Volume calculation from Axisymmetric Model

Submitted by shrimad on Thu, 2008-07-10 19:18.

Computational Mechanics Forum

Hi,

I am working on numerical simulation of compression glass molding process using FEM.

I want to calculate the volume of the glass after the FE analysis (axisymmetric). At the end of the analysis, all I have is the nodal co-ordinates and element connectivity of the deformed glass. Please guide me on calculating the volume using the above information.

Does ANSYS have the capability of giving the volume of an axisymmetric model?

Thanks,S

Shriram

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Re: Volume calculation from Axisymmetric Model

Submitted by Biswajit Banerjee on Thu, 2008-07-10 23:32.

I don't know whether ANSYS provides a direct way of calculating the deformed volume. However, the volume can be easily computed using the following approach.

Let the closed polygon representing the final profile of the deformed glass be given by $P = {p_1, p_2, p_3, ...., p_n, p_{n 1} = p_1}$ , where $n$ is the number of vertices of the polygon. We assume that the points are ordered in the counter-clockwise direction. Each point $p_i$ has a pair of coordinates ( $x_i, y_i$ ).

Then, the area of the profile ( $A_f$ ) is given by

$A_f = \tfrac{1}{2} \sum_{i=1}^n (x_i~y_{i 1} - x_{i 1}~y_i)$

The centroid of the profile is given by

$C_{xf} = \cfrac{1}{6 A_f}\sum_{i=1}^n (x_i~y_{i 1} - x_{i 1}~y_i) (x_i x_{i 1})$
$C_{yf} = \cfrac{1}{6 A_f}\sum_{i=1}^n (x_i~y_{i 1} - x_{i 1}~y_i) (y_i y_{i 1})$

The volume of the deformed cylinder is given by the Pappus theorem. The formula for the volume is

$V_f = 2 \pi C_{xf} A_f$