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Nonlinear%20Finite%20Element%20Procedures%20II

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8- (Constitutive Relations) 2-8- (Elastic Material Behaviour) : ... – PowerPoint PPT presentation

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Title: Nonlinear%20Finite%20Element%20Procedures%20II


1
(No Transcript)
2
??? ????? ????? ?????? II Nonlinear Finite
Element Procedures II
???? ?????
3
??? ??? ????? ?????? ????? ????? (??? ???)
4
8- ?????? ????? ????? (Constitutive
Relations) 1-8- ?????
?? ??? ???? ????? ????? ?? ????? ????????
?????? ???????? ??? ???? (????????? ?? ? ????? ??
? ???? ??? ????) ?? ?? ?????? ?????? ????? ????.
?? ????? ???? ??? ??????? ???????? ?? ????? ????
??? ?????? ????? ????? ?? ?????. ???? ????
??????? ??? ?? ???? ????? ????? ???? ?? ???? ????
?? ??? ???? ??? ???? (Special Response) ????
?????? ????? ???? ??? ?? ?? ??????? ????? ??????
??????? ???(Appropriate constitutive description).
5
8- ?????? ????? ????? (Constitutive
Relations) 1-8- ?????
- ???? ??? ?? ??????? ????? ????? ?????
???? ?? ??? ????? ?? ?????
?????? ??? ????????? (????? ????????)
(H)
?????? ????? ????? (????? ?????) (C)
???????? ???? ????? ?? ????? ???? ???? ???
???? ???? ???? ???? ?????? ????? ????? ???? ?????
???????? ? ????? ?????? ???. ?? ????? ???? ???
???? ?? ????? ???? TL ???? ????? ????? ????????
?? ???? ?? ???? ?? ??? ?? ???. ?? ????? ?????
???? ??????? ???? ?? ???? ?? ???? ???? ????? ????
??? ???? ????? ???? ??? ???. ?? ??? ????? ?????
?? ????? ???? ???? ??? ???? ?? ??? ?????? ??? ??
????? ???? ???????? TL ???? ??? ???? ?? ?? ?????.
6
8- ?????? ????? ????? (Constitutive
Relations) 1-8- ?????
- ??? ?? ??? ???? ????? ???? ???? ?????? ??
?????? ?? ?????? ?????? ????? ?? ????? ??????
????? ????? ???. ?? ??? ??? ??? ????? ?? ?? ???
?? ??? ?????? ?? ?? ???? ?????? ????? ??????? ??

