THE UNIVERSITY OF CALGARY Eric Snively A ... - Ohio University

forces are applied to nodes on the surface of the model. Boundary conditions,
which are constraints on the movement of elements and the displacement of
nodes, are also applied. Some nodes, typically at one end or side of a model, are
set to a boundary condition of zero displacement, as though the mode1 is fixed to
an immobile surface. Otherwise, little strain would occur at intemal nodes unless
tremendous energies were applied, and forces would cause the entire structure
to accelerate.
Boundary conditions, forces, and material properties are entered into a finite
element computer program. The program then solves the resulting systems of
Iinear equations, typically by Gaussian elimination. While this algorithm is tenable
for the solution of simple matrix equations by hand, the huge number of nodes in
a finite element model necessitates intensive use of computer resources.
Finite element stress modeling has a nurnber of practical and scientific
applications. FEA is a common procedure for investigating material stresses and
strains in engineering (Chandrupalta and Belegundu 1997). In modeling 30
solids, a sufficiently large number of elements approximates the continuity of the
original object. The finite element method is therefore able to accurately simulate
and predict stress-strain relationships in physical structures, if the correct values
for material properties are supplied. FEA provides crucially accurate predictions
for airfrarne and automotive design (Belytschko et al. 1975), and biomedical
engineering (Taylor et ai. 1998). The accuracy af the method thus has imrnediate
benefits for vehicle and building safety, as well as for the development of medical
prostheses.