Microsoft Word - 計算力学2007有限要素法.doc

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(17) !M[ nq o. "\n.+8Po. >W O/ G. Ed " S t . V1nl= D o:fn>Wo S @4 ,!. S t "jRg3 S u ?0 bC!. @4 ?0 ,!. . . n>W. -L ,!. -LN[ Jo S t *50k]H@4nak4o {t}T = {t x , t y } ,! S t *

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(19) sin t y ZY. {n} ={cos , sin} @9 S^'#&(. WO/ ,!. . (9). @9 S^'#&( x e. T. c. . . [ ]{n} = {t} n S t *o. V1ak*T

(20). l=. {t} = 0 g34BX>. G(9)$ $ ) %)(Cauchy)G ;!. . dSt {n} {t}. x dy. tx. . ty. xy dx. xy. y. <p >W*4h7 [2m 1] G(9)"< 1 "6UF

(21) . A` L9DS50i"_ x y L94h7"_ QG"J. . x dy + xy dx = t x dSt xy dy + y dx = t y dSt cos = dy / dSt sin = dx / dSt "_K. 3. *GQ?I G(9)"J.

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(29) xy y

(30) + X x u x + + + X y u y dxdy = 0 y y x . (a). H96\I+

(31) . u + xyuy + u + y u y x x x y xy x. (. ). =. (. ). xy xy y x u x + u y + u x + u x x y y y. ( ). ( ). u y u y (ux ) (ux ) + xy + xy + y x x y y. + x. xy xy y = x + + u x + u + x y y y y x x. {. xy. }. x . y .

(32) xy . (b). %99(13)]*M9(b)U?9(a)H1: h. x. x D. +. xy

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(34) + X x u x + + + X y u y dxdy y y x . x. =

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(36). y dxdy + h. xy . x . y

(37) dxdy

(38). xy . [ X u. ). + xy uy +. x. D. u + y u y y xy x. (. x. ]. + X y uy dxdy. ) dxdy. h { }T {}dxdy +h {X } {u}dxdy = 0 T. D. 9(c)F;S97YR$^( 9(c) . 2. ". ^ = h. [ n ( u S. x. (c). D. x. x. ^)N@4L2MH1: . ). )]. (. + xyu y + n y xy ux + y uy dS. !#WG3ET/J. 5.

(39) =h. x xy ux T ny

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(55) ux N 1

(56) = uy 0. 0 N1. N2 0. N3 0. 0 N2. Uxe1 e1 Uy e2 0 Ux e e2

(57) = [ N ]{U } N 3 Uy U e3 xe3 Uy . (29).

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(59) . N1 =. 1 {(x 2 y3 x 3y 2 ) + (y 2 y3 )x + (x 3 x 2 )y} 2. (30). N2 =. 1 {(x 3 y1 x1 y3 ) + (y 3 y1 )x + (x 1 x3 )y} 2. (31). N3 =. 1 {(x1 y2 x 2 y1 ) + ( y1 y2 )x + ( x 2 x1 )y} 2. (32). (C6G= A :5D> 2 = x1 y2 + x 2 y 3 + x 3 y1 x1 y3 x 2 y1 x 3 y2 :5(29)(32) 98<4 ?;2*F+:5E. N 1 u x. . x x. x. uy = 0 y = y . . xy ux uy N1 +. y x y. 0. N 1 y N 1 x. N2 x 0. N2 y. 0. N2 y N2 x. N 3 x 0. N 3 y. U e1 xe1. 0

(60) U y.

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(62) . Ux. e2 y

(63) Uy.

(64) N 3

(65) U e3. x x

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(71) mo nf d AQ V^ L 7R54D]L(>hi& h. { } { }dxdy = h { u} { X}dxdy + h { u} {t}dS T. T. D. D. (34). t. St. j< { } = [ D]{ } #bZI9. 'PB RbZI97R h. T. j<{} = [ B]{U e } 7. j<{} = [ B]{U e } (6=&. {U } [B] [D][B]{U }dxdy T. e T. e. D. =h. {U } { N} T. e. T. D. {X} dxdy + h S {U e } { N }T {t}dSt T. (35). t. 2L{U e} {U e } ''fd

