Split-radix FFT algorithm - Revision history

14.139.208.84 at 15:49, 13 August 2014

2014-08-13T15:49:07Z

← Older revision		Revision as of 17:49, 13 August 2014
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	The '''Ramberg–Osgood equation''' was created to describe the non linear relationship between [[Stress (physics)\|stress]] and [[Strain (materials science)\|strain]]—that is, the [[stress–strain curve]]—in materials near their [[Yield (engineering)\|yield points]]. It is ~~especially useful for metals that ''harden'' with plastic deformation (see [[work hardening\|strain hardening]]), showing a ''smooth'' elastic-plastic transition.~~		Nestor is the extended [http://holder11.dothome.co.kr/xe/center/733909 auto warranty] title my mothers and fathers gave me but [http://Www.Allstate.com/tools-and-resources/car-insurance/whats-in-a-new-car-warranty.aspx auto warranty] I don't like when people use my extended car warranty full name. Alabama is where he and his wife live and he has every thing that he [http://autos.aol.com/article/whats-in-car-warranty/ requirements] there. Meter reading is exactly where my primary earnings arrives from but soon I'll be on my [http://indianapolisfaith.org/UserProfile/tabid/320/userId/242895/Default.aspx extended auto warranty] own. To play croquet is the pastime I will by no means quit doing.<br><br>Here is my web-site: [http://Www.angieslist.com/articles/what-does-and-doesnt-your-auto-warranty-cover.htm extended auto] warranty ([http://14.63.168.193/index.php?document_srl=249897&mid=freeboard click for more info])

	~~In its original form,~~ the equation for strain (deformation) is<ref name=paper>Ramberg, W., & Osgood, W. R. (1943). Description of stress-strain curves by three parameters. ''Technical Note No. 902'', National Advisory Committee For Aeronautics, Washington DC. [http://~~ntrs~~.~~nasa~~.~~gov/archive/nasa/casi.ntrs.nasa.gov/19930081614_1993081614~~.~~pdf]<~~/~~ref>~~

	~~::: <math>\epsilon = \frac{\sigma}{E} + K \left(\frac{\sigma}{E} \right)^n<~~/~~math>~~

	~~where~~
	~~: <math>\epsilon<~~/~~math> is [[Strain (materials science)\|strain~~]],
	~~: <math>\sigma</math> is~~ [~~[Stress (physics)\|stress]],~~
	~~: <math>E</math> is [[Young's modulus]], and~~
	: ~~<math>K<~~/~~math> and <math>n<~~/~~math> are constants that depend on the material being considered~~.

	~~The first term on the right side, <math>{\sigma}~~/~~{E}\,</math>, is equal to the elastic part of the strain, while the second term, <math>\ K({\sigma}/{E})^n</math>, accounts for the plastic part, the parameters <math>K</math>~~ and ~~<math>n<~~/~~math> describing the ''hardening behavior'' of the material. Introducing the ''yield strength'' of the material, <math>\sigma_0<~~/~~math>, and defining~~ a new ~~parameter, <math>\alpha</math>, related to <math>K</math> as <math>\alpha = K ({\sigma_0}/{E})^{n~~-~~1}\,</math>, it~~ is ~~convenient to rewrite the term on the extreme right side as follows:~~

	~~::: <math>\ K \left(\frac{\sigma}{E} \right)^n = \alpha \frac{\sigma_0}{E} \left(\frac{\sigma}{\sigma_0} \right)^n</math>~~

	~~Replacing in the first expression, the Ramberg–Osgood equation can be written as~~

	~~::: <math>\epsilon = \frac{\sigma}{E} + \alpha \frac{\sigma_0}{E} \left(\frac{\sigma}{\sigma_0} \right)^n</math>~~

	~~==Hardening behavior and yield offset==~~

	~~In the last form of the Ramberg–Osgood model, the ''hardening behavior'' of the material depends on the material constants <math>\alpha\,</math>~~ and ~~<math>n\,</math>. Due to the [[power law\|power-law]] relationship between stress~~ and ~~plastic strain, the Ramberg–Osgood model implies~~ that ~~plastic strain is present even for very low levels of stress. Nevertheless, for low applied stresses and for the commonly used values of the material constants <math>\alpha<~~/~~math> and <math>n<~~/~~math>, the plastic strain remains negligible compared to the elastic strain~~. ~~On the other hand, for stress levels higher than <math>\sigma_0<~~/~~math>, plastic strain becomes progressively larger than elastic strain.~~

	~~The value <math>\alpha \frac{\sigma_0}{E}<~~/~~math> can be seen as a ''yield offset'', as shown~~ in ~~figure 1~~. ~~This comes~~ from ~~the fact that <math>\epsilon = (1+\alpha){{\sigma_0}~~/~~{E}}\,<~~/~~math>, when <math>\sigma = \sigma_0\,<~~/~~math>.~~

	~~Accordingly (see Figure 1):~~
	~~: ''elastic strain at yield'' = <math>{{\sigma_0}~~/~~{E}}\,<~~/~~math>~~
	~~: ''plastic strain at yield'' = <math>\alpha({\sigma_0}~~/~~E)\,<~~/~~math> = ''yield offset''~~

	~~Commonly used values for <math>n\,<~~/~~math> are ~5 or greater, although more precise values are usually obtained by fitting of tensile (or compressive) experimental data~~. ~~Values for <math>\alpha\,</math> can also be found~~ by means ~~of fitting to experimental data, although for some materials, it can be fixed in order to have the ''yield offset'' equal to the accepted value of strain of 0~~.~~2%, which means:~~

	~~:::~~ <~~math~~>~~\alpha \frac{\sigma_0}{E} = 0,002~~<~~/math~~>

	[~~[Image~~:~~Ramberg~~-~~osgood~~-2.~~png\|frame\|none\|'''Figure 1'''~~: ~~Generic representation of the Stress-Strain curve by means of the Ramberg–Osgood equation~~. ~~Strain corresponding to the yield point is the sum of the elastic and plastic components~~.]]

