Page 14 - Using ANSYS for Finite Element Analysis A Tutorial for Engineers

ChaPter 1

inTroducTion To finiTE

ElEmEnT AnAlysis

1.1 finite element method

The field of mechanics can be subdivided into three major areas: theo-
retical, applied, and computational. Theoretical mechanics deals with
fundamental laws and principles of mechanics studied for their intrinsic
scientific value. Applied mechanics transfers this theoretical knowledge
to scientific and engineering applications, especially through the con-
struction of mathematical models of physical phenomena. Computational
mechanics solves specific problems by simulation through numerical
methods implemented on digital computers.
One of the most important advances in applied mathematics in the
20th century has been the development of the finite element method as
a general mathematical tool for obtaining approximate solutions to
boundary-value problems. The theory of finite elements draws on almost
every branch of mathematics and can be considered as one of the richest
and most diverse bodies of the current mathematical knowledge.

1.1.1 MatheMatical Modeling of Physical
systeMs

In general, engineering problems are mathematical models of physical
situations. Two main goals of engineering analysis are to be able to iden-
tify the basic physical principle(s) and fundamental laws that govern the
behavior of a system or a control volume and to translate those princi-
ples into a mathematical model involving an equation or equations that
can be solved accurately to predict qualitative and quantitative behavior
of the system. The resulting mathematical model is frequently a single