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.(adsbygoogle = window.adsbygoogle || []).push({});

----

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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Structural analysis: matrix question

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**