(72) &7RbZI9bZI9% 'KU&_@J? &#X#W . & h {U e }. T. ( [B] [D][B]dxdy){U } T. e. D. = h {U e }. T. { N}. T. D. {X} dxdy + h{ U e}. T. { N } {t}dS T. (36). t. St. L(36)8S7RbZI9{U e} T`&XL(O& h. ( [B] [ D][ B]dxdy){U } = h { N} { X}dxdy + h {N} {t}dS T. T. e. D. T. D. St. t. (37). '(X#e. [K e ]{U e } = { Fe }. (38). . [K e ] = h. [B] [ D][B]dxdy T. (39). D. {F } = h { N} {X}dxdy + h { N } {t}dS T. e. D. T. t. St. (40). f d AQ . ,/ +) * {F e } ekB[:BNl(F!"%a a [K e ] f ;b ZB - ), 0 G'&\pbZ1gMfdHEL(39)3[ D] . [B]KU.,/+)*&_@J? $ h Ddxdy = h & YS&X#cC&. [K e ] = h[ B] [ D][ B] T. (41). 10.

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(99) z[pTOi* VO¡ ª] '>z¿¢`Z¢M pTbU*¡ '! $¢OS"k$¤n%( ' G¢o*VO¤ \µp«P¢OS* ). STRESS-YY RST CALC TIME 1.000 23. 54. 65 12. 55. 67 44. 64 1. 24. 13. 2. 56. 26. 46. 15. 69 45. 66 34. 25. 14. 3. 27. 47. 16. 71. 68 35. 57. 73. 70 36. 4. 58. 5. 59. 75 48. 72 37. 28. 17. 49. 74 38. 6. 29. 18. 7. 30. 61. 79 50. 76 39. 540.0. 60. 77. 19. 8. 62. 81 51. 78 40. 31. 20. 9. 360.0 63. 83 52. 80 41. 32. 21. 85 53. 82 42. 10. 33. 22 84. 43. 180.0 0.0 -180.0 -360.0 -540.0. 11 MAXIMUM 611.0 MINIMUM -611.0. (a) ８節点要素を用いた場合. STRESS-YY RST CALC TIME 1.000. 23. 24. 25. 26. 12. 13. 14. 15. 1. 2. 3. 4. 27. 28. 180.0. 29. 30. 31. 32. 33. 18. 19. 20. 21. 22. 120.0 60.0. 16. 5. 17. 6. 7. 8. 9. 0.0 -60.0 -120.0. 10. 11. -180.0. MAXIMUM 217.9 MINIMUM -213.9. (b)定ひずみ三角形要素を用いた場合 ^¾ 図13.4 片持ち梁の解析例. 14.

(100) 102. 82. 113. 78. 98. 107 70 106. 99. 80. 112 94. 71. 95. 66 86 67. 76. 72 92. 88. 25. 44. 61. 93. 77. 97. 20. 23. 3250. 64. 19. 57. 22. 15 37. 39. 89 52 38 21 49 12 16 34 48 51 11 7 47 30 6 50 46 26. 63. 36. 2. 13 55. 31. 8. 32. 3. 33. 28. 4. 10. 62. 58. 54 27. 9. 750. 250.. 59. 35. 1750. 1250.. 14. 56. 17. 2750. 2250.. 40. 18. 53. 1. TIME 1.000. 41. 60. 73. 42 69. 24. STRESS-ZZ RST CALC. 45. 101. 120. 43. 114 68. 81. 119. 118 87. 100. 96. 115. 91. 110. 105. 85 121. 116. 75 111. 90. 104. 84 117. 65. 79. 108 74. 103. 83. 109. 29. 5. MAXIMUM 3445. MINIMUM -110.1. L5 図13.5 穴開き板の引張の解析例. +. frpb +-=-~*. U2\-{*NF£eH>@c-[P&+. W. '](+1>@c¤c*|WcG¥-P& E g I!#Eg *u*-J¢E E g _ I! * nS-E t J ¢ 5.1 L 4 xalJ¢ 2\¨w'*>@c-P BEg_m'#)¦>@c-o¦)zq.0/-9`'§#¦K\©w¦K\ 8 w% Gnm-§. c)

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