4 Mindlin -Reissner 4 δ T T T εσdω= δ ubdω+ δ utd Γ Ω Ω Γ T εσ (1.1) ε σ u b t 3 σ ε. u T T T = = = { σx σ y σ z τxy τ yz τzx} { εx εy εz γ xy γ yz γ

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1 Mindlin -Rissnr δ εσd δ ubd+ δ utd Γ Γ εσ (.) ε σ u b t σ ε. u { σ σ σ z τ τ z τz} { ε ε εz γ γ z γ z} { u u uz} { b b bz} b t { t t tz}. ε u u u u z u u u z u u z ε (.) z z z (.) u u NU (.) N U (.) ε BU (.) (.)(.)(.) ( ) + B δ U σ d δ U N bd δ U N td Γ (.) Γ (.) ( σ + σ) ( + ) + ( + ) B σ σ d N b b d N t t dγ (.) Γ

2 0 (.) B d f b + f t + R 0 σ (.) fb, ft R 0 fb N bd t Γ f N tdγ (.) σ R N b d+ N t dγ B σ d Γ (.) σ D ε DB U (.) σ ε D (.)(.)(.) U f + f + R (.5) d b t 0 B DB (.6). (.) u { u u} u NU (.) N 0 N, N N N N N 0 N [ ] (.) U u, u u { u u u u } { u u u u } u N ( ξ )( η), N ( + ξ )( η ), N ( + ξ )( + η), N ( ξ )( + η) (.)

3 u ε u ε γ u u + (.) (.) 0 ε u 0 B U ε γ u (.5) η η ξ ξ ξ o η. N, N (.6) { }, { } (.7), ξ ξ ξ J (.8) η η η ξ η J (.9)

4 (.5) J J ξ ξ η ξ J, J J η η η ξ (.0) J (.) ξ η ξ η J J (.) ( η) ( η) ( + η) ( + η) ξ ( ξ) ( + ξ) ( + ξ) ( ξ) η (.) ξ J η (.6)(.5) B DB d 0 0 D D D D D D d d 0 D D D 0 (.) (.) D + D + D + D D + D + D + D D + D + D + D (.5) D ν 0 E D ν 0 ν (.6) 0 0 ( ν ) (.)

5 n n p q ( ξ, η ) ( ξ, η ) tb p q DB p q J wpwq (.7) t n ξ, η ξ, η w, w p q ξ η ξ η w w (.) D D D p q (.8) D D D u σ 0 DB U (.9) D D D u 0 5. z w Mindlin-Rissnr u, u, uz u zθ(, ), u zθ(, ), uz w (, ) (5.) w z θ, θ, z u z u u 5. (.) 5

6 u θ ε z u θ ε z u u θ θ γ + z u u z w γ z + θ z u uz w γ z + + θ z 5. ξ, η w ϕ, ϕ (5.) w Nw, θ N θ, θ N θ (5.) N w θ θ [ N N N N] { w w w w} { θ θ θ θ } { θ θ θ θ } N ( ξ )( η), N ( + ξ )( η ), N ( + ξ )( + η), N ( ξ )( + η) (5.5) (5.) η η ξ ξ ξ o η 5. (5.), N, N (5.6) 6

7 { }, { } (5.7) N ( ξ )( η), N ( + ξ )( η ), N ( + ξ )( + η), N ( ξ )( + η) (5.8), ξ ξ ξ J (5.9) η η η ξ η J (5.0) (5.7) J J ξ ξ η ξ J, J J η η η ξ (5.) J (5.) ξ η ξ η J J (5.8) ( η) ( η) ( + η) ( + η) ξ ( ξ) ( + ξ) ( + ξ) ( ξ) η (5.) ξ J η (5.) (5.)(5.) 0 0 ε w γ N 0 z w ε z 0 0 θ B U, θ B U γ z γ N θ 0 N θ 0 b s (5.5) (.8) 7

8 b b b s s s b s B DBd B D B d+ B D B d + (5.6) b b b D D D b b b b b b z 0 D D D d z 0 0 b b b 0 d b D b D D 0 N N 0 0 s s s s s D 0 N 0 s s s N 0 d s d 0 D N s s 0 N s 0 N b b b b b b b b b b b b b b b D + D + D + D D + D + D + D D D D D s s s s s D s s s D + D s s D N s s D N D N N 0 N N b s D, D (5.7) (5.8) (5.9) (5.0) ν 0 b E s 0 D ν 0, κg ν D 0 (5.) 0 0 ( ν ) κ Rissnr κ 5/6Mindlin κ π / 8

