⁐᥋ᵓ㐀ࢩ࣏ࣥࢪ࣒࢘ ㅮ₇ㄽᩥ㞟 ᖺ ᭶
㔜ྜ࣓ࢵࢩࣗἲࢆ⏝࠸ࡓ⌮㝧ゎἲ )(0 ࡼࡿ⁐᥋ኚᙧ࣭ṧ␃ᛂຊゎᯒ
㜰ᗓ❧ᏛᏛ㝔
⏕ۑᓥ ୍ᶞ
ᰘཎ ṇ
Analysis of Welding Distortions and Residual Stresses by Idealized Explicit FEM Using Mesh
Overlaying Technique
by Kazui IKUSHIMA and Masakazu SHIBAHARA
㸯㸬⥴ ゝ
⯪⯧ࡸᶫᱱࢆࡣࡌࡵ㸪ᏛࣉࣛࣥࢺࡸཎᏊຊࣉࣛࣥࢺ࠸ࡗࡓᵝࠎ࡞〇ရࡢ〇㐀⁐᥋ࡀᖜᗈࡃ⏝࠸ࡽࢀ࡚
࠸ࡿࡀ㸪⁐᥋ࡣ㸪ࡑࡢᕤక࠸ᚲ↛ⓗⓎ⏕ࡍࡿኚᙧࡸṧ␃ᛂຊࡀၥ㢟࡞ࡿࡇࡀ࠶ࡿ㸬ࡑࡢࡓࡵ㸪⁐᥋
ࡢᕤ๓㸪〇ရ⏕ࡌࡿ⁐᥋ኚᙧࡸṧ␃ᛂຊࡘ࠸᳨࡚ウྍ⬟࡞ᡭἲࡀồࡵࡽࢀ࡚࠸ࡿ㸬
㠀⥺ᙧ᭷㝈せ⣲ἲࡼࡿ⇕ᙎረᛶゎᯒࢆ⏝࠸ࡿࡇ࡛㸪⁐᥋ኚᙧṧ␃ᛂຊࢆண ྍ⬟ 1)࡛࠶ࡿࡀ㸪⁐᥋ၥ㢟
ࡣᮦᩱࡢ⁐⼥ࢆྵࡴ㠀⥺ᙧᛶࡢᙉ࠸ၥ㢟࡛࠶ࡿࡇࡽ㸪ࡑࡢண ࡣ⭾࡞ィ⟬㈨※ࢆᚲせࡍࡿ㸬ࡲࡓ㸪
㠀⥺ᙧ㡿ᇦࡀ⁐᥋ࢺ࣮ࢳ࿘㎶ࡢ⁐⼥㒊ࡢ㏆ഐ㞟୰ࡍࡿࡇࡽ㸪⁐⼥㒊ࡢ࿘㎶ࡢヲ⣽࡞ࣔࢹࣝࡀᚲせ࡞
ࡿ㸬ࡇࡢࡼ࠺࡞ࡇࡽ㸪⁐᥋ኚᙧ㸪ṧ␃ᛂຊࡢண ࡣィ⟬㛫㸪࣓ࣔࣜᾘ㈝㔞ࡢ㠃࡛ゎᯒつᶍࡀ㝈ᐃࡉࢀ࡚
࠾ࡾ㸪ຍ࠼࡚㸪ゎᯒࣔࢹࣝࡢసᡂேⓗ㸪㛫ⓗࢥࢫࢺࢆせࡍࡿࡓࡵᅔ㞴࡞ࡗ࡚࠸ࡿࡢࡀ⌧≧࡛࠶ࡿ㸬
⁐᥋ኚᙧ㸪ṧ␃ᛂຊゎᯒࡢィ⟬つᶍ㛵ࡍࡿၥ㢟ࢆᨵၿࡍࡿࡓࡵ㸪ⴭ⪅ࡽࡣ⌮㝧ゎἲ FEM ࡤࢀࡿ
つᶍ㧗㏿ゎᯒᡭἲࡢ㛤Ⓨࢆ㐍ࡵ࡚ࡁࡓ 2)㸬⌮㝧ゎἲ FEM ࡣ㸪ືⓗ㝧ゎἲ FEM3)ࢆᇶ⁐᥋ၥ㢟ᑐࡋ࡚ຠ
⋡ࢆᅗࡗࡓᡭἲ࡛࠶ࡾ㸪ᚑ᮶ᡭἲࡰྠ➼ࡢゎᯒ⢭ᗘࢆ᭷ࡋ㸪ࡘ㸪ᚑ᮶ᡭἲẚ࡚㧗㏿㸪┬࣓ࣔࣜ
࠸࠺≉ᚩࢆ᭷ࡋ࡚࠸ࡿ㸬ࡲࡓ㸪⌮㝧ゎἲ FEM ࡣືⓗ㝧ゎἲ FEM ࢆᇶࡋ࡚࠸ࡿࡓࡵ㸪୪ิᑐࡋ࡚㠀
ᖖ㐺ࡋ࡚࠾ࡾ㸪㏆ᖺ㸪୪ิᩘ್ィ⟬ࡢᐇ⾜⎔ቃࡋ࡚ὀ┠ࡉࢀ࡚࠸ࡿ⏬ീฎ⌮⨨(Graphics Processing Unit:
GPU)ࡼࡿ୪ิࢆᑟධࡍࡿࡇ࡛㸪୍ᒙࡢ㧗㏿ࢆᐇ⌧ࡋ㸪ᚑ᮶ᡭἲ࡛ࡣᅔ㞴࡞⛣ື⇕※ࢆ⪃៖ࡋࡓ 3 ḟඖ
ከᒙ⁐᥋ṧ␃ᛂຊゎᯒࢆᐇ⌧ࡋ࡚ࡁࡓ 4)㸬
୍᪉㸪ᵓ㐀ゎᯒ࠾ࡅࡿゎᯒࣔࢹࣝసᡂࡢ㧗ᗘ㈨ࡍࡿᡭἲࡋ࡚㔜ྜ࣓ࢵࢩࣗἲࡀᥦࡉࢀ࡚࠸ࡿ 5)㸬
㔜ྜ࣓ࢵࢩࣗἲࡣ㸪ゎᯒ㡿ᇦయࡢせ⣲ศᑐࡋ࡚㸪ヲ⣽࡞ゎᯒࢆᐇࡋࡓ࠸⟠ᡤヲ⣽࡞せ⣲ศࡢ࣓ࢵ
ࢩࣗࢆ㈞ࡾࡅࡿࡇ࡛ゎᯒࡢ㧗⢭ᗘࣔࢹࣝసᡂࡢ㧗ᗘࢆ㐩ᡂࡍࡿࡓࡵ⪃ࡉࢀࡓᡭἲ࡛࠶ࡿ㸬㔜ྜ
࣓ࢵࢩࣗἲࢆ⏝࠸࡚㸪ࡇࢀࡲ࡛⥺ᙧᙎᛶゎᯒ 6)㸪ᙎረᛶゎᯒ 7)㸪⇕ఏᑟゎᯒ 8)㸪⇕ᙎᛶゎᯒ 9)㸪ࡁ㐍ᒎ
ゎᯒ 10)࡞ࡀᐇࡉࢀ࡚࠸ࡿ㸬ࡲࡓ㸪ᵓ㐀యࡢࢩ࢙ࣝせ⣲ᑐࡋ࡚㸪ࢯࣜࢵࢻせ⣲ࢆ㔜ྜࡉࡏࡿࡇ࡛ࢬ࣮
࣑ࣥࢢゎᯒ௦ࢃࡾヲ⣽࡞ゎᯒࢆᐇࡋࡓࡶሗ࿌ࡉࢀ࡚࠸ࡿ 11)㸬⁐᥋ၥ㢟࠾࠸࡚ࡣ㸪㠀⥺ᙧ㡿ᇦࡀࢺ࣮
ࢳ࿘㎶㞟୰ࡍࡿࡇࡽ㸪㠀⥺ᙧ㡿ᇦࡢࣔࢹࣝࢆ㔜ྜ࣓ࢵࢩࣗἲࡼࡾ⾜࠺ࡇࡣ᭷ຠ࡛࠶ࡿ⪃࠼ࡽࢀ
ࡿ㸬ࡋࡋ࡞ࡀࡽ㸪㔜ྜ࣓ࢵࢩࣗἲࡣせ⣲ࢆ㔜ࡡྜࢃࡏࡿࡼ࠺࡞≉Ṧ࡞ฎ⌮ࢆᐇࡍࡿࡇࡽ㸪య๛ᛶ࣐
ࢺࣜࢵࢡࢫࡢ㠀㞽ᡂศࡢศᕸࡀ୍⯡ⓗ࡞᭷㝈せ⣲ゎᯒࡣ␗࡞ࡿࡓࡵ㸪ゎᯒせࡍࡿィ⟬㛫ࡀ⭾࡞ࡿࡇ
ࡀሗ࿌ࡉࢀ࡚࠸ࡿ 12)㸬
ࡑࡇ࡛㸪ᮏ◊✲࡛ࡣ㸪ゎᯒࣔࢹࣝసᡂࡢຠ⋡ゎᯒつᶍࡢྥୖࢆ┠ⓗ㸪㔜ྜ࣓ࢵࢩࣗἲᑐࡋ࡚⌮
㝧ゎἲࢆᑟධࡋࡓᡭἲࡢ㛤Ⓨࢆヨࡳࡿ㸬㛤Ⓨᡭἲࡘ࠸᳨࡚ドࡍࡿࡓࡵ㸪ᇶ♏ⓗ࡞⁐᥋ၥ㢟ᑐࡋ࡚㛤Ⓨᡭ
ἲࢆ㐺⏝ࡋ㸪ᚑ᮶ᡭἲࡢẚ㍑ࢆ⾜࠺㸬ࡲࡓ㸪㛤Ⓨᡭἲࡢ᭷⏝ᛶࢆ♧ࡍࡓࡵ㒊ᮦࡈసᡂࡋࡓゎᯒࣔࢹࣝ
ᑐࡋ࡚⁐᥋㒊ࢆࣔࢹࣝࡋࡓヲ⣽࣓ࢵࢩࣗࢆ㔜ྜࡉࡏ㸪㒊ᮦྠኈࡢ⤌❧⁐᥋ࢆ⾲⌧ࡍࡿゎᯒࢆᐇࡍࡿ㸬
㸰㸬㔜ྜ࣓ࢵࢩࣗἲࡼࡿ⁐᥋ኚᙧ࣭ṧ␃ᛂຊゎᯒࡢᐃᘧ
㸰㸬㸯 ⇕ఏᑟゎᯒࡢᐃᘧ
⁐᥋ኚᙧ㸪ṧ␃ᛂຊࡣ⇕ᙎረᛶゎᯒࢆ⾜࠺ࡇ࡛ண ྍ⬟࡛࠶ࡿࡀ㸪⇕ᙎረᛶゎᯒඛ❧ࡗ࡚ ᗘศᕸࡢᒚ
Ṕࡀᚲせ࡞ࡿ㸬ᮏ⠇࡛ࡣ㸪ࡲࡎ㔜ྜ࣓ࢵࢩࣗἲࢆ⏝࠸ࡓ⇕ఏᑟゎᯒࡢᐃᘧࢆ⾜࠺㸬
