Project Abstract:
This project focuses on the development of methods for the
efficient calculation of lower and upper bounds to outputs which
are functionals of the solutions to partial differential equations.
Such methods are extremely useful in engineering design where
outputs, such as temperatures, displacements and stresses
are needed at critical locations, provided of course that the
methods are accurate, efficient and inexpensive. Obviously,
coarse element discretizations are inexpensive but rather
inaccurate, while fine element discretizations are accurate but
expensive. The aim is to find methods which possess both accurate
and inexpensive characteristics, and which can also be implemented
with little difficulty in multiprocessor environments. In particular,
the primary objective of this project is to extend the recent work
of Patera and Peraire to fracture mechanics problems, where lower
and upper bounds to stress intensity factors will be of importance
to fracture-resistant design. This has been successfully achieved
for stress intensity factors in homogeneous and bimaterial crack
problems obtained with the displacement extrapolation method,
and for J-integral with a novel method which can treat the quadratic
functionals. Now we are computing the bounds to the exact values
of J-integral.
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