1.1 Concept
The Finite Element Analysis (FEA) method, originally introduced by Turner
et al. (1956), is a powerful computational technique for approximate solutions
to a variety of "real-world" engineering problems having complex
domains subjected to general boundary conditions. FEA has become an
essential step in the design or modeling of a physical phenomenon in various
engineering disciplines. A physical phenomenon usually occurs in a
continuum of matter (solid, liquid, or gas) involving several field variables.
The field variables vary from point to point, thus possessing an infinite
number of solutions in the domain. Within the scope of this book, a
continuum with a known boundary is called a domain.
The basis of FEA relies on the decomposition of the domain into a finite
number of subdomains (elements) for which the systematic approximate
solution is constructed by applying the variational or weighted residual
methods. In effect, FEA reduces the problem to that of a finite number of
unknowns by dividing the domain into elements and by expressing the
unknown field variable in terms of the assumed approximating functions
within each element. These functions (also called interpolation functions)
are defined in terms of the values of the field variables at specific points,
referred to as nodes. Nodes are usually located along the element boundaries,
and they connect adjacent elements.
The ability to discretize the irregular domains with finite elements makes the
method a valuable and practical analysis tool for the solution of boundary,
initial, and eigenvalue problems arising in various engineering disciplines.
Since its inception, many technical papers and books have appeared on the
development and application of FEA. The books by Desai and Abel (1971),
Oden (1972), Gallagher (1975), Huebner (1975), Bathe and Wilson (1976),
Ziekiewicz (1977), Cook (1981), and Bathe (1996) have influenced the
current state of FEA

1.1 Before an ANSYS Session
The construction of solutions to engineering problems using FEA requires
either the development of a computer program based on the FEA formulation
or the use of a commercially available general-purpose FEA program
such as ANSYS. The ANSYS program is a powerful, multi-purpose analysis
tool that can be used in a wide variety of engineering disciplines. Before
using ANSYS to generate an FEA model of a physical system, the following
questions should be answered based on engineering judgment and observations:
• What are the objectives of this analysis?
• Should the entire physical system be modeled, or just a portion?
• How much detail should be included in the model?
• How refined should the finite element mesh be?
In answering such questions, the computational expense should be balanced
against the accuracy of the results. Therefore, the ANSYS finite element
program can be employed in a correct and efficient way after considering
the following:
• Type of problem.
• Time dependence.
• Nonlinearity.
• Modeling idealizations/simplifications.
Each of these topics is discussed in this section.
2,2.1 Analysis Discipline
The ANSYS program is capable of simulating problems in a wide range of
engineering disciplines. However, this book focuses on the following disciplines:
Structural Analysis: Deformation, stress, and strain fields, as well as
reaction forces in a solid body.
Thermal Analysis: Steady-state or time-dependent temperature field and
heat flux in a solid body.
2,2.1,1 Structural Analysis
This analysis type addresses several different structural problems, for
example:
FUNDAMENTALS OF ANSYS® 17
Static Analysis: The applied loads and support conditions of the solid
body do not change with time. Nonlinear material and geometrical properties
such as plasticity, contact, creep, etc., are available.
Modal Analysis: This option concerns natural frequencies and modal
shapes of a structure.
Harmonic Analysis: The response of a structure subjected to loads only
exhibiting sinusoidal behavior in time.
Transient Dynamic: The response of a structure subjected to loads with
arbitrary behavior in time.
Eigenvalue Buckling: This option concerns the buckling loads and
buckling modes of a structure.
2.2.1.2 Thermal Analysis
This analysis type addresses several different thermal problems, for
example:
Primary Heat Transfer: Steady-state or transient conduction, convection
and radiation.
Phase Change: Melting or freezing.
Thermomechanical Analysis: Thermal analysis results are employed to
compute displacement, stress, and strain fields due to differential
thermal expansion.
2.2.1.3 Degrees of Freedom
The ANSYS solution for each of these analysis disciplines provides nodal
values of the field variable. This primary unknown is called a degree of
freedom (DOF). The degrees of freedom for these disciplines are presented
in Table 2.1. The analysis discipline should be chosen based on the quantities
of interest.
Table 2.1 Degrees of freedom for structural and
thermal analysis disciplines.
Discipline
Structural
Thermal
Quantity
Displacement, stress, strain,
reaction forces
Temperature, flux
DOF
Displacement
Temperature