An Approach to the Mechanics of Fluids

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

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Appendix A - An Alternate Structure for { Finite Elements }

Tetrahedra and Octahedra :

• We started-off here with the { Face-Centered-Cubic Packing Pattern } in Crystalline Solids :

  

  • and we present this { cube } , on the right-hand-side above , where the central { molecule } is surrounded by 12 other { molecules } .

  We then have 8 { equilateral tetrahedra } sitting inside the { cube } , as shown below :

  

  

• And we multi-stack the { cubes } in the { X , Y , and Z directions } ,
  • and the voids therefrom would be taken-up by filling them with { octohedra } :

  

  

  • so that the resultant { finite element } Structure is [ smack-face-to-face ] ,

  And the [ Tetrahedra vs. Octahedra ratio ] is then [ 8 : 4 ] .

• Interesting , eh !

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original dated 2008-6-08 / updated 2008-6-08