Environmental Engineering Reference
In-Depth Information
from.Hook's.law.and.Duhamel-Neumann.law.and.ind.results.from.positive.
and.negative.values.dependant.on.changing.temperature.and.coeficient.of.
thermal.expansions.for.composite.wind.turbine.blades.
5.9.2
Theoretical Investigation
When.properties.of.an.orthotropic.turbine.blade.have.been.changed.under.
acting.loads.and.temperature,.the.stress-strain.relations.must.be.signed.in.
matrix.form.
38
σ
ij.
=.Q
ij
*(ε
j.
-.α
j
*T).(i,j.=.1,2,6).
(5.89)
where:
Q
ij.
are.known.as.the.stiffness.constants;
α
j.
are.coeficients.of.temperature.expansion;
T.is.an.environmental.temperature.
For. orthotropic. materials,. we. have. 10. stiffness. constants. (see. Equation.
(5.89))..This.relation.V..Z..Parton
38
.called.the.Duhamel-Neumann.Law.
Here:
E
1
,.E
2
.are.modules.of.normal.elasticity.in.warp.and.ill.directions;
μ
12.
,μ
21
,.μ
23.
,μ
32
.are.Poisson's.ratio.of.material.
The.irst.symbol.designates.the.direction.of.force.and.second.symbol.des-
ignates.the.direction.of.transverse.deformation..α
1
,.α
2
.are.coeficients.of.ther-
mal.expansion.in.longitudinal.(warp).and.axial.(ill).directions.
Summarizing.Equation.(5.89).for.laminate.package,.we.get.in.longitudinal.
direction.x:
.
Σσ
-1x.
=.ΣQ
x
ε
xy.
-.ΣQ
x
α
x
*T)..
(5.90)
and.in.axial.direction.y:
.
Σσ
-1y.
=.ΣQ
y
ε
yx.
-.ΣQ
y
α
y
*T).
(5.91)
Here:
Σσ
-1x,
.Σσ
-1y.
.
=.Fatigue.stress.carbon/iberglass.sandwich;
ΣQ
x,
.Q
y.
=.Stiffness.of.combination.carbon/iberglass.in.x,.y.directions;
ε
xy,
.ε
yx.
=.deformations.in.x,.y.directions;
α
x,
.α
y..
=..coeficients. of. thermal. expansion. in. x,y. directions.. This.
coeficients.has.anisotropic.character;
T.
.
=.Temperature.gradient
Harmonic.fatigue.stress.is.illustrated.in.Figure 5.9
The.Fourier.series.is.described.as.a.function.
39
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