	==~~References==~~

	~~<references/>~~

	~~{{DEFAULTSORT:Ramberg-Osgood relationship}}~~
	~~[[Category:Mechanics]]~~
	~~[[Category:Materials science]~~]

en>Gryzzly92 at 12:35, 27 May 2013

2013-05-27T12:35:42Z

← Older revision		Revision as of 14:35, 27 May 2013
Line 1:		Line 1:
	~~Hi there~~, ~~I am Alyson Pomerleau and I think it seems quite good when you say it~~. It's ~~not~~ a ~~typical factor but what she likes performing~~ is to ~~perform domino but she doesn~~'~~t have~~ the ~~time recently~~. ~~He functions~~ as a ~~bookkeeper. For a while I~~'~~ve been in Alaska but I will have to move~~ in ~~a yr or two~~.<br><br>~~my site - are psychics real~~ (~~[http~~://~~breenq~~.~~com~~/~~index~~.~~php?do~~=/~~profile~~-~~1144~~/~~info/ simply click the following post~~])		The '''Ramberg–Osgood equation''' was created to describe the non linear relationship between [[Stress (physics)\|stress]] and [[Strain (materials science)\|strain]]—that is, the [[stress–strain curve]]—in materials near their [[Yield (engineering)\|yield points]]. It is especially useful for metals that ''harden'' with plastic deformation (see [[work hardening\|strain hardening]]), showing a ''smooth'' elastic-plastic transition.

			In its original form, the equation for strain (deformation) is<ref name=paper>Ramberg, W., & Osgood, W. R. (1943). Description of stress-strain curves by three parameters. ''Technical Note No. 902'', National Advisory Committee For Aeronautics, Washington DC. [http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19930081614_1993081614.pdf]</ref>

			::: <math>\epsilon = \frac{\sigma}{E} + K \left(\frac{\sigma}{E} \right)^n</math>

			where
			: <math>\epsilon</math> is [[Strain (materials science)\|strain]],
			: <math>\sigma</math> is [[Stress (physics)\|stress]],
			: <math>E</math> is [[Young's modulus]], and
			: <math>K</math> and <math>n</math> are constants that depend on the material being considered.

			The first term on the right side, <math>{\sigma}/{E}\,</math>, is equal to the elastic part of the strain, while the second term, <math>\ K({\sigma}/{E})^n</math>, accounts for the plastic part, the parameters <math>K</math> and <math>n</math> describing the ''hardening behavior'' of the material. Introducing the ''yield strength'' of the material, <math>\sigma_0</math>, and defining a new parameter, <math>\alpha</math>, related to <math>K</math> as <math>\alpha = K ({\sigma_0}/{E})^{n-1}\,</math>, it is convenient to rewrite the term on the extreme right side as follows:

			::: <math>\ K \left(\frac{\sigma}{E} \right)^n = \alpha \frac{\sigma_0}{E} \left(\frac{\sigma}{\sigma_0} \right)^n</math>

			Replacing in the first expression, the Ramberg–Osgood equation can be written as

			::: <math>\epsilon = \frac{\sigma}{E} + \alpha \frac{\sigma_0}{E} \left(\frac{\sigma}{\sigma_0} \right)^n</math>

			==Hardening behavior and yield offset==

			In the last form of the Ramberg–Osgood model, the ''hardening behavior'' of the material depends on the material constants <math>\alpha\,</math> and <math>n\,</math>. Due to the [[power law\|power-law]] relationship between stress and plastic strain, the Ramberg–Osgood model implies that plastic strain is present even for very low levels of stress. Nevertheless, for low applied stresses and for the commonly used values of the material constants <math>\alpha</math> and <math>n</math>, the plastic strain remains negligible compared to the elastic strain. On the other hand, for stress levels higher than <math>\sigma_0</math>, plastic strain becomes progressively larger than elastic strain.

			The value <math>\alpha \frac{\sigma_0}{E}</math> can be seen as a ''yield offset'', as shown in figure 1. This comes from the fact that <math>\epsilon = (1+\alpha){{\sigma_0}/{E}}\,</math>, when <math>\sigma = \sigma_0\,</math>.

			Accordingly (see Figure 1):
			: ''elastic strain at yield'' = <math>{{\sigma_0}/{E}}\,</math>
			: ''plastic strain at yield'' = <math>\alpha({\sigma_0}/E)\,</math> = ''yield offset''

			Commonly used values for <math>n\,</math> are ~5 or greater, although more precise values are usually obtained by fitting of tensile (or compressive) experimental data. Values for <math>\alpha\,</math> can also be found by means of fitting to experimental data, although for some materials, it can be fixed in order to have the ''yield offset'' equal to the accepted value of strain of 0.2%, which means:

			::: <math>\alpha \frac{\sigma_0}{E} = 0,002</math>

			[[Image:Ramberg-osgood-2.png\|frame\|none\|'''Figure 1''': Generic representation of the Stress-Strain curve by means of the Ramberg–Osgood equation. Strain corresponding to the yield point is the sum of the elastic and plastic components.]]

			==References==

			<references/>

			{{DEFAULTSORT:Ramberg-Osgood relationship}}
			[[Category:Mechanics]]
			[[Category:Materials science]]

en>Giftlite: /* Split-radix decomposition */ mv .

2011-10-28T17:10:30Z

Split-radix decomposition: mv .

New page

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