⇕ఏᑟゎᯒࡢᨭ㓄᪉⛬ᘧቃ⏺᮲௳ࡣ㸪ࡑࢀࡒࢀᘧ(1)㸪(2)࡛⾲ࡉࢀࡿ㸬
wT
w wT
cU
O
q in :
(1)
wt
wxi wx i
―301―
－301－
ΩG
Ω
ΩL
ΩL
ΓGL
Global mesh
(Rough mesh for the entire region)
Local mesh
(Detailed mesh near welding torch)
Analysis model
Fig. 1 Schematic illustration of analysis model for mesh overlaying method.
wT
D c T Tc on *
(2)
wn
ࡇࡇ࡛㸪 c 㸪 U 㸪 O 㸪 D c ࡣࡑࢀࡒࢀ㸪ẚ⇕㸪ᐦᗘ㸪⇕ఏᑟ⋡㸪⇕ఏ㐩ಀᩘ࡛࠶ࡾ㸪 T 㸪 Tc ࡣࡑࢀࡒࢀ ᗘ㸪ᐊ
㸪 q ࡣⓎ⇕ᐦᗘ㸪 : ࡣゎᯒ㡿ᇦ㸪 * ࡣ⇕ఏ㐩㠃ࢆ⾲ࡍ㸬
㔜ࡳ㛵ᩘࢆ T * ᐃ⩏ࡋ㸪ᨭ㓄᪉⛬ᘧᑐࡋ࡚㔜ࡳࡁṧᕪἲࢆ㐺⏝ࡋ㸪ḟᘧࢆᚓࡿ㸬
wT
w wT ·
*§
*
(3)
³: T ¨¨© cU wt O wxi wxi ¸¸¹ d: ³: T q d*
㔜ྜ࣓ࢵࢩࣗἲ࡛ࡣ㸪Fig. 1 ♧ࡍࡼ࠺㸪ゎᯒ㡿ᇦయ : ࢆ⾲ࡍ࣓ࢵࢩࣗ(௨㝆㸪ࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗ⛠
ࡍ)ᑐࡋ࡚㸪ヲ⣽࡞せ⣲ศࡢ࣓ࢵࢩࣗ(௨㝆㸪࣮࣓ࣟ࢝ࣝࢵࢩࣗ⛠ࡍ)ࢆ㡿ᇦ : L ᙇࡾࡅࡿࡇ࡛ゎᯒ㡿
ᇦࢆ⾲⌧ࡍࡿ㸬ࡲࡓ㸪ࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗࡢࡳࡀᏑᅾࡍࡿ㡿ᇦࢆ : G : / : L ᐃ⩏ࡋ㸪: G : L ࡢቃ⏺ࢆ * GL
ࡍࡿ㸬ࡑࢀࡒࢀࡢ㡿ᇦ࠾ࡅࡿ ᗘ㛵ࡋ࡚㸪 : G ࠾࠸࡚ࡣ㏻ᖖࡢ᭷㝈せ⣲ゎᯒྠᵝ㸪ᘧ(4)࡛⾲ࡉࢀ
ࡿ㛵ᩘࢆ⏝࠸࡚ ᗘሙࢆ㏆ఝࡍࡿ㸬୍᪉㸪 : L ࠾࠸࡚ࡣ㸪ᘧ(5)ࡼࡾ ᗘሙࢆ㏆ఝࡍࡿ㸬ࡲࡓ : G : L ࡢቃ
⏺࠾࠸࡚ࡣ㸪ᘧ(6)ࡢࡼ࠺࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢ ᗘᣊ᮰᮲௳ࢆ࠼ࡿ㸬ࡇࢀࡣࢢ࣮ࣟࣂ࣓ࣝࢵࢩ࣮ࣗࣟ
࣓࢝ࣝࢵࢩ࡛ࣗ ᗘሙࡢ㐃⥆ᛶࢆᢸಖࡍࡿࡓࡵࡢࡶࡢ࡛࠶ࡿ㸬
(4)
T N G T Gn in : G
> @^ `
(5)
T >N @^T ` >N @^T ` in :
(6)
^T ` 0 on *
ࡇࡇ࡛㸪>N @ 㸪>N @ ࡣࡑࢀࡒࢀࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗࡢᙧ≧㛵ᩘ㸪࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢᙧ≧㛵ᩘ࡛࠶ࡾ㸪^T `㸪
^T `ࡣࡑࢀࡒࢀࢢ࣮ࣟࣂ࣓ࣝࢵࢩ࣮࣓ࣗࣟ࢝ࣝࢵࢩࣗ࠾ࡅࡿ⠇Ⅼ ᗘ࡛࠶ࡿ㸬ᘧ(5)♧ࡍࡼ࠺㸪 :
G
Gn
L
Ln
Ln
L
GL
G
Gn
L
Ln
L
࠾࠸࡚ࡣ㸪ࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗࡢ㏆ఝ㛵ᩘᑐࡋ࡚㸪࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢ㏆ఝ㛵ᩘࢆ㔜ࡡྜࢃࡏࡿᙧ࡛ ᗘሙ
ࡢ㏆ఝ㛵ᩘࢆసᡂࡍࡿ㸬ࡲࡓ㸪㔜ࡳ㛵ᩘ㛵ࡋ࡚ࡶ㸪 ᗘሙྠᵝࡢ㛵ᩘࢆ⏝࠸࡚ḟᘧࡼࡾ㏆ఝࡍࡿ㸬
>N @^T ` in :
>N @^T ` >N @^T `
G
T*
*Gn
* Gn
G
T*
G
L
*Ln
(7)
(8)
in : L
ᘧ(4)-(8)ࢆᘧ(3)௦ධࡋ㸪㒊ศ✚ศ࠾ࡼࡧቃ⏺᮲௳ࢆ㐺⏝ࡍࡿࡇ࡛ḟᘧࢆᚓࡿ㸬
>C @ w T Gn >K @ T Gn >A@ T Gn ^Q`
(9)
wt
ªC GG C GL º w T Gn ½ ª K GG K GL º T Gn ½ ª AGG AGL º T Gn ½ Q G ½
