Properties for Design of Composite Structures. Neil McCartney

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Название Properties for Design of Composite Structures
Автор произведения Neil McCartney
Жанр Техническая литература
Серия
Издательство Техническая литература
Год выпуска 0
isbn 9781118789780
Properties for Design of Composite Structures - Neil McCartney
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alt="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 text 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 sum from i equals 1 to N of V subscript text f end text end subscript superscript i E subscript text A end text end subscript superscript text f end text left parenthesis i right parenthesis end superscript alpha subscript text A end text end subscript superscript text f end text left parenthesis i right parenthesis 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 plus sum from i equals 1 to N of V subscript text f end text end subscript superscript i fraction numerator 4 nu subscript text A end text end subscript superscript text f end text left parenthesis i right parenthesis end superscript left parenthesis alpha subscript text T end text end subscript superscript text f end text left parenthesis i right parenthesis end superscript plus nu subscript text A end text end subscript superscript text f end text left parenthesis i right parenthesis end superscript alpha subscript text A end text end subscript superscript text f end text left parenthesis i right parenthesis end superscript right parenthesis over denominator fraction numerator 1 over denominator k subscript text T end text end subscript superscript text f end text left parenthesis i right parenthesis 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. end cell end table"/>(4.160)

      4.8 Summary of Results for Multiphase Composites

      kappa Subscript upper A Superscript eff Baseline equals sigma-summation Underscript i equals 1 Overscript upper N Endscripts upper V Subscript f Superscript i Baseline kappa Subscript upper A Superscript f left-parenthesis i right-parenthesis Baseline zero width space zero width space plus upper V Subscript m Baseline kappa Subscript m Baseline comma(4.161)

      StartFraction 1 Over kappa Subscript upper T Superscript eff Baseline plus kappa Subscript m Baseline EndFraction equals sigma-summation Underscript i equals 1 Overscript upper N Endscripts StartFraction upper V Subscript f Superscript i Baseline Over kappa Subscript upper T Superscript f left-parenthesis i right-parenthesis Baseline plus kappa Subscript m Baseline EndFraction plus StartFraction upper V Subscript m Baseline Over kappa Subscript m Baseline plus kappa Subscript m Baseline EndFraction comma(4.162)

      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 sigma-summation Underscript i equals 1 Overscript upper N Endscripts StartStartFraction upper V Subscript f Superscript i Baseline OverOver StartFraction 1 Over k Subscript upper T Superscript f left-parenthesis i right-parenthesis 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(4.163)

      or StartFraction 1 Over k Subscript upper T Superscript eff Baseline plus mu Subscript m Baseline EndFraction equals sigma-summation Underscript i equals 1 Overscript upper N Endscripts StartFraction upper V Subscript f Superscript i Baseline Over k Subscript upper T Superscript f left-parenthesis i right-parenthesis 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(4.164)

      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 sigma-summation Underscript i equals 1 Overscript upper N Endscripts StartStartFraction upper V Subscript f Superscript i Baseline nu Subscript upper A Superscript f left-parenthesis i right-parenthesis Baseline OverOver StartFraction 1 Over k Subscript upper T Superscript f left-parenthesis i right-parenthesis 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(4.165)

      StartFraction 1 Over mu Subscript upper A Superscript eff Baseline plus mu Subscript m Baseline EndFraction equals sigma-summation Underscript i equals 1 Overscript upper N Endscripts StartFraction upper V Subscript f Superscript i Baseline Over mu Subscript upper A Superscript f left-parenthesis i right-parenthesis 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(4.166)

      StartFraction 1 Over mu Subscript t Superscript eff Baseline plus mu Subscript m Superscript asterisk Baseline EndFraction equals sigma-summation Underscript i equals 1 Overscript upper N Endscripts StartFraction upper V Subscript f Superscript i Baseline Over mu Subscript t Superscript f left-parenthesis i right-parenthesis 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 comma 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(4.167)

      upper E Subscript upper A Superscript </div> </div> </div> <hr> <div class=

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