9 shar locing b t [ t/, t/] z, t B D B J (5.) b b b b ( ξp, ηq) ( ξp, ηq) ww p q p q 0 γ z γ z γ z γ z s s s D D N 0 s s D 0 D N s s s D D d N N N 0 + d s s DN 0 DN N d d s s + (5.) ( ξ, η ) ( ξ, η ) s s s t p q wpwq + t p q wpwq p q p q J J (5.) (5.)(5.) ξ η ξ η w w ξ η 0, w 0 0 σ D D D w b b b b b b b b b σ zd D D 0 0 θ D B U b b b τ D D D θ σ 0 τ D 0 N 0 w σ s s z s s s θ DB U τ z 0 D 0 N θ (5.5) (5.6) (5.7) 9

10 (.7)(5.),(5.) U { u u uz θ θ θz u u u θ θ θz u u uz θ θ θz u u uz θ θ θz} z Ziniwicz M z θ z M z θ z t α EtA θz (6.) M θ z z M z θ z 7.,, z z,,, z (,, z) {,, z} (,, ) z {,, z} L (7.) l l lz L L l l lz L lz lz l zz L (7.) L ( l, l, lz ) (,, z) ( l, l, lz ),( lz, lz, lzz ) (7.) cos(, ) cos(, ) cos(, z) L cos(, ) cos(, ) cos(, z) (7.) cos(,) z cos(,) z cos(,) z z (, ) i j i j 0

11 z z 7. ( + ) ( + ) ( + ) ( + ) c c c c c c c c ( + ), ( + ), ( + ), ( + ) c c c z z z c z ( z + z) ( z + z) ( z + z) ( z + z) L A (7.) L A / A (7.5) {( ) ( ) ( z z )} c c c c c c c c c c c c ( ) ( ) ( z z ) A + + z L z (7.6) L A B/S z {( ) ( ) ( )} A B B A A B B A A B B A /S B {( ) ( ) ( z z )} c c c c c c ( ) ( ) ( ) + + S A B B A A B B A A B B A (7.7) (7.8) A, A, A B, B, B AB, L L L L z {( Lz L L Lz) ( Lz L L Lz) ( Lz L L Lz) } (7.9) (7.) L

12 ( c, c, c ) c c c c ( ) ( ) ( ) ( ) c c c c ( ) ( ) ( ) ( ) c c c c ( z z ) ( z z ) ( z z ) ( z z ) L (7.0) z ( ) c c ( ) (7.) c z ( z + z + z + z) (7.) L L L L L L L L (7.) (7.)(7.) von Miss f σ (8.) σ σ σ σ σ + σ + τ (8.) (8.) f c

13 D p p p D D D (8.) D D p S SYM. S SYM. D D (8.) E p SS S ν, ν S S 0 0 ( ν ) SS 6 SS 6 S 6 S S S S E ( σ + νσ ), S E ( νσ + σ ), S E τ Gτ ν ν + ν 6 (8.5) σ + σ σ + σ σ, σ σ σ (8.6) E ν G (8.) c D D p f c r min Nwton-Raphson Nwton-Raphson F F λf (8.7) λ /00/000 K U F (8.8) K U (8.8) U σ, σ, τ (8.)σ σ ( σ ma ) λ L c λl (8.9) σ λ L ma λ λ λ, U λ U, σ λ σ (8.0) L L L K U F (8.) p(0) (0) K p (.) K p, U Nwton-Raphson

14 (8.) U (0) (.) K p (0) (0) σ σ + σ (8.) (8.) ( λ λ) R + F B σ d (8.) (0) (0) R (0) 0 B (8.) D p D p (8.)(8.) U (0) σ (0) σ σ + σ (8.) (0) (0) ( λ λ) R (0) R + F B σ d (8.5) (0) (0) Nwton-Raphson 0 Nwton-Raphson p() () (0) K U R (8.6) (8.6) U () D p R n n n ( ) ( ), σ σ,, σ σ σ 0 0 U U σ σ U U + U σ σ + σ (8.7) (8.)(8.7) i λ i (8.) Nwton-Raphson 0 00

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微分積分サンプルページこの本の定価判型などは, 以下の URL からご覧いただけます. このサンプルページの内容は, 初版 1 刷発行時のものです. 微分積分サンプルページこの本の定価判型などは, 以下の URL からご覧いただけます. ttp://www.morikita.co.jp/books/mid/00571 このサンプルページの内容は, 初版 1 刷発行時のものです. i ii 014 10 iii [note] 1 3 iv 4 5 3 6 4 x 0 sin x x 1 5 6 z = f(x, y) 1 y = f(x)