Consideration of a biaxially loaded photoelastic plate with an elliptical discontinuity using an inverse problem methodology

JAIME F. CÁRDENAS-GARCÍA ; SERGIO PREIDIKMAN

Buenos Aires

Congreso; MECOM 2005 - VIII Congreso Argentino de Mecánica Computacional; 2005

AMCA - Asociación Argentina de Mecánica Computacional

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.