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Lisa Hacker: Redirected page to Time-Varying Stress Models#Cumulative Damage Power Relationship

2012-08-15T23:40:22Z

← Older revision		Revision as of 23:40, 15 August 2012
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	~~=Cumulative Damage Power Relationship=~~		#REDIRECT [[Time-Varying_Stress_Models#Cumulative_Damage_Power_Relationship]]

	~~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 power relationship. Given a time-varying stress <math>x(t)</math> and assuming the power law relationship, the life-stress relationship is given by:~~

	~~<br>~~
	~~::<math>L(x(t))={{\left( \frac{a}{x(t)} \right)}^{n}}</math>~~

	~~<br>~~
	~~In ALTA, the above relationship is actually presented in a format consistent with the general log-linear (GLL) relationship for the power law relationship:~~

	~~<br>~~
	~~::<math>L(x(t))={{e}^{{{\alpha }_{0}}+{{\alpha }_{1}}\ln \left( x(t) \right)}}</math>~~

	~~<br>~~
	~~Therefore, instead of displaying <math>a</math> and <math>n</math> as the calculated parameters, the following reparameterization is used:~~

	~~<br>~~
	~~::<math>\begin{align}~~
	~~{{\alpha }_{0}}=\ & \ln ({{a}^{n}}) \\~~
	~~{{\alpha }_{1}}=\ & -n~~
	~~\end{align}</math>~~

	~~<br>~~

	~~{{cd power exponential}}~~


	~~{{cd power weibull}}~~

	~~{{cd power lognormal}}~~

2012-02-22T17:19:19Z

Cumulative Damage Power Relationship

← Older revision		Revision as of 17:19, 22 February 2012
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	===Cumulative Damage Power Relationship===		=Cumulative Damage Power Relationship=

	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 power relationship. Given a time-varying stress <math>x(t)</math> and assuming the power law relationship, the life-stress relationship is given by:		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 power relationship. Given a time-varying stress <math>x(t)</math> and assuming the power law relationship, the life-stress relationship is given by:

2012-02-21T22:24:47Z

← Older revision		Revision as of 22:24, 21 February 2012
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	a		===Cumulative Damage Power Relationship===

			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 power relationship. Given a time-varying stress <math>x(t)</math> and assuming the power law relationship, the life-stress relationship is given by:

			<br>
			::<math>L(x(t))={{\left( \frac{a}{x(t)} \right)}^{n}}</math>

			<br>
			In ALTA, the above relationship is actually presented in a format consistent with the general log-linear (GLL) relationship for the power law relationship:

			<br>
			::<math>L(x(t))={{e}^{{{\alpha }_{0}}+{{\alpha }_{1}}\ln \left( x(t) \right)}}</math>

			<br>
			Therefore, instead of displaying <math>a</math> and <math>n</math> as the calculated parameters, the following reparameterization is used:

			<br>
			::<math>\begin{align}
			{{\alpha }_{0}}=\ & \ln ({{a}^{n}}) \\
			{{\alpha }_{1}}=\ & -n
			\end{align}</math>

			<br>

			{{cd power exponential}}


			{{cd power weibull}}

			{{cd power lognormal}}

2012-02-21T22:21:38Z

← Older revision	Revision as of 22:21, 21 February 2012
(No difference)

2012-02-21T22:21:18Z

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