Page 14 - Finite Element Analysis with ANSYS Workbench

1.3 ANSYS Software 5

The method starts by dividing the problem domain or
geometry into a number of small elements. These elements are
connected via nodes where the unknowns are to be determined.
The finite element equations for each element are derived from the
governing differential equations describing physics. These finite
element equations are assembled into a large set of algebraic
equations. The boundary conditions are then imposed to the set of
algebraic equations to solve for solutions at each node.

We will understand the procedure of the finite element
method in details in the following section.

1.2.2 Finite Element Method Procedure
The finite element method procedure generally consists
of 6 steps:

Step 1: The first step is to construct the domain geometry of the
given problem. The geometry may consist of straight lines, curves,
circles, surfaces or solid shapes in three dimensions. Different
software packages have their unique ways to create geometry.
Users may have to spend some times to familiarize with the
software. A finite element mesh is then generated on the
constructed geometry. Depending on the complexity of the
geometry, a mesh may consist of various element types such as
line, triangular or brick element. These elements are connected at
nodes for which the problem unknowns are located.

Step 2: The second step is to select the element types. For
examples, a line element may consist of two or three nodes, or a
triangular element may have three or six nodes. The number of
element nodes affects the interpolation functions used in that
element. Selecting an element with more nodes will increase the
number of unknowns and thus the computational time. However,
the solution accuracy can also increase when a more complicated
interpolation function is used.

Step 3: The third step is the most important step of the finite
element method. This step is the derivation of the finite element