# ramdas chennamsetti's blog

## Odd order governing equation - FE formulation

Hi!!

We generally encounter governing equations of even order. In FE formulation we get a symmetric coefficient matrix 'A' (AX = B). I have a few doubts as follwing.

[a] Any odd order governig equations ? If so, you may please write.

[b] Say, it has a functional also, then, what's the order of that differentiation?

## Body loads in wave propagation..

Hi all,

[1] In solids, the wave propagation equation is obtained from stress equilibrium equations. We make use of constitutive and strain-displacement relations to convert these equations in terms of displacements

[2] In the above equations we assume that there are no body loads.

[3] The form of solution we assume for displacements is harmonic

[4] Plug these three displacements, u1, u2 and u3 in the equilibrium equations stated in [1].

[5] We end up with an Eigenvalue problem. This is nice.

## Thin plate theory...

Hi all!

I have a small doubt in the assumptions made in thin plate theory.

We make some of the following assumptions in thin plate theory (Kirchoff's classical plate theory) (KCPT).

[1] The normal stress (out of plane=> sigma(z)) is zero. and

[2] The vertical deflection 'w' is not a function of 'z' => dw/dz = 0

Now there are three stress components sigma(x), sigma(y) and sigma(xy). The other three stress components sigma(z), sigma(xz) and sigma(yz). This is like a plane stress.

## Spectral Finite Elements

Hi all!

I just strated using Spectral FE technique for wave propagation applications. I am looking for some example code (for bar/beam or any geometry). If anybody has, I request them to kindly send me.

- R, Chennamsetti

## Mesh free methods - literature

Hi all!!

Where can I get literature on Mesh free methods (basics)?

I am suggested Dr. Liu's book.

Please suggest me some more good literature (some web sites, text books etc), assuming that I am zero in mesh free methods.