(10)
¾ «
¾ «
¾® ¾
»®
»®
« LG
» ®
C LL ¼ wt ¯T Ln ¿ ¬ K LG K LL ¼ ¯T Ln ¿ ¬ ALG ALL ¼ ¯T Ln ¿ ¯Q L ¿
¬C
ࡇࡇ࡛㸪ᘧ(9)ࡣ㡿ᇦ : G ᑐᛂࡍࡿ᪉⛬ᘧ࡛࠶ࡾ㸪ಀᩘ࣐ࢺࣜࢵࢡࢫ࠾ࡼࡧᐃᩘ࣋ࢡࢺࣝࡣ㏻ᖖࡢ᭷㝈せ⣲ἲ
ྠ➼ࡢᡭ㡰࡛ᑟฟࡉࢀࡿ㸬୍᪉㸪ᘧ(10)ࡣ㡿ᇦ : L ᑐᛂࡍࡿ᪉⛬ᘧ࡛࠶ࡾ㸪C ab 㸪K ab 㸪Aab 㸪Q a a, b : G, L
ࡣࡑࢀࡒࢀ⇕ᐜ㔞࣐ࢺࣜࢵࢡࢫ㸪⇕ఏᑟ࣐ࢺࣜࢵࢡࢫ㸪⇕ఏ㐩࣐ࢺࣜࢵࢡࢫ㸪࠾ࡼࡧ㸪Ⓨ⇕㔞࣋ࢡࢺ࡛ࣝ࠶ࡾ㸪
௨ୗࡢ✚ศ࡛࠼ࡽࢀࡿ㸬
^ `
^ `
^ `
> @ > @ > @^ `
>C @ ³
ab
:L
> @ >N @d:
cU N a
T
a
a, b : G, L
b
T
(11)
b
>K @ ³ O ª« wwNx º» ª« wwNx º»d: a, b : G, L
«¬
»¼ «¬
»¼
>A @ ³ D >N @ >N @d* a, b : G, L
^Q ` ³ q >N @ d: ³ D T >N @ d: a : G, L
ab
:L
ab
*L
i
a T
c
b
a T
a
:L
(12)
i
*L
c
c
a T
―302―
－302－
(13)
(14)
య㡿ᇦ : :G : L ࠾ࡅࡿ᪉⛬ᘧࢆᑟฟࡍࡿࡓࡵ㸪௨ୖࡢᡭ㡰࡛ồࡲࡿ༙㞳ᩓᘧ(9)࠾ࡼࡧ(10)ࡢࢆ
ྲྀࡾ㸪ゎᯒ㡿ᇦయࡢ༙㞳ᩓᘧࢆᚓࡿ㸬ࡲࡓ㸪⁐᥋⌧㇟࠾࠸࡚ࡣຍ⇕୰ࡢ ᗘኚࡣᛴᓧ࡛࠶ࡿࡶࡢࡢ㸪
෭༷㐣⛬࠾࠸࡚ࡣᩘ༑ศࡽᩘ㛫ࢆࡅ࡚⦆ࡸ෭༷⮳ࡿࡇࢆ⪃៖ࡋ㸪㛫ቑศ㛵ࡋ࡚ẚ㍑
ⓗ⮬⏤タᐃࡀྍ⬟࡞㝜ⓗ࡞㞳ᩓࢆ⾜࠺㸬ᮏᐃᘧ࠾࠸࡚ࡣ Crank-Nicolson ἲࢆ⏝࠸ࡿࡶࡢࡋࡓ㸬ࡲࡓ㸪
ᘧ(11)-(14)ࡢ✚ศࡣ㸪࢞࢘ࢫ✚ศࢆ⏝࠸࡚ᩘ್ⓗ⾜࠺ࡀ㸪ࡑࡢ㝿㸪࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢ࢞࢘ࢫ✚ศⅬ࠾ࡅ
ࡿࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗࡢᙧ≧㛵ᩘ࠾ࡼࡧࡑࡢ໙㓄ࡀᚲせ࡞ࡿ㸬ᮏ◊✲࡛ࡣ㸪ᩥ⊩ 11)ࢆཧ⪃㸪࣮࣓ࣟ࢝ࣝࢵ
ࢩࣗࡢ࢞࢘ࢫ✚ศⅬࡢయᗙᶆ⣔࡛ࡢ⨨ᗙᶆࡼࡾ㸪࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢ࢞࢘ࢫ✚ศⅬࡢࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗ
࠾ࡅࡿせ⣲ෆᗙᶆ⣔ࢆゎᯒࡢ㛤ጞ๓⟬ฟࡋ㸪✚ศ㏲ḟཧ↷ࡍࡿࡇ࡛㸪࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢ࢞࢘ࢫ✚
ศࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗࡢᙧ≧㛵ᩘ࠾ࡼࡧࡑࡢ໙㓄ࢆỴᐃࡍࡿࡶࡢࡋࡓ㸬
㸰㸬㸰 ⇕ᙎረᛶゎᯒࡢᐃᘧ
⇕ᙎረᛶゎᯒ࠾࠸࡚ࡣ㸪๓⠇࠾࠸࡚ᐃᘧࢆ⾜ࡗࡓ⇕ఏᑟゎᯒࡼࡾᚓࡽࢀࡿ ᗘሙࡢᒚṔࢆཧ↷ࡋྛ
้࠾ࡅࡿኚቑศࢆồࡵࡿ㸬ኚቑศ㛵ࡍࡿ௬ࡢཎ⌮ࡣḟᘧ࡛࠼ࡽࢀࡿ㸬࡞࠾㸪ᮏᐃᘧ࠾
࠸࡚ࡣ㸪እ㒊Ⲵ㔜ࡣ⪃៖ࡋ࡞࠸ࡶࡢࡋࡓ㸬
T
³: ^GH ` ^V ` ^'V `d:
0
G
(15)
ࡇࡇ࡛㸪 ^GH ` 㸪 ^V ` 㸪 ^'V `ࡣࡑࢀࡒࢀ௬ࡦࡎࡳ㸪ᛂຊ࠾ࡼࡧᛂຊቑศ࡛࠶ࡿ㸬
ኚቑศࡦࡎࡳቑศࢆḟᘧࡢ㏻ࡾᐃ⩏ࡍࡿ㸬
^'u`
^'u`
^'u `
>N @^'u ` in :
>N @^'u ` >N @^'u `
Ln
G
Gn
G
Gn
0 on *
G
L
Ln
(16)
in :
L
(17)
GL
(18)
(19)
>B @^'u ` in :
(20)
>B @^'u ` >B @^'u ` in :