??? ????? ??????? (Linear Elastic)
???? ????? ????????? ??? ????? ????? ???
???? ? ???? ??? ????
??? ????? ????????????? (Elasto-plastic)
- ???? ????? ?????? ??? ????? ( ?????????
?? ? ????? ??? ????)?
- ???? ????? ????????? ??? ????? ????? ???
???? ? ???? ??? ???? ?? ???? ??? ???????.
???? ??????? ????? ??? ??? ????? ???? ?????
?? ?? ???? ???? ??? ?????? ?? ???? ?? ??? ???????
??? ????? ????? ??? ???. ????? ?? ??? ??? ?????
?? ??? ? ????? ?? ???? ?? ??? ??? ????? ??????? ?
????????????? ?????? ??????.
7
8- ?????? ????? ????? (Constitutive
Relations) 2-8- ????? ??????? ?????(Elastic
Material Behaviour) ???? 1- ????????? ??? ????
2- ????? ??? ???? 3- ???? ??? ???? ??????? ???
???) ????? ???? TL - ?? ????? ????
????? ??????? ?? ?? ??? ?????? ?? ???? ?????
???????? ??? ???? ?? ??? ?? ???? ?? ???? ?????
???? ????? ??????? ??? ?? ?? ????? ??? ????
??????? ???? ?? ???? ?? ????? ???? TL? ?? ??? ??
???
? ????? ??? ?????? ??? ???
Piola-Kirchhoff ? ???? Green-Lagrange ?? ????? ?
????? ??? ?????? ???? ???????(Constant
Elasticity Tensor) ?????.
?? ?? ??? ????? ????? ??? ?? ???? ?????
???? ??? ?? ????? ??? ?????? ???????
?? ?????? ????? ??? ?? ???? ???? (?????? ???
????? ????? ???-???? ???? ????? ??????????) ?????
???
8
8- ?????? ????? ????? (Constitutive
Relations) 2-8- ????? ??????? ?????(Elastic
Material Behaviour) ???? 1- ????????? ??? ????
2- ????? ??? ???? 3- ???? ??? ???? ??????? ???
- ?? ?????? ??? ????? ?????? ?? ???? ?? ???
???? ??? ????? ???
???) ?? ????? ????????? ??? ?? ????? ?????
????? ?? ???? ?????
???? ??????? ?? ????? ??????? ??? ?? ?? ???? ????
??? ??? ?????? ???????? ??? ? ???? ?? ????????
??? ? ???? ?????? ????? ?? ????. ?) ??
????? ????????? ?? ? ????? ??? ???? ? ???? ???
????? ????? ???? ?? ????? ????? ?????(Natural
Material Description) ?? ????? ?? ????? ????
????? ??? ????????? ??? ??? Piola-Kirchhoff ?
???? Green-Lagrange ?? ??? ????? ??? ??? ????
????? ??? ????. ????????? ???? ?????? ?? ?????
??? ??? ???? ??? ????? ???? ?? ?????? ????? ???
?????? ??? ?????? ?? ?????. ?) ??
????? ?????? ?? ?? ???? ????? ????????? ??? ??
????? ???? ?? ??????? ?? ???????? ??? ? ????
?????? ??? ????? ???? ?? ???? ???????? ?? ?????
????????? ?? ? ????? ??? ????? ??? ???? ??? ????
?? ??? ???? ?? ??? ??? ?? ?? ????? ??? ???
Piola-Kirchhoff ? ????? ???? Green-Lagrange
??????? ???.
??? ???? ????? ??? ??? ???? ?? ??? ?????
Hooke ???? ???? ???? ??? ???? ???? ????? ??? ???
????? ????? ????? ?????? ???? ???? ?? ?? ???? ??
????? ????????? ??? ????? ????? ??? ???? ??? ????
??? ???? ????? ?????. ?? ????? ????? ????? ?????
???????? ????? ???? ??? ???? ???? ? ????? ??.
9
8- ?????? ????? ????? (Constitutive
Relations) 2-8- ????? ??????? ?????(Elastic
Material Behaviour) ???? 1- ????????? ??? ????
2- ????? ??? ???? 3- ???? ??? ???? ??????? ???
?) ????? ???? UL - ?? ????? ???-????
???? ??? ?? ?? ???
???? ??? ?? ??? ?? ?? ????? ???? TL ???? ?????
?????? ?? ??? ?? ???. ??? ??? ?? ???? ?? ??
?????? ?? ?? ????? ???? UL ??? ?? ??????? ?? ????
????? ????? ??????? ??????. ?? ??? ???? ??????
????
???????? ??? ?? ?????? ????? ???? ?? ?????
????
10
8- ?????? ????? ????? (Constitutive
Relations) 2-8- ????? ??????? ?????(Elastic
Material Behaviour) ???? 1- ????????? ??? ????
2- ????? ??? ???? 3- ???? ??? ???? ??????? ???
?? ???? ?? ???? ????? (6.192) ? (6.193) ?
(6.194) ?? ???? ????? ?????? ???? Almansi ?????
????.
11
8- ?????? ????? ????? (Constitutive
Relations) 2-8- ????? ??????? ?????(Elastic
Material Behaviour) ???? 1- ????????? ??? ????
2- ????? ??? ???? 3- ???? ??? ???? ??????? ???
????? ??? ?? ???? ?? ????? ???? UL ?? ?? ??? ???
?? ???? ???? ??? ???? ?? ????????? TL ?? ?? ???
?? ??? ?? ??? ??? ??

