The
computer revolution is profoundly impacting how scientists and engineers
can conduct their professional activities.
In the late 1950s, a computer fully occupied, and amply heated
(!), a space the size of a classroom.
The PC, introduced in the mid-1970s, started life as a “toy.” Yet by the millennia, Linux clusters of cheap gigahertz PCs
can execute truly large scale computational mechanics simulations.
Indeed, we now have the “desktop Cray” that was fantasized in
1980!
The
companion maturation of computational mechanics theory and practice has
been an evolutionary (not revolutionary!) process, and is highly
fragmented by discipline. Computational
fluid dynamics (CFD) and computational structural mechanics (CSM)
emerged simultaneously from the research laboratory in the late 1950s.
The former relied on finite difference (FD) methods to convert
theory to practice. Conversely,
the latter’s classical virtual work concept enabled a finite element
(FE) approximation for the underlying variational principle. Then in
chemical engineering, collocation methods enabled process simulations,
and on the surface these theories appeared absolutely “linearly
independent” of each other.
Research
completed in the last decade has proven that practically all theories
supporting computational continuum mechanics can be formulated as the
extremum of the mathematicians’ “weak form,” termed a “weak
statement (WS).” The weak
form process readily supports all
theorization using calculus, vector field theory and modern
approximation concepts. When completed, the discretized implementation of the
extremum can be accomplished using FE, FD and/or finite volume (FV)
procedures. The FE
implementation is guaranteed optimal
in its mathematical performance, i.e., accuracy, convergence rate, etc.
and in precise construction through the use of analytical calculus.
This
text develops FE implementation of WS algorithms for an expansive range
of problem statements in the engineering sciences.
Based on the view that “theory is fine, but show me the
numbers,” every developed aspect is converted to computational syntax
via “templates” capitalizing on object-oriented concepts.
Thereafter, introductory level problems are solved using Matlab
via a graphical user interface (GUI) to a specifically developed “Matlab toolbox.” More comprehensive
problem statement FE algorithms are exercised via FEMLAB, a commercial equation-driven expert system
interfacing Matlab.
Thereby, the student interacts with the concept of a problem
solving environment (PSEs) amenable to significant extension for handling
genuine problem statement complexities.
In
summary, FEm.PSE fully
develops modern FE discrete modeling, with applications aimed at available and emergent
PSEs. It’s
organization and content has benefited from a decade and a half of
teaching the material, and fully obsoletes the predecessor 1991 textbook
(with “spaghetti” PC code on a 5.25 floppy disk).
Further, the maturation is now fully Internet-enabled, with the
UT CFD Lab website supporting time-and distance-insensitive video-streaming of
both undergraduate and graduate courses for the full compliment of lectures.
An appendix contains the Matlab Primer, a
just-in-time reference. The
full compliment of computational test examples, the Matlab toolbox and
select lectures taken from the Internet course are on the included CD.
If you care, go to cfdlab.engr.utk.edu/Internet
to explore experiencing the millennial virtual
classroom!