ࡇࡇ࡛㸪>N @㸪>N @ 㸪>B @ 㸪 >B @ ࡣࡑࢀࡒࢀࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗ࠾ࡼࡧ࣮࣓ࣟ࢝ࣝࢵࢩࣗ࠾ࡅࡿᙧ≧㛵ᩘ࠾
ࡼࡧኚࡦࡎࡳ࣐ࢺࣜࢵࢡࢫ࡛࠶ࡾ㸪 ^'u `㸪 ^'u ` ࡣࡑࢀࡒࢀࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗ࠾ࡼࡧ࣮࣓ࣟ࢝ࣝࢵࢩࣗ
^'H `
^'H `
G
Gn
G
Gn
G
L
G
L
G
Ln
L
L
Gn
Ln
࠾ࡅࡿ⠇Ⅼኚቑศ࡛࠶ࡿ㸬
ࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗ࠾ࡼࡧ࣮࣓ࣟ࢝ࣝࢵࢩࣗ࠾ࡅࡿ⠇Ⅼ௬ኚࢆࡑࢀࡒࢀ Gu Gn 㸪 Gu Ln ࡋ㸪ࡦࡎࡳቑ
ศྠᵝࡢᙧ࡛ḟᘧࡼࡾ௬ࡦࡎࡳࢆᐃ⩏ࡍࡿ㸬
^ ` ^ `
^GH `
^GH `
>B @^Gu ` in :
>B @^Gu ` >B @^Gu `
G
Gn
G
Gn
G
L
Ln
(21)
in :
L
(22)
ᛂຊቑศࡣḟᘧࡼࡾᐃ⩏ࡍࡿ㸬
(23)
>D @^'H ` ^'H ` in :
(24)
>D @^'H ` ^'H ` ^'H ` ^'H ` in :
ࡇࡇ࡛㸪>D @ 㸪>D @ ࡣࡑࢀࡒࢀࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗ㸪࣮࣓ࣟ࢝ࣝࢵࢩࣗ࠾ࡅࡿᛂຊࡦࡎࡳ࣐ࢺࣜࢵࢡࢫ㸪^'H `㸪
^'H `ࡣࡑࢀࡒࢀࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗ࠾ࡅࡿᗄఱᏛࡦࡎࡳቑศ㸪 ᗘࡦࡎࡳቑศ㸪 ^'H `㸪 ^'H `㸪 ^'H `ࡣ
^'V `
^'V `
G
G
G
G
T
L
G
L
G
L
P
L
T
L
G
L
G
T
L
L
P
L
T
ࡑࢀࡒࢀ࣮࣓ࣟ࢝ࣝࢵࢩࣗ࠾ࡅࡿᗄఱᏛࡦࡎࡳቑศ㸪ረᛶࡦࡎࡳቑศ㸪⇕ࡦࡎࡳቑศࢆ⾲ࡍ㸬࡞࠾㸪ᮏᐃᘧ
࡛ࡣ㸪㠀⥺ᙧࡢረᛶኚᙧࡣ : L ࡢࡳ࡛⏕ࡌࡿࡶࡢࡋ㸪 : G ࠾࠸࡚ࡣᙎᛶኚᙧ⇕ኚᙧࡢࡳࢆ⪃៖ࡋࡓ㸬
ᘧ(19)-(24)ࢆᘧ(15)௦ධࡋḟᘧࢆᚓࡿ㸬
>K @^'u Gn ` ^'F` ^f `
GG
GL
(25)
Gn
G
G
ªK
K º 'u ½ 'F ½ f ½
(26)
¾ ®
¾® ¾
« LG
»®
K LL ¼ ¯'u Ln ¿ ¯ 'F L ¿ ¯ f L ¿
¬K
ࡇࡇ࡛㸪ᘧ(25)ࡣ㡿ᇦ : G ᑐᛂࡍࡿ᪉⛬ᘧ࡛࠶ࡾ㸪๓⠇ࡢ⇕ఏᑟゎᯒྠᵝ㸪㏻ᖖࡢ᭷㝈せ⣲ゎᯒྠࡌᡭ
⥆ࡁࡼࡾ๛ᛶ࣐ࢺࣜࢵࢡࢫ >K @ 㸪Ⲵ㔜ቑศ࣋ࢡࢺࣝ ^'F ` ࠾ࡼࡧ⠇Ⅼෆຊ࣋ࢡࢺࣝ ^ f ` ࢆồࡵࡿ㸬୍᪉㸪ᘧ(26)
ࡣ㡿ᇦ : L ᑐᛂࡍࡿ᪉⛬ᘧ࡛࠶ࡾ㸪ྛ㡯ࡣ௨ୗࡢ✚ศࡼࡾィ⟬ࡉࢀࡿ㸬
>K @ ³ >B @ >D @>B @d: a, b : G, L
^'F ` ³ >B @ >D @ ^'H `d: a : G, L
^f ` ³ >B @ ^V `d: a : G, L
a T
ab
L
b
(27)
:L
a T
a
L
:L
a T
a
L
T
(28)
L
(29)
:L
య๛ᛶ᪉⛬ᘧࡣᘧ(25)㸪(26)ࡢࢆྲྀࡿࡇ࡛ᚓࡽࢀ㸪యࡀ㟼ⓗᖹ⾮≧ែ᮰ࡍࡿࡲ࡛ồゎࢆ⧞ࡾ㏉ࡍ㸬
―303―
－303－
㸰㸬㸱 ⌮㝧ゎἲࡢᑟධ
๓⠇ࡢ㏻ࡾ㸪⇕ఏᑟゎᯒ㛵ࡋ࡚ࡣᘧ(9)࠾ࡼࡧᘧ(10)㸪⇕ᙎረᛶゎᯒ㛵ࡋ࡚ࡣᘧ(25)㸪(26)ࡢ㐃❧᪉⛬ᘧࢆ
㛫ࢫࢸࢵࣉẖ㏲ḟồゎࡍࡿࡇ࡛ゎࡀᚓࡽࢀࡿ㸬ࡋࡋ࡞ࡀࡽ㸪㔜ྜ࣓ࢵࢩࣗἲ࠾࠸࡚ࡣ㸪㏻ᖖࡢ᭷㝈
せ⣲ἲࡣ␗࡞ࡾ㸪㐃❧᪉⛬ᘧࡢಀᩘ⾜ิࡢ㠀㞽ᡂศࡢศᕸࡀ Fig. 2 ♧ࡍࡼ࠺࡞ᙧ࡞ࡿࡓࡵ㸪ᵓ㐀ゎᯒ
࠾࠸࡚⏝࠸ࡽࢀࡿࡇࡢከ࠸┤᥋ἲࢆ⏝࠸࡚㐃❧᪉⛬ᘧࢆồゎࡍࡿ㝿 Fill-in ࡀ⏕ࡌࡸࡍࡃ㸪ィ⟬㛫ࡸ࣓ࣔ
