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Structural analysis: matrix question

  1. Mar 27, 2006 #1
    I'm afraid I have another problem to be solved I don't quiet understand, thanks to my poor english and some information missing in the course notes.

    ----
    You are writing a 2-dimensional finite element programming code to be used in the structural analysis of a material with a newly discovered rheology. The constitutive equation, in index notation, for this rheology (in an isotropic medium) is:

    σij = Rθδij – Sεij

    where θ is cubical dilatation (take θ = ε11 + ε22 + ε33)
    δij is Knonecker’s delta
    R and S are temperature and pressure dependent material properties.

    Derive the “rheology” matrix [D] that you will use in your algorithm, for plane strain (no displacements or displacement gradients in the x3 direction).

    Define the 2-dimensional stress and strain matrices {σ} and
    {ε} as they are in the course notes (they are not!), i.e.,

    direction). Define the 2-dimensional stress and strain matrices {σ} and
    {ε} as they are in the course notes (paragraph IV.2.8), i.e.,


    {
    σ11
    σ22
    σ12
    }
    =[D]
    {
    ε11
    ε22
    ε12
    }

    (written as {}=[D]{}

    What is the value of σ33 in this case of plane strain?
     
  2. jcsd
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