Doctoral Dissertation Abstract

The derivation of an analytical method to examine the stress field near the edge of a simply supported, laminated beam is presented. Specific effort has been directed to accurately calculate the transverse shear and normal stress by incorporating the exact displacement relations derived by Kozik (1970). A system of second order, ordinary, linear, non-homogeneous differential equations result, and a numerical and analytical technique is used for their solution. The method is a versatile stress analysis procedure which can accommodate any combination of material lay-up and any type of normal load on the upper and lower surface. The reactions at the ends of the beam may be distributed in a fashion most accurately characterizing the physical supports. Three such distributions are considered. As a basis for comparison with Bernoulli-Euler and Timoshenko theory, and all steel lay-up is examined. To demonstrate the method's capability of analyzing laminated beams, a two layered, steel / aluminum lay-up is examined. The method can also be used to: 1) analyze homogeneous beams having small length to height ratios, and 2) determine the stress field near concentrated loads anywhere in the beam.