Freivalds' algorithm: Difference between revisions

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en>Frietjes
Cleaned up the math a bit
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#REDIRECT [[Deformation (mechanics)#Normal strain]]
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{{Mergeto|Deformation (mechanics)|discuss=Talk:Deformation (mechanics)#Merging articles|date=September 2008}}
As with [[stress (mechanics)|stress]]es, strains may also be classified as 'normal strain' and '[[shear strain]]' (i.e. acting perpendicular to or along the face of an element respectively). For an [[isotropic]] material that obeys [[Hooke's law]], a [[normal stress]] will cause a normal strain. [[Deformation (mechanics)|Strains]] are relative [[displacement field (mechanics)|displacements]] - they are the actual displacement divided by the length before the strain was applied. [[Rigid body motion]]s don't produce strains. '''Normal strains''' produce ''dilations'', however they merely [[Deformation (mechanics)#Stretch|stretch]] the body along the axis of application (negating [[poisson's ratio]] and the effects it causes).  As such, a normal strain will cause the following effects:
 
* Any line [[Parallel (geometry)|parallel]] to the strain axis will increase by an amount proportional to its length and the amount of strain. (See below).
* Any line [[perpendicular]] to the strain axis will have no length change (negating [[Poisson's effect]].)
* Any line not perpendicular nor parallel will have a length increase based upon [[vector algebra]].
* Normal Strains will become Shear strains for a rotation of the [[frame of reference]].  See [[Mohr's circle]] for strain.
 
Normal strain,
:<math>\epsilon = \frac{\text{extension}}{\text{original length}}</math>
 
The 'stretch' of an element over its original element length is thus:
:<math>\epsilon = \frac{\Delta u}{\Delta x} = \frac{du}{dx} = u'(x)</math>
 
==See also==
* [[Shear strain]]
 
{{DEFAULTSORT:Normal Strain}}
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[[Category:Continuum mechanics]]

Revision as of 16:18, 25 February 2014

The author is known as Irwin. California is where I've usually been living and I love each day residing here. I am a meter reader. To collect coins is 1 of the things I adore most.

Here is my webpage ... home std test kit (our website)