ࣜᾘ㈝㔞ࡢቑࡘ࡞ࡀࡿ㸬ࡇࡢၥ㢟ᑐࡋ࡚㸪య๛ᛶ࣐ࢺࣜࢵࢡࢫࡢᛶࢆ⏝ࡋ࡚ࢫࣃ࣮ࢫࢯࣝࣂ࣮13)
ࢆ⏝ࡍࡿ᪉ἲ㸪Fill-in ࡀᑡ࡞ࡃ࡞ࡿࡼ࠺⠇Ⅼ␒ྕࢆ᭱㐺ࡍࡿ᪉ἲ 14)ࡸ㸪ࢢ࣮ࣟࣂ࣓ࣝࢵࢩ࣮࣓ࣗࣟ࢝ࣝ
ࢵࢩࣗࢆูࠎồゎࡋ᭱⤊ⓗ㡿ᇦయࡀ᮰ࡍࡿࡲ࡛ࡍࡿࡼ࠺࡞ᡭἲ 15)ࡀ⪃࠼ࡽࢀࡿࡀ㸪ᮏ◊✲࠾࠸
࡚ࡣ㸪⌮㝧ゎἲࢆ㐺⏝ࡍࡿࡇ࡛ィ⟬㛫࣓ࣔࣜᾘ㈝㔞ࡢ๐ῶࢆヨࡳࡿ㸬
⌮㝧ゎἲ FEM ࡼࡿ⇕ఏᑟゎᯒ࠾ࡼࡧ⇕ᙎረᛶゎᯒࡣࡑࢀࡒࢀᩥ⊩ 2, 16)࠾࠸࡚ヲ⣽㏙ࡽࢀ࡚࠸ࡿ㸬
ࡋࡋ࡞ࡀࡽ㸪⌮㝧ゎἲࢆ㐺⏝ࡍࡿሙྜ㸪᮰ࡍࡿࡲ࡛ࡢ㛫ࢫࢸࢵࣉࡢィ⟬࠾࠸࡚ᘧ(26)ྑ㎶ࡢ✚ศ᧯
సࢆ⧞ࡾ㏉ࡍᚲせࡀ࠶ࡾ㸪᮰ࡍࡿࡲ࡛ᩘⓒࢫࢸࢵࣉ⛬ᗘࢆせࡍࡿ㸬ᘧ(26)ྑ㎶ࡢ✚ศࡣ࣮࣓ࣟ࢝ࣝࢵࢩࣗෆ
ࡢせ⣲࠾࠸࡚ࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗෆࡢせ⣲ࡢኚࡦࡎࡳ࣐ࢺࣜࢵࢡࢫࢆཧ↷ࡍࡿࡼ࠺࡞」㞧࡞᧯సࢆక࠺ࡓ
ࡵ㸪㏻ᖖࡢ✚ศẚ࡚ィ⟬㔞ࡢቑຍࡀぢ㎸ࡲࢀࡿ㸬ࡑࡢࡓࡵ㸪㔜ྜ࣓ࢵࢩࣗἲᑐࡋ࡚⌮㝧ゎἲࢆࡑࡢ
ࡲࡲ㐺⏝ࡍࡿሙྜ㸪㠀ຠ⋡࡞ゎᯒ࡞ࡿᜍࢀࡀ࠶ࡿ㸬
ࡑࡇ࡛㸪ᮏ◊✲࡛ࡣ㸪Fig. 3 ♧ࡍࡼ࠺࡞ᡭἲࢆ᥇ࡿ㸬ࡲࡎ㸪㉁㔞࣐ࢺࣜࢵࢡࢫ㸪ῶ⾶࣐ࢺࣜࢵࢡࢫࢆィ⟬ࡋ㸪
ྜࢃࡏ࡚๛ᛶ࣐ࢺࣜࢵࢡࢫࢆ⟬ฟࡍࡿ㸬ࡇࡇ࡛㸪๛ᛶ࣐ࢺࣜࢵࢡࢫ㛵ࡋ࡚ࡣ㸪ᅽ⦰⾜᱁⣡᪉ᘧࡢ⾜ิࡢᙧ
࡛ಖᏑࡍࡿ㸬⥆࠸࡚㸪ືⓗ㝧ゎἲᇶ࡙ࡁ㛫ࢫࢸࢵࣉࢆ㐍ࡵࡿࡇ࡛ኚࢆồࡵ㸪ᘧ(25)㸪(26)ࡢྑ㎶ࡢ✚ศ
ࡢ௦ࢃࡾ㸪ồࡵࡓኚ๛ᛶ࣐ࢺࣜࢵࢡࢫࡢ✚ࡼࡾṧᕪຊ࣋ࢡࢺࣝࢆ⟬ฟࡍࡿ㸬ᣦᐃࡋࡓ㛫ࢫࢸࢵࣉᩘࡢ
ศ(N ᅇ)ࡔࡅኚࡢ⟬ฟṧᕪຊࡢ⟬ฟࢆ⧞ࡾ㏉ࡋࡓࡢࡕ㸪ᘧ(25)㸪ᘧ(26)ࡢྑ㎶ࡢ✚ศࢆᐇ⾜ࡋṇ☜࡞ṧᕪຊ
࣋ࢡࢺࣝࢆ⟬ฟࡋ㸪㡿ᇦయࡀ㟼ⓗᖹ⾮≧ែ㐩ࡋ࡚࠸ࡿࢆ☜ㄆࡍࡿ㸬ࡇࡇ࡛㸪㟼ⓗᖹ⾮≧ែࡀᚓࡽࢀࡓሙ
ྜ㸪ḟࡢ ᗘࢫࢸࢵࣉࡢィ⟬⛣ࡾ㸪㟼ⓗᖹ⾮≧ែࡀᚓࡽࢀ࡚࠸࡞࠸ሙྜ㸪ṧᕪຊ࣋ࢡࢺࣝࢆⲴ㔜࣋ࢡࢺࣝ
ࡋ࡚㈇Ⲵࡋ㸪ᗘ㛫ࢫࢸࢵࣉࡢィ⟬ࢆ⾜࠺㸬௨ୖࡢᡭἲࢆ⏝࠸ࡿࡇ࡛㸪」㞧࡞✚ศࢆ⾜࠺ᅇᩘࢆ๐ῶࡋ㸪
ィ⟬ࡢຠ⋡ࢆᅗࡿ㸬࡞࠾㸪Fig. 3 ࡛ࡣ⇕ᙎረᛶゎᯒࡘ࠸࡚♧ࡋࡓࡀ㸪⇕ఏᑟゎᯒ࠾࠸࡚ࡶᘧ(9)㸪(10)ࢆᇶ
ྠᵝࡢᡭ㡰࡛ゎᯒࢆᐇࡍࡿ㸬
Start
㸱㸬ᇶ♏ⓗ⁐᥋ၥ㢟ࡢ㐺⏝ࡼࡿ㛤Ⓨᡭἲࡢ᳨ド
㸱㸬㸯 ゎᯒࣔࢹࣝ࠾ࡼࡧ᮲௳
㛤Ⓨᡭἲࢆ Fig. 4 ♧ࡍᇶ♏ⓗ࡞ࣅ࣮ࢻ࢜ࣥࣉ࣮ࣞࢺၥ㢟
ᑐࡋ࡚㐺⏝ࡋ㸪ᚑ᮶ᡭἲࡼࡿゎᯒẚ㍑ࡍࡿࡇ࡛㸪㛤Ⓨᡭ
ἲࡢ᳨ドࢆ⾜࠺㸬ᮏゎᯒࣔࢹࣝࡣᯈ㛗 100 mm㸪ᯈᖜ 100 mm㸪
ᯈཌ 10mm ࡢᯈᮦࢆᶍᨃࡋ࡚࠾ࡾ㸪⁐᥋⥺ࡣᯈᖜ᪉ྥࡢ୰ኸ⥺
ࢆ௬ᐃࡋ㸪ၥ㢟ࡢᑐ⛠ᛶࡼࡾᯈᖜ᪉ྥ༙ศࡢࡳࢆࣔࢹࣝࡋ
ࡓ㸬⁐᥋᮲௳ࡣ㸪㟁㏻ 120 A㸪㟁ᅽ 10 V㸪⁐᥋㏿ᗘ 4.0 mm/s㸪
⇕ຠ⋡ 0.5 ࢆ௬ᐃࡋࡓ㸬ᖹᯈࡣ㌾㗰ᮦࢆ௬ᐃࡋ㸪Fig. 5 ♧ࡍᮦ
ᩱᐃᩘࡢ ᗘ౫Ꮡᛶࢹ࣮ࢱࢆゎᯒ⏝ࡋࡓ㸬ゎᯒ⏝࠸ࡓせ
⣲ศࢆ Fig. 6 ♧ࡍ㸬ྠᅗ(a)ࡣࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗࡢせ⣲ศ
࡛࠶ࡾ㸪ࡣẚ㍑ⓗ⢒࠸せ⣲ศࢆ⾜࠸ 400 せ⣲ࡋࡓ㸬ࡲࡓ㸪
࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢせ⣲ศࢆྠᅗ(b)♧ࡍ㸬࣮࣓ࣟ࢝ࣝࢵࢩ
ࣗ࠾࠸࡚ࡣ㠀⥺ᙧᣲືࢆゎᯒࡍࡿࡓࡵヲ⣽࡞せ⣲ศࢆ⾜࠸
10,620 せ⣲ࡋࡓ㸬ᚑ᮶ᡭἲࡢゎᯒ⏝࠸ࡓせ⣲ศࡣ Fig. 7
Renew temperature field
Compute [M], [C], [K], {ΔF}
{F} ←{ΔF}, {U} ← 0, t ← 0
Convergence loop
Compute displacement {u}
by explicit FEM
t←t+1
Compute unbalanced force
vector by {F} - [K]{u}
t<N?
