THE SEPARATION OF MEMBRANE AND BENDING SHEARS IN SHELLS WITH TWO BIREFRINGENT COATINGS
BROWN UNIV PROVIDENCE RI DIV OF ENGINEERING
Pagination or Media Count:
The directions and the differences of the principal membrane and bending stresses at a point of a shell or plate are calculated from the birefringence observed at normal incidence on two birefringent coatings, one on each face of the shell. A unique neutral surface is assumed, which is exact for identical coatings or for identical Poissons ratios in shell and coating. Explicit formulas are obtained with the simplifying approximations of a negligible effect of the rotation of the principal directions and of a linear variation of the magnitude of the principal stress-difference over the finite coating thickness. These assumptions are strictly valid for very thin coatings, but give also reasonably good results for ordinary birefringent coatings. The validity of the derived expressions was checked experimentally in square plates subjected to anticlastic bending and membrane stress of known magnitude at various orientations. Two types of tests were performed. At first 1 the membrane tension was applied through a series of pins in holes around the perimeter of a plate with relatively thick and optically insensitive coatings. Agreement between observed and calculated birefringence under these unfavorable conditions was reasonably good at the higher loads, but not good enough to permit an accurate inverse calculation of the stress-differences from the observed birefringence. The errors were found to be partly due to the difficulty of applying a true membrane force through pins without introducing any bending.
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