Consideration Of A Biaxially Loaded Photoelastic Plate With An Elliptical Discontinuity Using An Inverse Problem Methodology.

Abstract

The direct problem of an elliptical hole in a uniaxially and biaxially loaded,
homogeneous, isotropic infinite plate in plane stress is a classical result that has been
extensively studied, especially in relation to the assessment of cracks in plates. This
theoretical formulation leads naturally into consideration of relevant inverse problems based
on using full field stress data, in the form of photoelastic fringes or lines of maximum shear
stress. The resulting inverse problems are twofold: (a) from known geometry, biaxial loading
and photoelastic response around the elliptical hole determine the material stress fringe
value; and, (b) from known geometry, stress fringe value and photoelastic response around
the elliptical hole determine the applied far-field loads. Modeling of the elliptical hole in a
plate is approached analytically and using finite elements (FE). The inverse problem
methodology used relies on least-squares optimization. Initial comparison between the
analytical and FE approaches shows that for the experimental results of interest the FE
approach should yield better comparisons. Application of the inverse problem methodology
allows seamless integration between the FE model results and experimental photoelastic
results. The robustness of this approach is tested using noisy data.