### 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.

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.

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**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**