  0.00E+00  6.00E+00  1.36E+01 

56  2.50E‐01  6.00E+00  1.37E+01 

57  5.00E‐01  6.00E+00  1.39E+01 

58  7.50E‐01  6.00E+00  1.42E+01 

59  1.00E+00  6.00E+00  1.48E+01 

60  1.25E+00  6.00E+00  1.56E+01 

61  1.50E+00  6.00E+00  1.70E+01 

62  1.75E+00  6.00E+00  1.91E+01 

63  2.00E+00  6.00E+00  2.31E+01 

64  0.00E+00  7.00E+00  1.09E+01 

65  2.50E‐01  7.00E+00  1.09E+01 

66  5.00E‐01  7.00E+00  1.11E+01 

67  7.50E‐01  7.00E+00  1.13E+01 

68  1.00E+00  7.00E+00  1.16E+01 

69  1.25E+00  7.00E+00  1.20E+01 

70  1.50E+00  7.00E+00  1.24E+01 

71  1.75E+00  7.00E+00  1.26E+01 

72  2.00E+00  7.00E+00  1.19E+01 

73  0.00E+00  8.00E+00  7.19E+00 

74  2.50E‐01  8.00E+00  7.21E+00 

75  5.00E‐01  8.00E+00  7.29E+00 

76  7.50E‐01  8.00E+00  7.40E+00 

77  1.00E+00  8.00E+00  7.52E+00 

78  1.25E+00  8.00E+00  7.62E+00 

79  1.50E+00  8.00E+00  7.67E+00 

80  1.75E+00  8.00E+00  7.69E+00 

81  2.00E+00  8.00E+00  8.02E+00 

Hence the FEA solution is obtained.