Properties for Design of Composite Structures. Neil McCartney

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Properties for Design of Composite Structures - Neil McCartney

Properties for Design of Composite Structures - Neil McCartney

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rel="nofollow" href="#ulink_081d40a5-54f2-5c02-bf72-0202dfe6969b">4.1), relation (4.66) may also be expressed as

      On using (4.1) and (4.66), relations (4.67) and (4.68) may be written as

      nu Subscript upper A Superscript eff Baseline equals left-parenthesis sigma-summation Underscript i equals 1 Overscript upper N Endscripts StartFraction upper V Subscript f Superscript i Baseline k Subscript upper T Superscript f left-parenthesis i right-parenthesis Baseline nu Subscript upper A Superscript f left-parenthesis i right-parenthesis 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 k Subscript upper T Superscript m Baseline nu Subscript m Baseline Over k Subscript upper T Superscript m Baseline plus mu Subscript m Baseline EndFraction right-parenthesis slash left-parenthesis sigma-summation Underscript i equals 1 Overscript upper N Endscripts StartFraction upper V Subscript f Superscript i Baseline k Subscript upper T Superscript f left-parenthesis i right-parenthesis 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 k Subscript upper T Superscript m Baseline Over k Subscript upper T Superscript m Baseline plus mu Subscript m Baseline EndFraction right-parenthesis comma(4.70)

      alpha Subscript upper T Superscript eff Baseline plus nu Subscript upper A Superscript eff Baseline alpha Subscript upper A Superscript eff Baseline equals StartStartFraction sigma-summation Underscript i equals 1 Overscript upper N Endscripts StartFraction upper V Subscript f Superscript i Baseline k Subscript upper T Superscript f left-parenthesis i right-parenthesis Baseline left-parenthesis alpha Subscript upper T Superscript f left-parenthesis i right-parenthesis Baseline plus nu Subscript upper A Superscript f left-parenthesis i right-parenthesis Baseline alpha Subscript upper A Superscript f left-parenthesis i right-parenthesis Baseline right-parenthesis 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 k Subscript upper T Superscript m Baseline alpha Subscript m Baseline left-parenthesis 1 plus nu Subscript m Baseline right-parenthesis Over k Subscript upper T Superscript m Baseline plus mu Subscript m Baseline EndFraction OverOver sigma-summation Underscript i equals 1 Overscript upper N Endscripts StartFraction upper V Subscript f Superscript f left-parenthesis i right-parenthesis Baseline k Subscript upper T Superscript f left-parenthesis i right-parenthesis 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 k Subscript upper T Superscript m Baseline Over k Subscript upper T Superscript m Baseline plus mu Subscript m Baseline EndFraction EndEndFraction period(4.71)

      4.4 Axial Shear of Anisotropic Fibres

      4.4.1 Solution for an Isolated Fibre Perfectly Bonded to the Matrix

      A solution is now sought of the following form

      where A, α and β are constants to be determined. On differentiating the displacement field using the strain-displacement relations (2.139), it follows that

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