Least-Squares Penalty-Constraint Finite Element Method For Generating Strain Fields From Moire Fringe Patterns

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Abstract
An essential phase in moire techniques is the generation of strain fields from optical fringe patterns. In this effort we explore a finite element method based upon a new least-squares penalty-constraint variational principle, which will be shown to be extremely effective in producing accurate, two-dimensional displacement and strain fields over the full-fringe domain. The approach encompasses the full-field analyses of optical fringes, which include: (1) an effective and theoretically sound noise filtering/smoothing and differentiating of the optical intensity fringes, from which displacement fringes are accurately determined, (2) subsequent smoothing/differentiating of the displacement fringes, producing continuous displacement and strain fields of high quality, (3) computational efficiency, (4) the ability to routinely process distorted mismatch fields which occur, for example, with large fields of view, avoiding the need for any special care to eliminate such distortion, (5) ease of implementation within a conventional finite element program. Several examples are carried out which demonstrate the attractiveness of the methodology.

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