Computational Mechanics of Composite Materials Part 1 ppsx

... )()( SXPSPP ⊂== (1. 73) Contents 1 Mathematical Preliminaries 1 1. 1 Probability Theory Elements 1 1. 1 .1 Introduction 1 1. 1.2 Gaussian and Quasi-Gaussian Random Variables 7 1. 2 Monte Carlo ... processing I. Title 620′.0 015 18 ISBN 18 52334274 Library of Congress Cataloging-in-Publication Data Kamin ´ ski, M. M. (Marcin M.), 19 69– Computational mechanics...

Ngày tải lên: 10/08/2014, 11:22

... Preliminaries 15 () [] 2 2 2 1 2 1 1 exp yyx +−= (1. 83) 1 2 2 2 1 y y arctgx ⋅= π (1. 84) with the Jacobian determinant of the form () )(exp ),( ),( 2 2 2 1 2 1 2 1 21 21 2 2 1 2 2 1 1 1 yy yy xx y x y x y x y x +−−== π ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ (1. 85) ... 2.6). There holds [] [] ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −= Ω tc SE S eEeE c1 1 1][ 11 (2.42) and [] [] [] [] [] [] [] 1...

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... 0 .10 0 .10 2 0 .10 0.05 3 0.05 0 .10 4 0.05 0.05 46 Computational Mechanics of Composite Materials 0 0.05 0 .1 0 .15 0.2 0.25 0.3 0.35 4.00E-03 6.00E-03 8.00E-03 1. 00E-02 1. 20E-02 1. 40E-02 1. 60E-02 ... present version of computer program includes only the first two components, which correspond with expected values of displacement functions. 1 1.05 1. 1 1. 1...

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... Materials ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = 11 4 411 4 311 4 211 41 113 411 3 311 3 211 31 112 411 2 311 2 211 21 111 411 1 311 1 211 11 11 DDDD DDDD DDDD DDDD D (A3 .15 ) then () 11 11 11 11 2 22 1 lk k k D + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −−= µ µ () () ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ −−+− −+−+−+− × 21 2 21 2 21 2 21 2 211 22 211 )()( )()()(2)(2 llkk kkkklkkl µµ µµ (A3 .16 ) ... + ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +−= µ...

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... 7.4 /1. 94 8.4 /1. 94 8.9/2.06 3 8 10 .1/ 2 .19 10 .9/2 .19 11 .0/2. 31 4 16 14 .1/ 2.62 14 .9/2.62 17 .3/2.69 5 32 20.7/3.25 25.7/3. 31 31. 8/3.44 6 64 53.0/4.56 53.7/4.56 70.5/4.94 7 12 8 13 1.0/7.06 13 0.7/7.06 ... he periodic composites. Comput. Mat. Sci. 22(3-4):2 21- 239. 95. of curved layered composites. Comput. & Struct. 81( 18 -19 ) :18 65 -18 73. 376 Compu...

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... variation () )( )( 11 11 ωα eff C in test 1 Figure 2 .11 3. Coefficients of variation () )( )( 11 11 ωα eff C in test 2 Figure 2 .11 4. Coefficients of variation () )( )( 11 11 ωα eff C in test ... decrease of () )( )( 11 11 ωα eff C and () )( )( 11 22 ωα eff C ; 12 2 Computational Mechanics of Composite Materials Figure 2 .10 6. Expected values [] )( )(...

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... () Ω ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ν−ν+ ν− = Ω= βα = Ω ν− ν− ν− ν = Ω βααβ ∑ ∫ ∑ ∫ dBB symm ))(( e dBBCK klij E e e )( E e e klijijkl 1 12 21 1 1 00 01 01 211 1 (2.206) () Ω ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎣ ⎡ ν−ν+ ν− = Ω= βα = Ω ν− ν− ν− ν = Ω βααβ ∑ ∫ ∑ ∫ dBB symm ))(( dBBCK klij E e e )( E e e klij r, ijkl r, 1 12 21 1 1 01 01 211 1 (2.207) ... GPa 0.0905 () [] 12 12 inf CE 13 .13 GPa 13...

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... () {}{}() {}{}() ∫ ∫ ∫∫ Ω Ω ΩΩ Ω++++ Ω+++= Ω+++=Ω= dCCCC dCCCC ddG effeffeffeff effeffeffeff ijij 2222 )( 2222 11 )( 2 211 211 2 )( 211 2 21 )( 212 1 2 1 12 21 )( 12 21 12 )( 12 12 11 22 )( 11 22 11 )( 11 11 2 1 2222 212 112 1 211 11 2 1 2 1 εεεεεε εεεεεε εσεσεσεσεσ (4 .17 ) The strain state relevant ... effective parameter e (eff) with respect to the modulus of...

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... ()() ()() 11 11 12 21 12 21 +++ +−+ = κκ κκ α GG GG and ()() ()() 11 11 12 21 12 21 +++ −−− = κκ κκ β GG GG (5. 61) Then, it is possible to rewrite (5.58) in the following way: ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + − ∈= β β π 1 1 ln 2 1 (5.62) ... approaches (A5.8) (A5 .11 ), crack opening displacement (COD) based approaches (A5 .12 ), (A5 .15 ) (A5 .17 ), (A5 .19 ) and (A5.20), continuous 2...

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... ) sr rss rrs rs s rrs rss r rs rss rrs bbCov SSSY YYXX XXXX f , 11 2 11 1 2 11 1 2 11 1 2 1 ; , 2 12 2 , 2 12 , 2 2 12 , 2 , 2 1 2 , 2 1 , 2 2 1 , 2 , 21 2 , 21 , 2 21 , 2 , 2 1 2 , 2 1 , 2 2 1 , 2 )2( ⎪ ⎭ ⎪ ⎬ ⎫ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ++ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ +− ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎪ ⎩ ⎪ ⎨ ⎧ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −+ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = τττσ σσσσσσ σσσσσ σ X...

Ngày tải lên: 10/08/2014, 11:22