No
t←0
{F} ← {R}
{u} ← 0
Yes
{U} ← {U} + {u}
[KGG]
GG
ªK
« LG
¬K
GL
K º
»
K LL ¼
[KGL]
Half
band
width
Compute unbalanced force vector {R}
by RHS of Eq. (25), (26) using {U}
Static equilibrium state?
[KLG]
[KLL]
Zero components
No
Yes
No
Welding finished?
Non-zero components
Yes
Fig. 2 Schematic illustration of non-zero components of
stiffness matrix in mesh overlaying method.
―304―
－304－
End
Fig. 3 Flow of developed method.
10.0
F
A㼿
D
10 mm
A
Torch
Physical constants
8.0
C
B
Density (㼤10-3 g/mm3)
Yielding stress
(㼤102 MPa)
6.0
Specific heat
(㼤10-1 J/g/rC)
2.0
E
0.0
Fig. 4 Bead-on-plate analysis model.
Poisson’s ratio
(㼤10-1)
Heat conductivity
(㼤10-1 J/mm/s/rC)
4.0
Thermal expansion (㼤10-1 /rC)
Young’s modulus (㼤105 MPa)
0.0
300.0
600.0
900.0
Temperature (Υ)
1200.0
1500.0
Fig. 5 Temperature dependent material properties.
((a)) Global
Gl b l mesh.
h
(b) Local me
mesh.
(c) Analysis model.
(overlaid)
Fig. 6 FE mesh divis
Fig
divisions for developed method.
Fig. 7 FE mesh
h di
divisions
ii
ffor existing
i i method.
h d
♧ࡍ㏻ࡾ࡛࠶ࡾ㸪せ⣲ᩘࡣ 11,970 ࡛࠶ࡿ㸬ẚ㍑ᑐ㇟ࡋ࡚㸪⇕ఏᑟゎᯒ㛵ࡋ࡚ࡣ㸪㝜ゎἲ FEM㸪⇕ᙎረᛶ
ゎᯒ㛵ࡋ࡚ࡣ㸪㟼ⓗ㝜ゎἲ FEM ࢆ⏝࠸㸪ࡑࢀࡒࢀࡢᡭἲ࠾࠸࡚㸪㐃❧᪉⛬ᘧࡢồゎࡣࢫ࢝ࣛࣥἲࢆ
⏝࠸ࡓ㸬࡞࠾㸪๓❶࡛♧ࡋࡓ✚ศ᧯సࡼࡾṧᕪ࣋ࢡࢺࣝࢆ⟬ฟࡍࡿ㛫ࢫࢸࢵࣉᩘ N 㛵ࡋ࡚㸪ᮏゎᯒ࡛ࡣ
N = 200 ࡋࡓ㸬⇕ᙎረᛶゎᯒ࠾࠸࡚㸪ṧᕪຊ࣋ࢡࢺࣝࡢ 2 ࣀ࣒ࣝ⠇Ⅼຊ࣋ࢡࢺࣝࡢ 2 ࣀ࣒ࣝࡢẚࡀ
10㸫3 ௨ୗ࡞ࡗࡓሙྜ᮰ࡋࡓࡶࡢࡋࡓ㸬
㸱㸬㸰 ᚑ᮶ᡭἲࡢẚ㍑ࡼࡿ⇕ఏᑟゎᯒࡢ᳨ド
Fig. 8 ᭱㧗฿㐩 ᗘศᕸࢆ♧ࡍ㸬ྠᅗࡼࡾ㸪୧ᡭἲࡼࡿ᭱㧗฿㐩 ᗘศᕸࡀᐃᛶⓗ୍⮴ࡋ࡚࠸ࡿࡇࡀ
☜ㄆ࡛ࡁࡿ㸬ࡲࡓ㸪Fig. 9 ᖹᯈୖ㠃ࡢ⁐᥋⥺୰ኸᶓ᩿㠃࠾ࡅࡿ A-A’⥺ୖࡢ᭱㧗฿㐩 ᗘศᕸࡢẚ㍑ࢆ♧ࡍ㸬
ྠᅗࡼࡾ㸪ᮏᡭἲ㝜ゎἲ FEM ࡢ᭱㧗฿㐩 ᗘศᕸࡣ㸪ᐃ㔞ⓗ୍⮴ࡋ࡚࠸ࡿࡇࡀ☜ㄆ࡛ࡁࡿ㸬≉㸪ࢢࣟ
࣮ࣂ࣓ࣝࢵࢩ࣮࣓ࣗࣟ࢝ࣝࢵࢩࣗࡢቃ⏺࠾࠸࡚ࡶ㸪㐃⥆ⓗ࡞ ᗘศᕸ࡞ࡗ࡚࠸ࡿࡇࡀศࡿ㸬Fig. 10
⁐᥋㛤ጞࡽ 50 ⛊ᚋࡲ࡛ࡢ Fig. 4 ♧ࡍⅬ B㸪C㸪D ࠾ࡅࡿ㐣Ώ ᗘᒚṔࢆ♧ࡍ㸬Fig. 10 ࡼࡾ㸪 ᗘᒚṔ
㛵ࡋ࡚ࡶ㸪㛤Ⓨᡭἲᚑ᮶ᡭἲࡢゎᯒ⤖ᯝࡣࡰ୍⮴ࡋ࡚࠸ࡿࡇࡀศࡿ㸬
㸱㸬㸱 ᚑ᮶ᡭἲࡢẚ㍑ࡼࡿ⇕ᙎረᛶゎᯒࡢ᳨ド
Fig. 11 㛤Ⓨᡭἲᚑ᮶ᡭἲࡼࡿᶓ⦰ศᕸࡢẚ㍑ࢆ♧ࡍ㸬Fig. 11 ࡼࡾ㸪㛤Ⓨᡭἲᚑ᮶ᡭἲࡢᶓ⦰ࡣ
ࡰྠ➼ࡢศᕸࢆ᭷ࡋ࡚࠸ࡿࡇࡀ☜ㄆ࡛ࡁࡿ㸬ྠᵝ㸪Fig. 12 㸪⁐᥋⥺᪉ྥ୰ኸᶓ᩿㠃ୖ࠾ࡅࡿ㠃እ᪉
(rC)
2000.0
1800.0
1600.0
1400.0
1200.0
1000.0
800.0
600.0
y
400.0
200.0
0.0
z
x
(a) Existing method.
(b) Developed method.
Fig. 8 Maximum temperature distribution.
―305―
－305－
2000.0
sfem
Existing method
800.0
A’
A
1200.0
y
800.0
z
x
Boundary ΓGL between
global and local mesh
400.0
B
Temperature (rC)
Temperature (rC)
1600.0
0.0
1000.0
Developedfem
method
A
600.0
10.0
20.0
30.0
40.0
0.0
50.0
-0.02
F
-0.03
-0.04
y
-0.05
z
x
E
E
F
-0.06
-0.07
0.0
20.0
40.0
60.0
80.0
20.0
30.0
40.0
50.0
Fig. 10 Comparison of temperature history.㻌
0.45
H
Angular distortion SA (mm)
Transverse shrinkage ST (mm)
St method
- sfem
Existing
10.0
Time (s)
Developed
method
St - fem
ST
Existing
method
x
0.0
Fig. 9 Comparison of maximum temperature distribution.
-0.01
D
C
200.0
Coordinate in y-direction (mm)
0.00
z
D
B
400.0
A’
0.0
y
C
Developed
method
100.0
0.36
0.27
y
z
H
B’
G
x
0.18
Developed
Sa - method
fem
Samethod
- sfem
Existing
0.09
0.00
Coordinate in x-direction (mm)
G
B
0.0
10.0
20.0
30.0
40.0
50.0
Coordinate in y-direction (mm)
Fig. 12 Comparison of angular distortion distribution.㻌
Fig. 11 Comparison of transverse shrinkage distribution.
