Dynamics of a class of vortex rings

The contour dynamics method is extended to vortex rings with vorticity varying linearly from the symmetry axis. An elliptic core model is also developed to explain some of the basic physics. Passage and collisions of two identical rings are studied focusing on core deformation, sound generation and stirring of fluid elements. With respect to core deformation, not only the strain rate but how rapidly it varies is important and accounts for greater susceptibility to vortex tearing than in two dimensions. For slow strain, as a passage interaction is completed and the strain relaxes, the cores return to their original shape while permanent deformations remain for rapidly varying strain. For collisions, if the strain changes slowly the core shapes migrate through a known family of two-dimensional steady vortex pairs up to the limiting member of the family. Thereafter energy conservation does not allow the cores to maintain a constant shape. For rapidly varying strain, core deformation is severe and a head-tail structure in good agreement with experiments is formed. With respect to sound generation, good agreement with the measured acoustic signal for colliding rings is obtained and a feature previously thought to be due to viscous effects is shown to be an effect of inviscid core deformation alone. For passage interactions, a component of high frequency is present. Evidence for the importance of this noise source in jet noise spectra is provided. Finally, processes of fluid engulfment and rejection for an unsteady vortex ring are studied using the stable and unstable manifolds. The unstable manifold shows excellent agreement with flow visualization experiments for leapfrogging rings suggesting that it may be a good tool for numerical flow visualization in other time periodic flows

AFIT School of Engineering Contributions to Air Force Research and Technology Calendar Year 1973

This report contains abstracts of Master of Science Theses, Doctoral dissertations, and selected faculty publications completed during the 1973 calendar year at the School of Engineering, Air Force Institute of Technology, at Wright-Patterson Air Force Base, Ohio

AFIT School of Engineering Contributions to Air Force Research and Technology Calendar Year 1973

This report contains abstracts of Master of Science Theses, Doctoral dissertations, and selected faculty publications completed during the 1973 calendar year at the School of Engineering, Air Force Institute of Technology, at Wright-Patterson Air Force Base, Ohio

Residual stress and fatigue crack growth life prediction in fastener holes cold-worked by uniform indentation in 2024-T351 aluminium alloy

This thesis concerns primarily the residual stress characterisation in fastener holes coldworked by a novel StressWave process, and the prediction of the fatigue crack growth under the influence of such residual stress. Aerospace 2024—T351 aluminium alloy plate of 6.35 mm thickness containing a nominal 06.35 mm hole was used. Using neutron and laboratory X-ray diffraction measurements, a large compressive residual stress was found in StressWave and split-sleeve cold-worked holes. Detailed stress mapping indicates that a StressWave hole contains a highly symmetric residual stress field with a wider compressive region. Conversely, the split-sleeve technique generates a complex asymmetric stress variation through the specimen thickness and around the hole. Independently, a comprehensive finite element study was conducted to reveal the residual stress development associated with the two distinct cold-working techniques at various stages. Favourable agreement was achieved between the experiment and simulations. The deformation mechanism associated with the cold-working process is decisive to the behaviour of the residual stress field created. The symmetric crack growth behaviour observed in StressWave specimens permits a through-thickness crack geometry to be considered. Accordingly, Green’s functions for a single crack and two symmetric cracks originating from the edge of a circular hole were developed. These solutions were verified using weight function and finite element analysis and are therefore appropriate for subsequent study of fatigue crack growth. A theoretical framework was proposed to explicate the interaction of residual stress with the superimposed loading at the crack tip, which was mathematically expounded as a function of stress intensity factor and stress ratio. This analytical framework provides a reasonable correlation between the mean stress and crack closure criteria. As a demonstration, a finite-width plate containing a centre hole with a single crack, with surface residual stress measured by X-Ray diffraction was analysed. It was revealed that for a predictive task, both the mean stress and crack closure definitions necessitate different requirements of material database and parametric definitions. Next, the fatigue testing suggested that the fatigue durability of fastener holes treated by the StressWave method generally outperformed those observed for split-sleeve samples. Prediction according to the unified theory produced encouraging results matching the experimental fatigue crack growth measurement. Detailed analysis showed that suitable parametric calibration and the appropriate use of crack models were imperative to achieve reliable prediction. Future efforts necessary for accuracy of prediction work for StressWave cold-worked holes are discussed

Survey and development of finite elements for nonlinear structural analysis. Volume 1: Handbook for nonlinear finite elements

A survey of research efforts in the area of geometrically nonlinear finite elements is presented. The survey is intended to serve as a guide in the choice of nonlinear elements for specific problems, and as background to provide directions for new element developments. The elements are presented in a handbook format and are separated by type as beams, plates (or shallow shells), shells, and other elements. Within a given type, the elements are identified by the assumed displacement shapes and the forms of the nonlinear strain equations. Solution procedures are not discussed except when a particular element formulation poses special problems or capabilities in this regard. The main goal of the format is to provide quick access to a wide variety of element types, in a consistent presentation format, and to facilitate comparison and evaluation of different elements with regard to features, probable accuracy, and complexity

3D non-linear and multi-region boundary element stress analysis

The new findings can be outlined as follows: Two new simple auxiliary equations which are required to supplement the fundamental boundary integral equations in solving traction-discontinuity problems using multiple-node technique are derived from the symmetric property and the equilibrium equations of the stress tensor. These equations have been used to deal with the corners and edges of single region and multi-region problems. A sub-structure algorithm is developed for solving multi-region problems with corners and edges, using the derived auxiliary equations. This algorithm can deal with nodes where more than two materials intersect.A novel infinite element formulation suitable for multi-layered media was developed. In particular, a set of useful analytical expressions was derived for evaluating strongly singular surface integrals over the infinite surface. A set of unified elastoplastic constitutive relationships dealing with hardening, softening and ideal plasticity behaviour is derived from the Il'iushin postulate in strain space. These relationships are suitable for both small and finite deformation rate-independent elastoplastic problems. Some new identities are derived for the initial stress and strain kernels. Based on these, a new transformation technique from domain integrals to cell boundary integrals is developed, for accurate evaluation of the strongly singular domain integrals pertaining to interior stresses. Two new iterative schemes are introduced for the first time in the incremental variable stiffness method for solving the non-linear system of equations. In particular, in the second one, a novel assembly process was proposed, in which the system equations are expressed in terms of the plastic multiplier.These formulations have been implemented within a Fortran computer code and illustrative numerical examples have been solved to demonstrate its practical utility