A hybrid/finite element is proposed to calculate stresses or stress intensity factors at notches, fillets, cutouts, or other geometric discontinuities in plane-loaded anisotropic materials. Stress and displacement fields assumed in the element satisfy all governing elasticity equations. Furthermore, the shape and stress-free conditions of the discontinuity are modeled exactly using conformal mapping and analytic continuation. Continuity of analytic and finite element displacement fields on the remaining element boundary are enforced in an approximate manner with a variational principle. Numerical results are presented for both elliptical void and circular fillet hybrid elements. Comparisons are made to analytic solutions. Results indicate that structural models using a hybrid element with a coarse conventional element mesh yield efficient and accurate calculations of critical stresses.
Current shear design technology in the United States for lumber or glued-laminated beams is confusing. This report summarizes shear stress and strength research including both analytical and experimental approaches. Both checked and unchecked beams are included. The analytical work has been experimentally verified for only limited load conditions and span-to-depth ratios. Future research is required to better define the effects of beam size, load configuration, checks, and combined stresses on shear design.
A closed-form elasticity solution is developed to predict stresses and strains in spiral paper tubes loaded axisymmetrically. No assumptions are made on stress distributions through the tube wall. Thus, the solution is valid for thick-walled tubes. The validity of this solution is established by comparison with experimental results. Measured strains in tubes subjected to external pressure showed remarkable agreement with the elasticity solution. After experimental verification, the elasticity solution is used to examine stress distributions in paper tubes loaded in external pressure. In both paper and isotropic tubes, the hoop stress dominates the other three stresses. However, the hoop stress distribution in paper tubes was radically different from the isotropic case. In paper tubes: (1) hoop stress was concentrated at the outer wall, especially for thicker tubes and (2) maximum hoop stress remained constant as tube thickness was increased. These differences can be attributed to the extremely small modulus in the radial direction of a paper tube. The hoop stress distributions indicate that isotropic, thick-walled cylinder theory is inapplicable for modeling paper tubes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.