(MPa)
400.0
345.0
290.0
235.0
180.0
125.0
70.0
15.0
y
-40.0
-95.0
-150.0
z
x
(a) Existing method.㻌
(b) Developed method.㻌
Fig. 13 Distribution of residual stress in x direction (σx).㻌
600.0
A’
A
A
400.0
Stress (MPa)
ྥࡢኚศᕸࢆ♧ࡍ㸬ྠᅗࡼࡾ㸪㠃እ᪉ྥࡢኚ
㛵ࡋ࡚ࡶ㸪㛤Ⓨᡭἲࡣᚑ᮶ᡭἲࡰྠ➼ࡢ⢭ᗘ࡛
ゎᯒྍ⬟࡛࠶ࡿࡇࡀศࡿ㸬
Fig. 13 x ᪉ྥࡢṧ␃ᛂຊศᕸࢆ♧ࡍ㸬ࡲࡓ㸪Fig.
14 A-A’⥺ୖࡢṧ␃ᛂຊศᕸࡢẚ㍑ࢆ♧ࡍ㸬ࡇࢀ
ࡽࡢᅗࡼࡾ㸪㛤Ⓨᡭἲ㟼ⓗ㝜ゎἲ FEM ࡢゎᯒ⤖
ᯝ༑ศ୍⮴ࡋ࡚࠸ࡿࡇࡀศࡿ㸬≉㸪࣮ࣟ
࣓࢝ࣝࢵࢩࣗࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗࡢቃ⏺㒊࠾
࠸࡚ࡶ㐃⥆ࢆ⏕ࡌࡿࡇ࡞ࡃゎᯒ࡛ࡁ࡚࠸ࡿ㸬
௨ୖࡢ⤖ᯝࡼࡾ㸪ᇶ♏⥅ᡭၥ㢟࠾࠸࡚㸪⇕ఏᑟ
ゎᯒ㸪⇕ᙎረᛶゎᯒࡶ㛤Ⓨᡭἲࡣ㸪ᚑ᮶ᡭἲ࡛
࠶ࡿ㝜ゎἲ FEM ࡰྠ➼ࡢゎᯒ⢭ᗘ࡛࠶ࡿࡇ
ࡀ☜ㄆ࡛ࡁࡓ㸬
y
z
Developed
method
Existing
method
σx
x
Boundary ΓGL between
global and local mesh
200.0
σy
A’
0.0
-200.0
0.0
10.0
20.0
30.0
Coordinate in y-direction (mm)
40.0
Fig. 14 Comparison of residual stress distribution.
―306―
－306－
50.0
㸲㸬」㞧ࣔࢹࣝࡢゎᯒࡢ㐺⏝
㸲㸬㸯 ゎᯒࣔࢹࣝ࠾ࡼࡧ᮲௳
ᮏ❶࡛ࡣ㸪㛤Ⓨᡭἲࡢ」㞧ࣔࢹࣝ࠾ࡅࡿ㐺⏝ᛶ㸪୪ࡧ᭷ຠᛶࢆ☜ㄆࡍࡿࡓࡵ㸪Fig. 15 ♧ࡍࣔࢹࣝࡢ
ゎᯒᑐࡋ࡚㛤Ⓨᡭἲࢆ㐺⏝ࡍࡿ㸬ྠᅗ♧ࡍ㏻ࡾ㸪ᮏゎᯒ࡛ࡣ㸪እᚄ 200 mm㸪ෆᚄ 160 mm㸪㧗ࡉ 500 mm
ࡢࣃࣉ㸪ᖜ㸪㛗ࡉ 1000 mm㸪ཌࡉ 50 mm ࡢ㗰ᯈࡢ⁐᥋ࢆࣔࢹࣝࡋ࡚࠸ࡿ㸬ࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗࡢせ⣲ᩘ㸪
⠇Ⅼᩘࡣࡑࢀࡒࢀ㸪1,440㸪2,379 ࡛࠶ࡾ㸪࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢせ⣲ᩘ㸪⠇Ⅼᩘࡣࡑࢀࡒࢀ㸪47,872㸪41,984 ࡛࠶
ࡿ㸬ࡲࡓ㸪ᮏࣔࢹࣝ࠾࠸࡚ࡣ㸪Fig. 15 (a)♧ࡍࡼ࠺㸪ࣃࣉᯈᮦࡣࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗ࠾࠸࡚ಶู
ࣔࢹࣝࢆసᡂࡋ࡚࠾ࡾ㸪ࣃࣉᯈᮦࢆ᥋ྜࡍࡿ⟠ᡤࢆ࣮࣓ࣟ࢝ࣝࢵࢩࣗ࠾࠸࡚ࣔࢹࣝࡋ࡚࠸ࡿ㸬ࡇࢀ
ࡼࡾ㸪ࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗ࠾࠸࡚ࣔࢹࣝࡉࢀࡓྛ㒊ᮦᑐࡋ࡚㸪࣮࣓ࣟ࢝ࣝࢵࢩࣗ࠾࠸࡚ࣔࢹࣝࡉࢀ
ࡓ᥋ྜ㒊ࢆ㔜ࡡྜࢃࡏࡿࡇ࡛㸪ࡑࢀࡒࢀࡢ㒊ᮦࢆ⤖ྜࡍࡿ㸬࡞࠾㸪ࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗࡢྛ㒊ᮦྠኈࡣ⠇Ⅼ
ࢆඹ᭷ࡋ࡚࠸࡞࠸ࡓࡵ㸪ࡃಶูࡢ㒊ᮦ࡞ࡗ࡚࠸ࡿ㸬࣮࣓ࣟ࢝ࣝࢵࢩࣗ࠾࠸࡚ࡣ㸪Fig. 15 (b)ࡢᩳ⥺㒊♧
ࡍ㏻ࡾ㸪ᯈᮦ࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢቃ⏺㸪ࣃࣉ࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢቃ⏺ࡢኚࢆᣊ᮰ࡋ㸪ࣃࣉࡢෆ㠃
┦ᙜࡍࡿ⠇Ⅼࡣኚࢆᣊ᮰ࡋ࡞࠸ࡇ࡛㸪ᯈᮦ㸪ࣃࣉ࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢኚࡢ㐃⥆ᛶࢆ☜ಖࡋ㸪ࣃࣉ
ࡼࡿᯈᮦࡢ㈏㏻ࢆ⾲⌧ࡍࡿ㸬ࣃࣉᯈᮦࡢᮦ㉁ࡣ㸪㌾㗰ᮦࢆ௬ᐃࡋ㸪Fig. 5 ࡢᮦᩱᐃᩘࢆ⏝࠸ࡓ㸬