12
8- ?????? ????? ????? (Constitutive
Relations) 2-8- ????? ??????? ?????(Elastic
Material Behaviour) ???? 1- ????????? ??? ????
2- ????? ??? ???? 3- ???? ??? ???? ??????? ???
13
8- ?????? ????? ????? (Constitutive
Relations) 2-8- ????? ??????? ?????(Elastic
Material Behaviour) ???? 1- ????????? ??? ????
2- ????? ??? ???? 3- ???? ??? ???? ??????? ???
14
8- ?????? ????? ????? (Constitutive
Relations) 3-8- ????? ?????????? ?????(Inelastic
Material Behaviour) ? ????????????????
  • ???) ?????
  • ?? ???? ?????? ?? ?? ?????? ????? ??????? ? ?????
    ??? ??????? ?????? ?? ??? ??? ??? ?? ?? ??? ??
    ??????? ?? ??? ?? ?? ???? ?? ?????? ?? ?? ????
    ????? ????? ???? ???? ?? ??????
  • ?? ???? ?? ?? ?????? ???? ??? ???????? ?? ??? ??
    ???? t ?? ??????? ??? ? ???? ????? ????.
  • ?? ????? ???? ???? ??? ??????? ?????? ?? ?? ???
    ???????? ? ?? ??? ?? ?? ?? ??? ?????? ?????
    ?????? ??

