Prob,4.16
Define angle,stress,strain,compliance as functions of time,
> Theta:=t -> gamma(t)*l/r;
γ()tl
Θ,= t →
r
> sigma:=Gamma/(2*Pi*r^2*b);
1 Γ
σ,=
2
π r
2
b
> unprotect(gamma):gamma:=t -> J(t)*sigma;
γ,= t → () J t σ
> J:=t -> (.75+.15*log10(t)+.018*(log10(t))^2)/1e9;
J,= t →,75 10
-9
+,15 10
-9
()log10 +,18 10
-10
()log10 t t
2
Set values of numerical parameters,
> Digits:=4:l:=2;r:=.04/2;Gamma:=8;b:=.002;
(1) Compute angle after 20 hrs at 20C:
> 'Theta(deg)'=evalf((180/Pi)*Theta(20*3600));
Θ( deg) = 17.36
(2) Compute effective time and angle for 60C:
> a_60:=.001;t_60:=20*3600/a_60;
> 'Theta(deg)'=evalf((180/Pi)*Theta(t_60));
Θ( deg) = 27.72
(3) Compute effective time and twist for two-step temperature program:
> t_eff:=19.75*3600+(.25*3600)/a_60;
> 'Theta(deg)'=evalf((180/Pi)*Theta(t_eff));
Θ( deg) = 20.91
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