Evaluation of the Edge and Membrane Effects in Moderately Thick Beams by a Singular Perturbation Technique

摘要

Engineering theories in the analysis of stress and displacement fields embody many assumptions. While the tractability of these simplified models is enhanced, the validity of their solution becomes doubtful once the original assumptions are violated. Ordinary beam theory, for example, is obviously unsuitable for thick beam problems. As a matter of fact, it fails to describe the significant phenomena of membrane and end effects, which are physically apparent. As a first step toward developing a theory and a technique which will be applicable to other structural elements as well, the higher order mathematical models of an elastic, linear, homogeneous, isotropic, moderately thick beam are derived. A limiting case of the higher order equation, when depth-span ratio approaches zero, generalizes the Euler-Bernoulli beam equation. A singular perturbation technique is employed to obtain uniformly valid expansion solutions for the higher order equation. (Author)