Forward: There Are Still Plenty of Opportunities On the Boundaries

Yijun Liu



rizzo.gifThis is the second of the two special issues of Electronic Journal of Boundary Elements
in honor of Professor Frank Rizzo. There are thirteen technical papers in this issue,
contributed by Professor Rizzo’s colleagues, friends and former students. These papers
cover a broad range of topics in the boundary integral equation and boundary element
method (BIE/BEM), including Galerkin BEM for anisotropic elasticity (Gray, Griffith, et
al.), evaluations of hypersingular integrals in Galerkin BEM (Bonnet and Guiggiani),
Green’s function BEM for bimaterials (Denda), new 3-D Green’s functions for
piezoelectric bimaterials (Pan), new formulations using local integral equations (Sladek
and Sladek), BEM in sensitivity analysis with stress concentrations (Burczynski and
Habarta), fracture of thermopiezoelectric materials (Qin), BEM for 3-D gradient
elastodynamics (Polyzos, Tsepoura and Beskos), time-domain large-scale elastodynamic
analysis (Yoshikawa and Nishimura), acoustic BEM for analyzing mufflers and silencers
(Wu and Cheng), analysis of solids with randomly distributed inclusions (Yao, Kong and
Zheng), thermal and stress analyses of thermal barrier coatings (Lu and Dong), and
finally, modeling of carbon nanotube-based composites (Liu and Chen). These authors
are gratefully acknowledged for their excellent contributions, and for their patience and
cooperation in the process of preparing this special issue.
It is interesting to note that the wide applications of the elasticity BIE/BEM in
engineering all started with a simple idea. That is, boundary-value problems can be
solved by boundary-only methods. The first result in this direction is also amazingly
concise. During a recent trip to Urbana, Illinois, I checked out Professor Rizzo’s Ph.D.
dissertation from the UIUC library. The thirty-page dissertation is without doubt a
masterpiece that many current and future Ph.D. candidates may like to follow, for its
originality and succinct writing. The dissertation laid a solid foundation for what is now
called the BEM for elasticity and many other problems, and eventually led to the seminal
paper of 1967. Behind this masterpiece are Professor Rizzo’s affection and conviction in
the BIE/BEM and his willingness to explore a different route in research. This spirit of
exploration and his serious attitude in research have inspired and influenced many of his
former students and colleagues in the last forty years.
Researchers in the pursuit of boundary-only methods can be described as explorers in a
Flatland (see Professor Rizzo’s article in Issue No. 1). They can have different
perspectives, but can also discover treasures that others could not uncover. As younger
researchers come into this playground, new breakthroughs, just like the one made by
Professor Rizzo in the 1960s, may not be far away. There will certainly be more
innovative boundary-only methods emerging in the near future. More special numerical
tools will be developed and more emerging problems will be solved by these new
modeling tools. The fields of computational mechanics will be further diversified and
thus prosperous. There are still plenty of opportunities on the boundaries!

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