Page 11 - Finite Element Analysis with ANSYS Workbench

2 Chapter 1 Introduction

the simulated results can be understood easily. Without knowing
how the software solves the problem, it is difficult for new users to
be confident with the validity of output solutions.
Mathematics and engineering governing equations
embedded in these CAE software packages represent the nature of
the problem being considered. As an example of fluid flow
problem, mass and momentums must be conserved at any location
in the flow domain. Such conservations are expressed in form of
partial differential equations that are taught in fluid flow courses.
This means users should have some background in mathematics
together with the understanding of their physical meanings. By
employing the finite volume method, these partial differential
equations are transformed into a large set of algebraic equations. A
computer program is developed to solve these algebraic equations
for the flow solutions. The computed solutions are displayed as
color graphics on computer screen.

Similarly, users need to understand the equilibrium
equations before analyzing a structural problem. These equilibrium
equations are again in form of the partial differential equations as
seen in many solid mechanics textbooks. The finite element
method transforms these differential equations into their
corresponding algebraic equations. A computer program is
developed to solve such algebraic equations for the deformed shape
and stresses that occur in the structure.

The explanation above indicates that users should have
backgrounds in mathematics and physics of the problem being
solved. Users are also needed to understand the finite
element/volume method prior to use any CAE software package.
They can then convince themselves on the solutions generated by
the software. This is one of the main reasons that most universities
are offering the finite element/volume method courses to
engineering students.

1.1.1 Problem Ingredients

Solutions to an engineering problem depend on the
three components: