E.3 Solid Element and In-Plane Behavior of Shell Element

The cantilever was verified through static and eigenvalue analyses with varying mesh sizes.

Figure E.3.1 Analysis Model and Analytic Solutions

Table E.3.1 Tip Load Results (Reference : 200mm)

Mesh CPS3 CPS4 S3F S4F S3 S4 CS6 CS8
10×1 46.8761 138 46.8761 138 46.8761 138 45.3629 137.217
20×2 109.486 180.285 109.486 180.285 109.486 180.285 107.166 179.425
30×3 146.461 191.318 146.461 191.318 146.461 191.318 144.409 190.569
40×4 166.208 195.531 166.208 195.531 166.208 195.531 164.543 194.856
50×5 177.3 197.553 177.3 197.553 177.3 197.553 175.932 196.924
60×6 183.98 198.673 183.98 198.673 183.98 198.673 182.821 198.074
Mesh C3D4 C3D6 C3D8 C3D8I
30×3×1 - - 190.569 200.695
60×6×2 184.347 183.208 198.33 200.989

Table E.3.2 Gravity Load Results (Reference : 0.51981mm)

Mesh CPS3 CPS4 S3F S4F S3 S4 CS6 CS8
10×1 0.123254 0.360598 0.123254 0.360598 0.123254 0.360598 0.119257 0.35816
20×2 0.285687 0.469677 0.285687 0.469677 0.285687 0.469677 0.279514 0.467071
30×3 0.381671 0.498273 0.381671 0.498273 0.381671 0.498273 0.37616 0.496027
40×4 0.432967 0.509214 0.432967 0.509214 0.432967 0.509214 0.428454 0.507205
50×5 0.461797 0.514472 0.461797 0.514472 0.461797 0.514472 0.458056 0.512612
60×6 0.479166 0.517386 0.479166 0.517386 0.479166 0.517386 0.475971 0.515624
Mesh C3D4 C3D6 C3D8 C3D8I
30×3×1 - - 0.496027 0.522385
60×6×2 0.479903 0.478154 0.516267 0.523201

Table E.3.3 Surface Load Results (Reference : 0.51981mm)

Mesh CPS3 CPS4 S3F S4F S3 S4 CS6 CS8
10×1 0.123314 0.360589 - - - - 0.119319 0.358151
20×2 0.285855 0.469896 - - - - 0.27968 0.467288
30×3 0.381905 0.498553 - - - - 0.376394 0.496307
40×4 0.433238 0.509518 - - - - 0.428725 0.507509
50×5 0.462088 0.514787 - - - - 0.458348 0.512928
60×6 0.47947 0.517708 - - - - 0.476276 0.515948
Mesh C3D4 C3D6 C3D8 C3D8I
30×3×1 - - 0.496307 0.522681
60×6×2 0.48021 0.47728 0.516588 0.523527

Table E.3.4 TemperatureLoad 결과 (Reference : 1.5 mm)

Mesh CPS3 CPS4 S3F S4F S3 S4 CS6 CS8
10×1 1.54851 1.51046 1.54851 1.51046 1.54851 1.51046 1.56504 1.52459
20×2 1.52875 1.50676 1.52875 1.50676 1.52875 1.50676 1.53841 1.51409
30×3 1.51903 1.50572 1.51903 1.50572 1.51903 1.50572 1.52584 1.51094
40×4 1.51398 1.50525 1.51398 1.50525 1.51398 1.50525 1.51933 1.50948
50×5 1.51112 1.50498 1.51112 1.50498 1.51112 1.50498 1.51564 1.50869
60×6 1.50937 1.50481 1.50937 1.50481 1.50937 1.50481 1.51337 1.50819
Mesh C3D4 C3D6 C3D8 C3D8I
30×3×1 - - 1.51094 1.50967
60×6×2 1.51613 1.5127 1.50807 1.50756

*(End displacement) = alpha*temperatue*length = 1E-5*50*3000 = 1.5 mm

Table E.3.5 Frequency Analysis Results (Strong-Axis Bending Modes 1 and 2: 27.1792 Hz, 170.295 Hz)

