Boundary Shape Identification Problems in Two-Dimensional Domains Related to Thermal Testing of Materials.
Abstract
Domain identification problems are important in the design of engineering systems and frequently such problems are treated as a branch of the calculus of variations which involves nonlinear optimization techniques, optimal control theory, partial differential equations (elliptic, parabolic, hyperbolic, etc.) and related numerical methods. Domain identification for elliptic systems has been studied theoretically and numerically by many others. For parabolic systems, a couple of numerical methods for identifying the domain or boundary have been investigated. In this paper, our concern for domain identification is motivated by an application that is different from these shape design problems. However, as we shall see, the resulting theoretical aspects are closely related. Recently, associated with the use of fiber reinforced composite materials for aerospace structures, there is growing interest in the detection and characterization of large structural flaws which may not be detectable by visual inspection. One recent effort has focused on non-destructive evaluation methods (NDE) based on the measurement of thermal diffusivity in composite materials. Motivated by these problems, we consider the domain identification for parabolic systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1988
- Accession Number
- ADA194917
Entities
People
- Fumio Kojima
- H. Thomas Banks