Properties for Design of Composite Structures. Neil McCartney
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Название: Properties for Design of Composite Structures

Автор: Neil McCartney

Издательство: John Wiley & Sons Limited

Жанр: Техническая литература

Серия:

isbn: 9781118789780

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СКАЧАТЬ rectangular plate made of an orthotropic fibre reinforced material where the in-plane directions x1 and x2 are parallel to the edges of the plate and where the through-thickness direction is parallel to the x3-axis. The straight fibres in the plate are all parallel to the x1-axis. For this situation, the elastic constants SIJ in (2.170) are written in the form

      StartLayout 1st Row upper S 11 equals StartFraction 1 Over upper E Subscript upper A Baseline EndFraction comma upper S 12 equals minus StartFraction nu Subscript upper A Baseline Over upper E Subscript upper A Baseline EndFraction comma upper S 13 equals minus StartFraction nu Subscript a Baseline Over upper E Subscript upper A Baseline EndFraction comma 2nd Row upper S 21 equals minus StartFraction nu Subscript upper A Baseline Over upper E Subscript upper A Baseline EndFraction comma upper S 22 equals StartFraction 1 Over upper E Subscript upper T Baseline EndFraction comma upper S 23 equals minus StartFraction nu Subscript t Baseline Over upper E Subscript upper T Baseline EndFraction comma 3rd Row upper S 31 equals minus StartFraction nu Subscript a Baseline Over upper E Subscript upper A Baseline EndFraction comma upper S 32 equals minus StartFraction nu Subscript t Baseline Over upper E Subscript upper T Baseline EndFraction comma upper S 33 equals StartFraction 1 Over upper E Subscript t Baseline EndFraction comma 4th Row upper S 44 equals StartFraction 1 Over mu Subscript t Baseline EndFraction comma upper S 55 equals StartFraction 1 Over mu Subscript a Baseline EndFraction comma upper S 66 equals StartFraction 1 Over mu Subscript upper A Baseline EndFraction comma 5th Row upper V 1 equals alpha Subscript upper A Baseline comma upper V 2 equals alpha Subscript upper T Baseline comma upper V 3 equals alpha Subscript t Baseline comma EndLayout(2.195)

      where Young’s moduli are denoted by E, shear moduli by μ, Poisson’s ratios by ν and thermal expansion coefficients by α. The stress-strain relations (2.170) may then be written as

      The subscripts ‘A’ and ‘T’ refer to axial and transverse thermoelastic constants, respectively, involving in-plane stresses and deformations. The subscripts ‘a’ and ‘t’ refer to axial and transverse constants, respectively, associated with out-of-plane stresses and deformations. The parameter ΔT is the difference between the current temperature of the material and the reference temperature for which all strains are zero when the sample is unloaded.

      It is clear that when the plate is uniaxially loaded in the x1-direction, the parameter νA is the Poisson’s ratio determining the in-plane transverse deformation in the x2-direction whereas νa is Poisson’s ratio determining the transverse through-thickness deformation in the x3-direction. When the plate is uniaxially loaded in the x2-direction, the parameter νt is the Poisson’s ratio determining the transverse through-thickness deformation in the x3-direction.

      It is useful, first, to show the form of the stress-strain equations (2.196) when the material is transverse isotropic about the x3-axis, so that they may be used when considering the properties of unidirectional plies in a laminate where the fibres are aligned in the x3-direction of the ply, and so that use can be made of analysis given in the previous section. It follows from (2.196) that when the material is transverse isotropic about the x3-axis, the stress-strain relations are of the form

      As S11=1/υT, S12=−νt/υT and S66=1/μt it follows from (2.189) that for a transverse isotropic solid the following condition must be satisfied:

      In Chapter 4 considering fibre-reinforced materials, stress-strain relations are required for the cylindrical polar coordinates (r,θ,z) corresponding to the relations (2.197), which are given by

      table attributes columnalign left end attributes row cell epsilon subscript r r end subscript equals 1 over E subscript text T end text end subscript sigma subscript r r end subscript minus nu subscript text t end text end subscript over E subscript text T end text end subscript sigma subscript theta theta end subscript minus nu subscript text A end text end subscript over E subscript text A end text end subscript sigma subscript z z end subscript plus alpha subscript text T end text end subscript capital delta T comma epsilon subscript r z end subscript equals fraction numerator sigma subscript r z end subscript over denominator 2 mu subscript text A end text end subscript end fraction comma end cell row cell epsilon subscript theta theta end subscript equals negative nu subscript text t end text end subscript over E subscript text T end text end subscript sigma subscript text rr end text end subscript plus 1 over E subscript text T end text end subscript sigma subscript theta theta end subscript minus nu subscript text A end text end subscript over E subscript text A end text end subscript sigma subscript z z end subscript plus alpha subscript text T end text end subscript capital delta T comma epsilon subscript theta z end subscript equals fraction numerator sigma subscript theta z end subscript over denominator 2 mu subscript text A end text end subscript end fraction comma end cell <a href=СКАЧАТЬ