Civil Engineering Reference
In-Depth Information
9
Finite Element Modeling of
Frames and Walls
9.1 Overview
9.1.1 Finite Element Analysis (FEA)
The rapid development of computers has completely revolutionalized research and practice
in every scientific and engineering field. The dream that every office and home would have a
computer terminal and/or personal computers has become a reality. Since the 1990s personal
computers have become as popular as pocket calculators were in the 1970s and slide rules
in the 1950s. Following this trend, analysis and design methods that provide computerized
solutions to scientific and engineering problems have been developing rapidly for increasingly
routine use. In this chapter, we focus on one such significantly developed method, the finite
element method. Although this method is applicable to many scientific and engineering fields,
we deal only with the field of structural analysis and design.
The finite element method has long been a fertile research field. It has also been increasingly
used as a research tool for numerical experiment. Most importantly, the finite element method
has become an analysis and design tool used routinely by structural engineers.
The finite element method in structural analysis is a technique that first divides a structure
into a set, or different sets, of structural components. The components of a particular set
would share some similar geometric pattern and physical assumption. Each pattern of such
components is called a specific kind of
finite element
. Each kind of finite element has a specific
type of structural shape and is interconnected with the adjacent elements by nodal points.
Acting at each node point are nodal forces, and the node is subjected to displacements
(degrees of freedom). In a general sense, these nodal physical quantities are not limited
to being forces and displacements, but extend to cases involving thermal, fluid, electrical,
and other problems. Thus for each element
,
a standard set of simultaneous equations can be
formulated to relate these physical quantities. Physically assembling these elements to form the
whole structure is equivalent to superimposing these element equations mathematically. The
result is a large set of simultaneous equations, which are suited for solution by computer. Upon
implementing the loading and boundary conditions for structural problems, the assembled set
