{ [ 18 ] on [ 18 ]

An Approach to the Mechanics of Fluids

Section IX - { [ 18 ] on [ 18 ] } for the { Six-Face Object }

In this Section , we shall look at the [ 18 stresses ] and the [ 18 strains ] for the { GRT-SFO } .

We bring-back , at this point from Section V , the set of 18 { forces } acting on the { cube } :

And we simply note here that these 18 { forces } are directly related to the 18 { stresses } acting on the { cube } .
Let us now bring-in the { General-Random-Type Six-Face Object } , the ( GRT-SFO ) , for a quick comparison :

And we see here that there are also 3 { forces } acting on the { face } here ,
- so that there are always 3 { Degrees-Of-Freedom } associated with the { forces } acting on each { face } .
Two (2) special notes of interest here :
- [ F1 ] is { normal } to [ Plane A-B-D-C } and
  - [ F2 ] and [ F3 ] acting in-plane may be combined together to form a single { force } ,
    
    but the 2 [ DOF's ] here are always maintained .
- We have assumed here that the 3 forces [ F1 ] , [ F2 ] and [ F3 ] are acting upon the { area-centroid } of { quadrilateral A-B-D-C } .
Thus , there are also 18 [ DOF's ] associated with the { Stresses } on the { GRT-SFO } .

We take note here , again , that the { GRT-SFO } has 18 [ DOF's ] associated with it ,
and these are always related to the strains for the said-{ GRT-SFO } .

{ 18 Stresses } on { 18 Strains } for the { GRT-SFO } :
- Need we say more ?
Clearly , further investigations are called-for here .