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Properties for Design of Composite Structures. Neil McCartney

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Properties for Design of Composite Structures - Neil McCartney

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subscript end fraction plus V subscript text m end text end subscript fraction numerator 4 nu subscript text m end text end subscript left parenthesis alpha subscript text m end text end subscript plus nu subscript text m end text end subscript alpha subscript text m end text end subscript right parenthesis over denominator fraction numerator 1 over denominator k subscript text T end text end subscript superscript text m end text end superscript end fraction plus 1 over mu subscript text m end text end subscript end fraction comma end cell end table"/>(4.170)

      4.9 Results for Two-phase Fibre-reinforced Composites

      For two-phase composites N = 1 so that, on writing Vf1=Vf=1−Vm, κAf(1)=κAf, κTf(1)=κTf, kTf(1)=kTf, μAf(1)=μAf, μtf(1)=μtf, EAf(1)=EAf, ETf(1)=ETf, νAf(1)=νAf, νtf(1)=νtf, αAf(1)=αAf and αTf(1)=αTf, the results of Section 4.8 may be written as

      kappa Subscript upper A Superscript eff Baseline equals upper V Subscript f Baseline kappa Subscript upper A Superscript f Baseline plus upper V Subscript m Baseline kappa Subscript m Baseline comma(4.172)

      StartStartFraction 1 OverOver StartFraction 1 Over k Subscript upper T Superscript eff Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction equals StartStartFraction upper V Subscript f Baseline OverOver StartFraction 1 Over k Subscript upper T Superscript f Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction plus StartStartFraction upper V Subscript m Baseline OverOver StartFraction 1 Over k Subscript upper T Superscript m Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction comma(4.174)

      or StartFraction 1 Over k Subscript upper T Superscript eff Baseline plus mu Subscript m Baseline EndFraction equals StartFraction upper V Subscript f Baseline Over k Subscript upper T Superscript f Baseline plus mu Subscript m Baseline EndFraction plus StartFraction upper V Subscript m Baseline Over k Subscript upper T Superscript m Baseline plus mu Subscript m Baseline EndFraction comma(4.175)

      StartStartFraction nu Subscript upper A Superscript eff Baseline OverOver StartFraction 1 Over k Subscript upper T Superscript eff Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction equals StartStartFraction upper V Subscript f Baseline nu Subscript upper A Superscript f Baseline OverOver StartFraction 1 Over k Subscript upper T Superscript f Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction plus StartStartFraction upper V Subscript m Baseline nu Subscript m Baseline OverOver StartFraction 1 Over k Subscript upper T Superscript m Baseline EndFraction plus StartFraction 1 Over mu Subscript m Baseline EndFraction EndEndFraction comma(4.176)

      StartFraction 1 Over mu Subscript upper A Superscript eff Baseline plus mu Subscript m Baseline EndFraction equals StartFraction upper V Subscript f Baseline Over mu Subscript upper A Superscript f Baseline plus mu Subscript m Baseline EndFraction plus StartFraction upper V Subscript m Baseline Over mu Subscript m Baseline plus mu Subscript m Baseline EndFraction comma(4.177)

      StartFraction 1 Over mu Subscript t Superscript eff Baseline plus mu Subscript m Superscript asterisk Baseline EndFraction equals StartFraction upper V Subscript f Baseline Over mu Subscript t Superscript f Baseline plus mu Subscript m Superscript asterisk Baseline EndFraction plus StartFraction upper V Subscript m Baseline Over mu Subscript m Baseline plus mu Subscript m Superscript asterisk Baseline EndFraction with mu Subscript m Superscript asterisk Baseline equals StartFraction k Subscript upper T Superscript m Baseline mu Subscript m Baseline Over k Subscript upper T Superscript m Baseline plus 2 mu Subscript m Baseline EndFraction comma(4.178)

      upper E Subscript upper A Superscript eff Baseline plus StartFraction 4 k Subscript upper T Superscript eff Baseline left-parenthesis nu Subscript upper A Superscript eff Baseline right-parenthesis squared mu Subscript m Baseline Over k Subscript upper T Superscript eff Baseline plus mu Subscript m Baseline EndFraction equals upper V Subscript f Baseline left-parenthesis upper E Subscript upper A Superscript f Baseline plus StartFraction 4 k Subscript upper T Superscript f Baseline left-parenthesis nu Subscript upper A Superscript f Baseline right-parenthesis squared mu Subscript m Baseline Over k Subscript upper T Superscript f Baseline plus mu Subscript m Baseline EndFraction right-parenthesis plus upper V Subscript m Baseline left-parenthesis upper E Subscript m Baseline plus StartFraction 4 k Subscript upper T Superscript m Baseline nu Subscript m Superscript 2 Baseline mu Subscript m Baseline Over k Subscript upper T Superscript m Baseline plus mu Subscript m Baseline EndFraction right-parenthesis comma(4.179)

      StartFraction 1 Over upper E Subscript upper T Superscript eff Baseline EndFraction equals StartFraction 1 Over 4 mu Subscript t Superscript eff Baseline EndFraction plus StartFraction 1 Over 4 k Subscript upper T Superscript eff Baseline EndFraction plus StartFraction left-parenthesis nu Subscript upper A Superscript eff Baseline right-parenthesis squared Over upper E Subscript upper A Superscript eff Baseline EndFraction comma StartFraction nu Subscript t Superscript eff Baseline Over upper E Subscript upper T Superscript eff Baseline EndFraction equals StartFraction 1 Over 4 mu Subscript t Superscript eff Baseline EndFraction minus StartFraction 1 Over 4 k Subscript upper T Superscript eff Baseline EndFraction minus StartFraction 4 left-parenthesis nu Subscript upper A Superscript eff Baseline right-parenthesis squared Over upper E Subscript upper A Superscript eff Baseline EndFraction comma(4.180)

      table attributes columnalign left end attributes row cell E subscript text A end text end subscript superscript text eff end text end superscript alpha subscript text A end text end subscript superscript text eff end <noindex><p style= Скачать книгу


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