Plate Equations And Formulas for Stresses Strains And Displacements
Plate Equations And Formulas for Stresses Strains And Displacements
Chester B Sensenig
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7) y/he ^^I'O 1 7272^ - ^ =3^ . 5£, ^B3, . -^ (S, m^ . . , m^) e D ^32=(:!^t ^^-2-^ + ^ (8^+62)^31-^ ^ ^32+ "7= (">i^l+"^2^2) 9 D h/h ^l-'^2 /h (^^2^] ^ ^(e^^32) 31 ^ e/h D ^ ^1 31 1 32 1 ^ £, +£ £^ - + M„ ^ ) /IT 2 /h B-^9=(9[ ^^ + ^ A32+ (£^+£2)^3^+ 6^632+ ^ ^ (M, +MJ] 32 e/h D /h 1 2' A-, and B-, can be eliminated from the right-hand sides of the 3oj 3a) ^ above equations when is sufficiently small, just as when k = 2, to obtain (3. 14) y/h e \i/h € A. N^ {9 [ ' 9"^ + -^ (e„m +£ m„)+ -^ ^ M.... + -^ M„] ^1 ^ e^D^ h/h ^ ^ ^ ^ /h ^ /h 2 ■^^ t e D ■^-^ '^ e/h D h 2- + — I ^ (m^+m2) + M^ + M2 ] /h GD 80 2 2 — 6 D [M (e +£2) '•■'^2^1^ "^ ~2 (rti-ie2+ "^2^1^ h"/h eD i/h D h/E (£^^+£2) [M^+ M2+ -^ (m^+m2)] }■ • -45- From the last line of (3. 3) 2 ^ Co I t I = /^^ (A^ + -^ II t 11 . + -^-^ B^ ) 9D 3' to' L^ 3co ^2^2 co 3 ^2^2 3oj /h 6 e D Since Iltjl3 =6?(IUitJl3) = 6^ (" ^^tjl^) =^ (A^J =^(y/h e^), we have •^ ^ I Z 1 /^ / y/h -, ,, h n > 9D ^3' w' "^ q2_2 oj 3co q2_^2 3to SO that /O, ^^0) ^ 60 ^ ^ h/h „ .
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