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. 21 ,.μ 23. 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, yx.
=.deformations.in.x,.y.directions;
α x, 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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