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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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end superscript plus fraction numerator 4 nu subscript text A end text end subscript superscript text eff end text end superscript left parenthesis alpha subscript text T end text end subscript superscript text eff end text end superscript plus nu 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 text end superscript right parenthesis over denominator fraction numerator 1 over denominator k subscript text T end text end subscript superscript text eff end text end superscript end fraction plus 1 over mu subscript text m end text end subscript end fraction equals V subscript text f end text end subscript E subscript text A end text end subscript superscript text f end text end superscript alpha subscript text A end text end subscript superscript text f end text end superscript plus V subscript text m end text end subscript E subscript text m end text end subscript alpha subscript text m end text end subscript end cell row cell space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space plus V subscript text f end text end subscript fraction numerator 4 nu subscript text A end text end subscript superscript text f end text end superscript left parenthesis alpha subscript text T end text end subscript superscript text f end text end superscript plus nu subscript text A end text end subscript superscript text f end text end superscript alpha subscript text A end text end subscript superscript text f end text end superscript right parenthesis over denominator fraction numerator 1 over denominator k subscript text T end text end subscript superscript text f end text end superscript end fraction plus 1 over mu subscript text m end text end 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 "/>(4.181)

      These results (4.173)–(4.182) can also be written in the form of a mixtures estimate plus a correction term as follows

      StartFraction 1 Over k Subscript upper T Superscript eff Baseline EndFraction equals StartFraction upper V Subscript f Baseline Over k Subscript upper T Superscript f Baseline EndFraction plus StartFraction upper V Subscript m Baseline Over k Subscript upper T Superscript m Baseline EndFraction minus StartFraction lamda Over 2 EndFraction left-parenthesis StartFraction 1 Over k Subscript upper T Superscript f Baseline EndFraction minus StartFraction 1 Over k Subscript upper T Superscript m Baseline EndFraction right-parenthesis squared upper V Subscript f Baseline upper V Subscript m Baseline comma(4.184)

      nu Subscript upper A Superscript eff Baseline equals upper V Subscript f Baseline nu Subscript upper A Superscript f Baseline plus upper V Subscript m Baseline nu Subscript m Baseline minus StartFraction lamda Over 2 EndFraction left-parenthesis StartFraction 1 Over k Subscript upper T Superscript m Baseline EndFraction minus StartFraction 1 Over k Subscript upper T Superscript f Baseline EndFraction right-parenthesis left-parenthesis nu Subscript m Baseline minus nu Subscript upper A Superscript f Baseline right-parenthesis upper V Subscript f Baseline upper V Subscript m Baseline comma(4.185)

      mu Subscript upper A Superscript eff Baseline equals upper V Subscript f Baseline mu Subscript upper A Superscript f Baseline plus upper V Subscript m Baseline mu Subscript m Baseline minus StartFraction left-parenthesis mu Subscript upper A Superscript f Baseline minus mu Subscript m Baseline right-parenthesis squared upper V Subscript f Baseline upper V Subscript m Baseline Over left-parenthesis 1 plus upper V Subscript f Baseline right-parenthesis mu Subscript m Baseline plus upper V Subscript m Baseline mu Subscript upper A Superscript f Baseline EndFraction comma(4.186)

      mu Subscript t Superscript eff Baseline equals upper V Subscript f Baseline mu Subscript t Superscript f Baseline plus upper V Subscript m Baseline mu Subscript m Baseline minus StartStartFraction left-parenthesis mu Subscript t Superscript f Baseline minus mu Subscript m Baseline right-parenthesis squared upper V Subscript f Baseline upper V Subscript m Baseline OverOver upper V Subscript m Baseline mu Subscript t Superscript f Baseline plus upper V Subscript f Baseline mu Subscript m Baseline plus 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 EndEndFraction comma(4.187)

      upper E Subscript upper A Superscript eff Baseline equals upper V Subscript f Baseline upper E Subscript upper A Superscript f Baseline plus upper V Subscript m Baseline upper E Subscript m Baseline plus 2 lamda left-parenthesis nu Subscript m Baseline minus nu Subscript upper A Superscript f Baseline right-parenthesis squared zero width space zero width space upper V Subscript f Baseline upper V Subscript m Baseline comma(4.188)

      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(4.189)

      upper E Subscript upper A Superscript eff <noindex><p style= Скачать книгу


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