Project Abstract:
Modern engineering analysis requires accurate, reliable and efficient
evaluation of outputs of interest. Typical outputs of interest include
critical stresses or strains, or measures of temperature are used as
ultimate measurements of system performance. These outputs are
functions of “input” parameter that serve to describe a particular
configuration of the system, typical input geometry, material
properties, or boundary condition and loads. In many case, the
input-output relationship is usually a functional of the field variable – which is the solution to an input-parametrized partial differential
equations (PDE). The reduced-basis approximation, adopting
off-line/on-line computational procedures, allows us to compute
accurate–and reliable functional outputs of PDE. The operation
count for the on-line stage depends only on a small number
N and the parametric complexity of the problem, which make the
reduced-basis approximation especially suitable for complex
analysis such as optimizations and designs.
In this work we focus on the development of finite-element and
reduced-basis methodology for the accurate, fast, and reliable
prediction of critical stress factors related to failure and crack growth
in solids. In particular, stress intensity factors or strain-energy release
rate are used to characterize the stress and strain fields at cracks,
thus can be used to predict crack growth in elastic bodies. We
applied the reduced-basis approximation to fracture mechanic
problems to evaluate outputs such as stress intensity factors and
the J-integral quantities. With the use of off-line/on-line
computational strategy, stress intensity factors for an arbitrary
particular problem can be obtained in seconds.
The method opens a new promising prospect: not only the
numerical results can be obtained only in seconds with great savings
in computational time but also are rigorously and robustly – thanks
to the rigorous and sharp a posteriori error bound estimation.
Complex analysis such as crack propagation simulation or fatigue
estimation can be done in real-time and are certified.
Keywords: reduced-basis approximation, fracture mechanics |
