## FELIPE

# Elasticity analysis 1

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If you have not already done so, please read through the Poisson equation demo
which shows the basic operation of the pre-processor.

In this demonstration, we shall analyse the deformations and stresses induced in a thick cylinder of
linear elastic material, when a compressive normal pressure is applied at top and bottom.
The parameters used are::

inner radius of cylinder = 1 m

outer radius of cylinder = 10 m

Young's modulus = 20,000 N/sq.m

Poisson's ratio = 0.3

pressure applied = 50 N/sq.m

This is a plane strain problem, and we will use the symmetry of the problem to only model one quarter of it.
We start with a data file for a mesh consisting of a single element: an eight-noded quadrilateral ("serendipity")
element with two curved sides, which models the quarter-cylinder shape. A listing of the data file is
shown in the picture below.

Note that nodes 1,7,8 have constraint code 10, meaning they are constrained in the x direction but free to move
in the y direction, while nodes 3,4,5 have constraint code 01, meaning free in the x direction and fixed in the
y direction. This can be seen in the pre-processor graph of the mesh, below.

In the next picture, the automatic mesh refinement facility (in which each quadrilateral element is divided into
four) has already been applied twice, and further manual refinement close to the loading region is about
to be applied.

The following picture shows the final mesh geometry. Element and node renumbering is about to be performed,
starting at the node indicated by the cursor.

After renumbering, the sturcture of the global stiffness matrix is viewed.