An Approach to the Mechanics of Fluids

by Frank C. Fung - 1st published in June, 2008.

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Section III - The { Cube } and other { Six-Face Objects }

Summary for the Section :

• In this Section , we shall look at the { cube } as a { finite element } , and :
  • move onto other types of { Six-Face Objects } that might be the { resultant object } when the { Cube } is subjected to stresses .

  This then prepares the ground-work for our discussion of { Stress-Strain Relations } and other matters in later Sections .

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The { Cube } and other Quasi-Symmetric { Six-Face Objects } :

• Let us start-off with the { Cube } as a { finite element } , and also identify :
  • the { Rhombus-Type Six-Face Object } , abbreviated as { RHO-SFO } , as shown in the diagram in-the-middle below .

  

  And for the { Rhombus-Type Six-Face Object } , all 12 { edge-sides } are always all [ of-equal-lengths ] ,

  • so that each face is always , by definition , a { rhombus } .

• The object in right-hand-side diagram above is then the { Parallelogram-Type Six-Face Object } , abbreviated as { PAR-SFO } , and is characterized by :
  • each set of { 4-lines } , as shown below , always being parallel and always being [ of-equal-lengths ] .

  

  Thus , each face of the [ PAR-SFO ] is always a { parallelogram } .

• For the { Cube } , the { RHO-SFO } and the { PAR-SFO } ,
  • each pair of { opposite-faces } are always [ of-identical-shapes ] ,

    whether these are { squares } , { rhombus's } , or { parallelograms } .

  And to this extent , they are deemed to be { symmetric } or { quasi-symmetric } ;

  • and we shall refere to these 3 types of { Six-Face Objects } collectively as { Symmetric or Quasi-Symmetric Six-Face Objects } ,

    in our discussions to follow .

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The { General-Random-Type Six-Face Object } :

• The { General-Random-Type Six-Face Object } , abbreviated as { GRT-SFO } :

  

  • is simply a { six-Face Object } with { 8 nodal-points } ,
    • where the { 8 nodal-points } do not follow any specific or predetermined pattern .

  And we shall look at , next , the { Degrees-Of-Freedoms } associated with the { GRT-SFO } .

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go to the next section : Section IV - 18 [ Degrees-Of Freedom ] associated with a { General-Random-Type Six-Face Object }

go to the last section : Section II - The Diversity of Fluid Types

return to the Mechanics of Fluids HomePage

original dated 2008-6-08