Template:Cd exponential: Difference between revisions

Latest revision as of 00:40, 16 August 2012

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-=Cumulative Damage Exponential Relationship=
+#REDIRECT [[Time-Varying_Stress_Models#Cumulative_Damage_Exponential_Relationship]]
-<br>
-This section presents a generalized formulation of the cumulative damage model where stress can be any function of time and the life-stress relationship is based on the exponential relationship. Given a time-varying stress  <math>x(t)</math>  and assuming the exponential relationship, the life-stress relationship is given by:
-::<math>L(x(t))=C{{e}^{bx(t)}}</math>
-In ALTA, the above relationship is actually presented in a format consistent with the general log-linear (GLL) relationship for the exponential relationship:
-Therefore, instead of dis<math>C</math>playing    and  <math>b</math>  as the calculated parameters, the following reparameterization is used:
-::<math>\begin{align}
- {{\alpha }_{0}}=\ & \ln (C) \\
- {{\alpha }_{1}}=\ & b
-\end{align}</math>
-{{cd exponential exponential}}
-{{cd exponential weibull}}
-{{cd exponential lognormal}}