User:Eml5526.s11.team6.deshpande/hwk7

=Problem 7.3 Static Solution for Unit Circle with quadratic and triangular elements=

Given
Let $$ \displaystyle \Omega = $$ circle with unit radius.

$$ \displaystyle T = 4 $$

$$ \displaystyle f (x) = 1 \quad in \quad \Omega $$

$$ \displaystyle g = 0 \quad on \quad \Gamma_g = \partial \Omega \quad to \quad 10^{-6} $$ accuracy at center.

Find
For both quad and triangle elements.

sym $$ \displaystyle \Rightarrow $$ use $$\displaystyle \frac{1}{4} $$ of meshes.

Plot deformed shape in 3-D.

Solution
By using MATLAB, quarter circle is created with 9 elements and the datapoints are also located and calculated using MATLAB. Following figure shows the mesing of the unit circle.



The co-ordinates are obtained using matlab code and the nodes are numbered from 1 to 16 for 9 elements.

The boundary conditions are defined for harizontal and vertical axes above as

Hence, we can say that nodes on the arc of the circle are fixed and don't have any displacement and remaining nodes can be moved. The MATLAB code is as follows:

The result of the MATLAB code in the form of Deformed 3D shape is shown below.



As we can see, the boundary of the circle is not deflected but other nodes show deflection.

The displacement contour is as shown below