Mesh CPS3 CPS4 S3F S4F S3 S4 CS6 CS8
10x1

55.6152

315.154

32.5794

198.74

55.6152

315.154

32.5794

198.74

55.6152

315.154

32.5794

198.74

9.09644(W.B.1)

56.5352(S.B.1)

57.5109(W.B.2)

160.604(T.B.1)

165.464(W.B.3)

319.16(S.B.2)

9.08809(W.B.1)

32.691(S.B.1)

58.0442(W.B.2)

166.157(T.B.1)

169.013(W.B.3)

199.374(S.B.2)
20x2

36.5603

217.139

28.5272

172.686

36.5603

217.139

28.5272

172.686

36.5603

217.139

28.5272

172.686

9.08135(W.B.1)

36.9611(S.B.1)

56.8575(W.B.2)

159.245(W.B.3)

163.649(T.B.1)

219.275(S.B.2)

9.07819(W.B.1)

28.6069(S.B.1)

56.9748(W.B.2)

160.281(W.B.3)

165.604(T.B.1)

173.138(S.B.2)
30x3

31.6341

189.365

27.6917

167.066

31.6341

189.365

27.6917

167.066

31.6341

189.365

27.6917

167.066

9.07693(W.B.1)

31.8647(S.B.1)

56.7231(W.B.2)

158.282(W.B.3)

162.156(T.B.1)

190.643(S.B.2)

9.07524(W.B.1)

27.7543(S.B.1)

56.7725(W.B.2)

158.708(W.B.3)

162.228(T.B.1)

167.42(S.B.2)
40×4

29.7018

178.204

27.3907

165.019

29.7018

178.204

27.3907

165.019

29.7018

178.204

27.3907

165.019

9.07492(W.B.1)

29.8577(S.B.1)

56.6727(W.B.2)

157.922(W.B.3)

160.927(T.B.1)

179.079(S.B.2)

9.07368(W.B.1)

27.4449(S.B.1)

56.6984(W.B.2)

158.15(W.B.3)

160.582(T.B.1)

165.326(S.B.2)
50×5

28.7599

172.709

27.2495

164.054

28.7599

172.709

27.2495

164.054

28.7599

172.709

27.2495

164.054

9.07379(W.B.1)

28.877(S.B.1)

56.648(W.B.2)

157.748(W.B.3)

160.003(T.B.1)

173.37(S.B.2)

9.07281(W.B.1)

27.2989(S.B.1)

56.6631(W.B.2)

157.889(W.B.3)

159.543(T.B.1)

164.334(S.B.2)
60×6

28.2339

169.623

27.1722

163.524

28.2339

169.623

27.1722

163.524

28.2339

169.623

27.1722

163.524

9.07307(W.B.1)

28.3285(S.B.1)

56.6338(W.B.2)

157.651(W.B.3)

159.329(T.B.1)

170.159(S.B.2)

9.07226(W.B.1)

27.2186(S.B.1)

56.6435(W.B.2)

157.745(W.B.3)

158.873(T.B.1)

163.787(S.B.2)
Mesh C3D4 C3D6 C3D8 C3D8I
30×2×1 - -

11.0201(W.B.1)

27.7543(S.B.1)

68.8381(W.B.2)

162.816(T.B.1)

167.42(S.B.2)

191.968(W.B.3)

9.07515(W.B.1)

27.0458(S.B.1)

56.772(W.B.2)

158.706(W.B.3)

162.218(T.B.1)

163.344(S.B.2)
60×6×2

13.5954(W.B.1)

28.389(S.B.1)

84.5334(W.B.2)

170.494(S.B.2)

233.86(W.B.3)

243.065(T.B.1)

9.26158(W.B.1)

28.247(S.B.1)

57.8122(W.B.2)

160.965(W.B.3)

169.7(S.B.2)

175.881(T.B.1)

9.60045(W.B.1)

27.2017(S.B.1)

59.9194(W.B.2)

159.056(T.B.1)

163.688(S.B.2)

166.767(W.B.3)

9.07605(W.B.1)

27.021(S.B.1)

56.6671(W.B.2)