15
8- ?????? ????? ????? (Constitutive
Relations) 3-8- ????? ?????????? ?????(Inelastic
Material Behaviour) ? ????????????????
1) ????? ????????? ?? ? ????? ??? ???? ?
???? ??? ???? ??? ??????? ?? ????? ?????? ???
????? (Materially nonlinear-only Analysis)
- ?? ??? ???? ?? ?? ????? ???? ?????? ??? ?????
??????? ?? ??? ?? ?? ?? ????????? ?? ? ????? ???
??????? ???? ??? ?? ???? ? ????? ?????? ??? ?????
?? ??? ????? ?? ????. - ?? ?????? ?? ?????
??????? ????? ??? ??? ?? ?? ??? ????? ????
??????? ?? ???? ?? ??? ?? ??????? ??? ???? ??? ??
????? ??? ????? ???.
-
???????? ??? ? ???? ???? ??????? ???????? ??? ?
???? ?????? ?????.
- ?????? ????? ???? ???????
16
8- ?????? ????? ????? (Constitutive
Relations) 3-8- ????? ?????????? ?????(Inelastic
Material Behaviour) ? ????????????????
2) ????? ????????? ?? ? ????? ??? ???? ???
???? ??? ???? ??? ??????? - ?? ??? ????
????? ???? ???????? ??? (TL) ?? ?????? ??????
???? ?? ???. - ?? ??? ????? ????? ?? ???
???? ??? ???? ??? ???????? ??? ????? ???? ???????
???? ????? ?????? ??? ????? ?? ?? ???? ????????
?? ????? ???? TL ???? ????? ????????? ?? ? ?????
??? ???? ?? ???????? ??? ??? ??? Piola-Kirchhoff
? ???? ??? ???? ??? Green-Lagrange ?? ???
???????? ??? ? ???? ?????? ?? ????? ????????? ??
? ????? ??? ???? ???? ???. - ????????
?????? ????? ???? TL ?? ????? ??? ??????? ???
?????? ??????? ?? ????? ???? TL ?? ????? ???????
????????? ?? ? ????? ??? ???? ??? ???? ??? ????
???.
?????? ????? ???? ???????
17
8- ?????? ????? ????? (Constitutive
Relations) 3-8- ????? ?????????? ?????(Inelastic
Material Behaviour) ? ????????????????
3) ????? ????????? ?? ? ????? ??? ???? ?
???? ??? ???? ??? ??????? - ?? ??? ????
????? ???? ???????? ??? (TL) ? ?? ????? ??? (UL)
?? ?? ???? ?? ?????? ?????? ???? ?? ???.
- ??? ????? ???? ??? ????? ????? ?????? ??
?????. ???? ???? ???? ????? ?? ???? ?? ???? ???
???? ????? ???? ??? ???? ???? ??? ???? ?????.
18
8- ?????? ????? ????? (Constitutive
Relations) 3-8- ????? ?????????? ?????(Inelastic
Material Behaviour) ? ????????????????
?? ????? ??? ?? ???? ?? ?????? ????? ?????? ?????
???? ??? ?? ?????? ?? ?? ????? ???? ??? ??? ?????
????? ???? ??? ? ????? ???? ????. ???? ???? ???
?????? ?? ?? ???? ???? ?? ???.
19
8- ?????? ????? ????? (Constitutive
Relations) 3-8- ????? ?????????? ?????(Inelastic
Material Behaviour) ? ????????????????
???) ????? ??? ?? ??? ???
?? ??? ?? ?? ?? ???? ??????? ???? ?? ?????
1) ?????? ???????? ?????? ???? ????
2) ????? ?????? ???? ????? ??????
????? ?????? ??? ?????
????? TL
????? TL
?????? ??? ??? ??? Piola-Kirchhoff
????? ??? ??? ??? Piola-Kirchhoff
????? UL
????? UL
?????? ??? ??? Cauchy
????? ??? ??? Cauchy
20
8- ?????? ????? ????? (Constitutive
Relations) 3-8- ????? ?????????? ?????(Inelastic
Material Behaviour) ? ????????????????
1) ?????? ?????? ??? ???? ???? ???
????? ?????? ??? ?????
????? TL
????? UL
???? ???? ????? ?? ??????? ???? ????? ???
(i-1) ?? ?? ????? ???? ?? ???? ????? ???. ???
??????? ???? ?? ?? ???? ?? ???????? ?????? ?????
??? ?????.
21
8- ?????? ????? ????? (Constitutive
Relations) 3-8- ????? ?????????? ?????(Inelastic
Material Behaviour) ? ????????????????
22
8- ?????? ????? ????? (Constitutive
Relations) 3-8- ????? ?????????? ?????(Inelastic
Material Behaviour) ? ????????????????
  • ?? ????? ???? ?????? ??? ???? ? ????? ????? ???
    ?? ? ?????? ??? ????? ???- ???? ?? ?? ????
    ??????? ???? ????? ????? ?? ????. ?????????
    ??????? ????? ???? ??? ??????? ?? ?????? ?????
    ????.
  • ?? ????? ??? ???????? ?? ?????? ??????? ???? ??
    ???? ????? ?? ???? t ?? ???? t?t ???? ???? ????
    ??? ?? ????? ??????? ??????? ???? ??? ?? ????
    ????. ???? ?? ????? ??????? ?? ????? ???? ????
    ??????? ?? ???.
  • ?? ????? ?????? ??? ?????? ?????? ???-???? ?????
    ?? ????? ??? ????? ?? ???

23
8- ?????? ????? ????? (Constitutive
Relations) 3-8- ????? ?????????? ?????(Inelastic
Material Behaviour) ? ????????????????
?? ???? ?? ???? ????????? ????- ???? ????
??? ??????? ( ?? ??????? ?? TL) ?? ???? ???
???????? ??????? ?? ??? ???? ???? ??? ??? ???
????? ???? ?? ??? ??? ?? ??? ???? ???? ?????
????????? ?? ? ????? ??? ???? ????? ??? ???? ???
??????? ?? ????? ?? ?????.
(Materially-Nonlinear-Only-Analysis)
???? ???? ???? ?? ??? ?? ????? ????? ????
???????? ??? ?? ????? ????????? ?? ? ????? ???
???? ? ???? ??? ???? ??? ??????? ?? ?? ???? ??
??? ???? ????? ???? ?????? ??? ????? ???? ????
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