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Inverse Problems in Nondestructive Evaluation

The detection of structural flaws in flexible structures is a very important problem in the aircraft industry. One idea for flaw detection involves embedding piezoceramic patches in composite viscoelastic members (in a so-called "smart material'' configuration). To test for cracks or delaminations, one can introduce a heat source on one side of the member. The temperature difference induces a deformation in the member, and this deformation generates a strain in the patch. An alternative test could involve production of strain via vibrations induced by the patches themselves. The polarized patch, in response to this strain, produces a voltage which can be monitored. Cracks and delaminations will of course produce different deformational behavior, and a question of great practical importance is whether the differences in deformation can be detected in a manner which characterizes the flaw. A third approach involves the use of SQUIDs (superconducting quantum interference devices) in detection of eddy current flow disruptions by internal damages.

The CRSC research program in this area focuses on mathematical and computational questions involved in developing reliable damage detection algorithms. In particular, researchers are currently developing differential equation models that describe the deformation of viscoelastic solids under high temperature gradients or due to vibrations induced by the piezoceramic patches themselves. The next step is to infer from the temperature or piezo inputs and measured viscoelastic responses the nature of the interior of the solid (that is, whether damage is present). For SQUID measurements, one must develop electromagnetic models for dielectrics with damage. For each of these, solving the differential equations and fitting the model to the observed data, computational methods play a crucial role. An important component of the research program is the development of efficient computer implementations, especially using distributed memory parallel machines and groups of workstations networked to allow parallel computation across the network. This research is a part of ongoing efforts in the CRSC on identification and control methodologies for ``smart material'' structures which are capable of self-excitation and self-sensing.

CRSC researchers on this project include H. T. Banks, K. Ito, M. Joyner and J. Peach. The efforts are in collaboration with NASA Langley Research Center scientists and scientists in Japan.











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