157.812(W.B.3)

158.878(T.B.1)

162.645(S.B.2)

W.B.: Weak-Axis Bending, S.B.: Strong-Axis Bending, T.B.: Torsional Bendin

Input File

  • CantS4F-10x1.inp : 10x1 elements, S4F

  • CantS4F-20x2.inp : 20x2 elements, S4F

  • CantS4F-30x3.inp : 30x3 elements, S4F

  • CantS4F-40x4.inp : 40x4 elements, S4F

  • CantS4F-50x5.inp : 50x5 elements, S4F

  • CantS4F-60x6.inp : 60x6 elements, S4F

  • CantS4-10x1.inp : 10x1 elements, S4

  • CantS4-20x2.inp : 20x2 elements, S4

  • CantS4-30x3.inp : 30x3 elements, S4

  • CantS4-40x4.inp : 40x4 elements, S4

  • CantS4-50x5.inp : 50x5 elements, S4

  • CantS4-60x6.inp : 60x6 elements, S4

  • CantS3F-10x1.inp : 10x1x2 elements, S3F

  • CantS3F-20x2.inp : 20x2x2 elements, S3F

  • CantS3F-30x3.inp : 30x3x2 elements, S3F

  • CantS3F-40x4.inp : 40x4x2 elements, S3F

  • CantS3F-50x5.inp : 50x5x2 elements, S3F

  • CantS3F-60x6.inp : 60x6x2 elements, S3F

  • CantS3-10x1.inp : 10x1x2 elements, S3

  • CantS3-20x2.inp : 20x2x2 elements, S3

  • CantS3-30x3.inp : 30x3x2 elements, S3

  • CantS3-40x4.inp : 40x4x2 elements, S3

  • CantS3-50x5.inp : 50x5x2 elements, S3

  • CantS3-60x6.inp : 60x6x2 elements, S3

  • CantCS8-10x1.inp : 10x1 elements, CS8

  • CantCS8-20x2.inp : 20x2 elements, CS8

  • CantCS8-30x3.inp : 30x3 elements, CS8

  • CantCS8-40x4.inp : 40x4 elements, CS8

  • CantCS8-50x5.inp : 50x5 elements, CS8

  • CantCS8-60x6.inp : 60x6 elements, CS8

  • CantCS6-10x1.inp : 10x1x2 elements, CS6

  • CantCS6-20x2.inp : 20x2x2 elements, CS6

  • CantCS6-30x3.inp : 30x3x2 elements, CS6

  • CantCS6-40x4.inp : 40x4x2 elements, CS6

  • CantCS6-50x5.inp : 50x5x2 elements, CS6

  • CantCS6-60x6.inp : 60x6x2 elements, CS6

  • CantCPS4-10x1.inp : 10x1 elements, CPS4

  • CantCPS4-20x2.inp : 20x2 elements, CPS4

  • CantCPS4-30x3.inp : 30x3 elements, CPS4

  • CantCPS4-40x4.inp : 40x4 elements, CPS4

  • CantCPS4-50x5.inp : 50x5 elements, CPS4

  • CantCPS4-60x6.inp : 60x6 elements, CPS4

  • CantCPS3-10x1.inp : 10x1x2 elements, CPS3

  • CantCPS3-20x2.inp : 20x2x2 elements, CPS3

  • CantCPS3-30x3.inp : 30x3x2 elements, CPS3

  • CantCPS3-40x4.inp : 40x4x2 elements, CPS3

  • CantCPS3-50x5.inp : 50x5x2 elements, CPS3

  • CantCPS3-60x6.inp : 60x6x2 elements, CPS3

  • CantC3D8-30x3x1.inp : 30x3x1 elements, C3D8

  • CantC3D8-60x6x2.inp : 60x6x2 elements, C3D8

  • CantC3D8I-30x3x1.inp : 30x3x1 elements, C3D8I

  • CantC3D8I-60x6x2.inp : 60x6x2 elements, C3D8I

  • CantC3D4-60x6x2.inp : 60x6x2x6 elements, C3D4

  • CantC3D6-60x6x2.inp : 60x6x2x2 elements, C3D6