The Separation of Membrane and Bending Shears in Shell With Two Birefringent Coatings

The determination of magnitude and principal direction of membrane and bending stress differences in plates or thin shells requires four independent items of information, such as the photoelastic retardations and principal directions in two birefringent coatings, one on each face. However, the superposition of a constant membrane and a linearly varying bending stress in general result in a change of direction of the total principal stress through the finite coating thickness. Such rotation of stress introduces considerable difficulties even in the direct determination of the photoelastic effect in known stress fields, and makes the inverse solution of stress distribution from birefringence impossible without additional techniques and data. This paper presents an explicit approximate inverse solution based on simple photoelastic observations in the two coatings, with only partial consideration of the effects of rotation. In its double, reversing path through a coating, polarized light is assumed to suffer the same changes as in a field of linearly varying stress of constant direction parallel to that at incidence and exit. The validity of the direct and inverse solutions was checked experimentally in square plates containing residual membrane stress and subjected to anticlastic bending of various magnitudes and directions. Agreement was very good, especially at the higher loads, even when large stress rotation occurred. Criteria for recognizing potentially inaccurate states with large rotation are also suggested. The proposed method should prove useful in the experimental study of shells.