Pipe
50 mm
Plate
500 mm
㸲㸬㸰 ゎᯒ⤖ᯝ
Fig. 16 㸪෭༷ᚋࡢ x ᪉ྥࡢኚศᕸࢆ♧ࡍ㸬Fig. 16 ࡼࡾ㸪⁐᥋⥺ᆶ┤᪉ྥ⦰ࡢኚᙧࡀศᕸࡋ࡚࠸
ࡿࡇࡀ☜ㄆ࡛ࡁࡿ㸬ࡲࡓ㸪ᮏゎᯒࣔࢹࣝࡣ㸪ᯈᮦࡢࢢ࣮ࣟࣂ࣓ࣝࢵࢩ࣮࣓ࣗࣟ࢝ࣝࢵࢩࣗࡢቃ⏺㒊࠾࠸
࡚㸪࣓ࢵࢩࣗศࡀ୍⮴ࡋ࡚࠸࡞࠸ࡀ㸪ቃ⏺㒊࠾࠸࡚㸪㐃⥆ⓗ࡞ኚศᕸ࡞ࡗ࡚࠸ࡿࡇࡀศࡿ㸬
ࡇࢀࡣ㸪࣮࣓ࣟ࢝ࣝࢵࢩࣗࡢቃ⏺᮲௳ࡋ࡚㸪ࢢ࣮ࣟࣂ࣓ࣝࢵࢩࣗࡢቃ⏺㒊ᣊ᮰ࢆ࠼ࡓࡇࡼࡿ㸬
ྠᵝ㸪Fig. 17 ෭༷ᚋࡢ z ᪉ྥࡢኚศᕸࢆ♧ࡍ㸬z ᪉ྥࡢኚศᕸ㛵ࡋ࡚ࡣ㸪ゅኚᙧࡼࡾ㸪୰ኸ
㒊ᑐࡋ࡚࿘㎶㒊ࡀᣢࡕୖࡀࡿࡼ࠺࡞ኚᙧ࡞ࡗ࡚࠸ࡿࡇࡀศࡿ㸬ࡲࡓ㸪z ᪉ྥ㛵ࡋ࡚ࡶ㸪ࢢ࣮ࣟࣂࣝ
࣓ࢵࢩ࣮࣓ࣗࣟ࢝ࣝࢵࢩࣗࡢቃ⏺࡛㐃⥆ࡋࡓኚศᕸ࡞ࡗ࡚࠸ࡿ㸬
௨ୖ♧ࡋࡓࡼ࠺㸪⁐᥋⤌❧ࡢࡼ࠺࡞」㞧࡞ࣔࢹࣝࡢゎᯒ࠾࠸࡚㸪㔜ྜ࣓ࢵࢩࣗἲࢆ⏝࠸ࡿࡇ࡛㸪㒊ᮦ
ࡈసᡂࡋࡓࣔࢹࣝᑐࡋ࡚㸪⁐᥋㒊ࡢヲ⣽࡞ࣔࢹࣝࢆ㔜ࡡྜࢃࡏࡿࡇ࡛ゎᯒࣔࢹࣝࢆᵓ⠏ࡍࡿࡇࡀྍ
⬟࡛࠶ࡾ㸪ゎᯒࣔࢹࣝࡢసᡂࢆᖜ⡆␎࡛ࡁࡿྍ⬟ᛶࡀ࠶ࡿࡇࡀศࡗࡓ㸬
Global mesh
Welding
torch
Local mesh
Inner
surface
of pipe
(a) Whole model.㻌
Boundary
between
global and
local mesh
(b) Zoomed view of welding part.㻌
Fig. 15 Welding assembly analysis model.㻌
(mm)
0.10
(mm)
0.50
0.08
0.43
0.06
0.37
0.04
0.31
0.02
0.24
0.00
0.18
-0.02
0.11
-0.04
0.05
-0.06
-0.08
-0.10
y
z
-0.02
-0.09
x
-0.15
Fig. 16 Distribution of displacement in x-direction.㻌
―307―
－307－
y
z
x
Fig. 17 Distribution of displacement in z-direction.㻌
㸳㸬⤖ゝ
ᮏ◊✲࡛ࡣ㸪⁐᥋ຊᏛゎᯒ࠾ࡅࡿゎᯒᡭἲࡢ㧗ᗘࢆ┠ⓗ㸪㔜ྜ࣓ࢵࢩࣗἲࢆ⏝࠸࡚⇕ᙎረᛶゎᯒ㸪⇕
ఏᑟゎᯒࡢᐃᘧࢆ⾜ࡗࡓ㸬㔜ྜ࣓ࢵࢩࣗἲࢆ⏝࠸ࡓ⁐᥋ຊᏛゎᯒᡭἲࡢᵓ⠏ᙜࡓࡾ㸪㔜ྜ࣓ࢵࢩࣗἲࡢ≉
ᛶࡽ㸪ィ⟬㛫㸪࣓ࣔࣜᾘ㈝㔞ࡀ⭾࡞ࡿྍ⬟ᛶࡀ࠶ࡿࡓࡵ㸪ⴭ⪅ࡽࡀ㛤Ⓨࢆ㐍ࡵ࡚࠸ࡿ⌮㝧ゎἲ FEM
ᇶ࡙ࡃᡭἲࢆᑟධࡋࡓ㸬㛤Ⓨᡭἲࡢᛶ㉁ࡘ࠸࡚☜ㄆࡍࡿࡓࡵ㸪ᇶ♏ⓗ࡞ࣅ࣮ࢻ࢜ࣥࣉ࣮ࣞࢺ⁐᥋ၥ㢟ࡢ
ゎᯒᑐࡋ࡚㛤Ⓨᡭἲࢆ㐺⏝ࡋ㸪ᚑ᮶ᡭἲࡼࡿゎࡢẚ㍑ࢆ⾜ࡗࡓ㸬ࡲࡓ㸪㛤Ⓨᡭἲࡢ᭷⏝ᛶࢆ♧ࡍࡓࡵ㸪
ཌᯈࣃࣉࢆ⁐᥋ࡼࡾ⤌❧࡚ࡿၥ㢟ࡢゎᯒᑐࡋ࡚㛤Ⓨᡭἲࢆ㐺⏝ࡋࡓ⤖ᯝ㸪௨ୗࡢ▱ぢࡀᚓࡽࢀࡓ㸬
1) 㛤Ⓨᡭἲࢆࣅ࣮ࢻ࢜ࣥࣉ࣮ࣞࢺ⁐᥋ၥ㢟ࡢ⇕ఏᑟゎᯒᑐࡋ࡚㐺⏝ࡋ㸪㝜ゎἲ FEM ࡢẚ㍑ࢆ⾜ࡗࡓ㸬
ࡑࡢ⤖ᯝ㸪㛤Ⓨᡭἲࡣ ᗘᒚṔ㸪 ᗘศᕸඹ㝜ゎἲ FEM ࡰྠ➼ࡢゎᯒ⢭ᗘ࡛࠶ࡿࡇࢆ☜ㄆࡋࡓ㸬
ࡲࡓ㸪
ࢢ࣮ࣟࣂ࣮࣓ࣝࣟ࢝ࣝࢵࢩࣗࡢቃ⏺㒊࠾࠸࡚ࡶ ᗘศᕸࡀ㐃⥆ⓗ࡞ࡗ࡚࠸ࡿࡇࢆ☜ㄆࡋࡓ㸬
2) ࣅ࣮ࢻ࢜ࣥࣉ࣮ࣞࢺ⁐᥋ၥ㢟ࡢ⇕ᙎረᛶゎᯒᑐࡋ࡚㛤Ⓨᡭἲࢆ㐺⏝ࡋ㸪㟼ⓗ㝜ゎἲ FEM ࡢゎᯒ⤖ᯝ
ࡢẚ㍑ࢆ⾜ࡗࡓ㸬ࡑࡢ⤖ᯝ㸪㛤Ⓨᡭἲࡣኚศᕸ㸪ᛂຊศᕸඹ㟼ⓗ㝜ゎἲ FEM ࡰྠ➼ࡢゎᯒ⢭ᗘ
࡛࠶ࡿࡇࢆ☜ㄆࡋࡓ㸬ࡲࡓ㸪ࢢ࣮ࣟࣂ࣓ࣝࢵࢩ࣮࣓ࣗࣟ࢝ࣝࢵࢩࣗࡢቃ⏺㒊࠾࠸࡚ࡶ㸪ኚ㸪ᛂຊ
ඹ㐃⥆ⓗ࡞ศᕸࡀᚓࡽࢀ࡚࠸ࡿࡇࢆ☜ㄆࡋࡓ㸬
3) ࣃࣉཌᯈࢆ⁐᥋ࡼࡾ⤌❧࡚ࡿၥ㢟࠾࠸࡚㸪ࣃࣉཌᯈࢆಶูࣔࢹࣝࡋ㸪⁐᥋㒊ࢆ⾲ࡍ࣮ࣟ
࣓࢝ࣝࢵࢩࣗࡼࡾࡑࢀࡒࢀࡢ㒊ᮦࢆ⤖ྜࡉࡏࡓゎᯒࣔࢹࣝࢆ⏝࠸࡚㸪㛤Ⓨᡭἲࡼࡾゎᯒࢆᐇࡋࡓ㸬
ࡑࡢ⤖ᯝ㸪㛤Ⓨᡭἲࡣ」ᩘࡢ㒊ᮦࢆ࣮࣓ࣟ࢝ࣝࢵࢩࣗࡼࡾ⤖ྜࡍࡿࡼ࠺࡞ၥ㢟࠾࠸࡚ࡶ⁐᥋ຊᏛゎᯒ
ࢆ⾜࠺ࡇࡀ࡛ࡁ㸪㛤Ⓨᡭἲࡣ」㞧ᵓ㐀≀ࡢࣔࢹࣝᑐࡋ࡚ຠᯝⓗ࡛࠶ࡿࡇࢆ♧ࡋࡓ㸬
ཧ⪃ᩥ⊩
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