Introduction to Finite Element Modeling | 6

Real-life systems and structures, such as civil structures, bridges, piping
systems, etc., are continuous systems. The mathematical modeling using
the standard differential equations based on theory may be complicated for
such systems, and their solution would be even more complex. However, the
mathematical models are important for several requirements, which include
design, impact of design modification, vibration behavior, etc. Any small
change in the system may require complete new formulation all over again
using the standard differential equations based on the elasticity theories
(Fenner, 1986). Considering these difficulties, nowadays the finite element
(FE) modeling method is most popular, well accepted, and useful to meet
the requirements perhaps in a much simpler than the earlier approach. The
simplified concept of the FE method is presented in this chapter through
a few simple examples to aid understanding and visualizing of FE modeling and analysis either through in-house developed computational code or
through any commercially available FE codes. The well-known textbooks by
Zienkiewicz and Taylor (1994) and Cook et al. (1989) can be referred to for
further details of the FE method and modeling if needed.