Review of continuum, finite element and hybrid techniques in the analysis of stress concentrations in structures

When a uniform flow of any nature is interrupted, the readjustment of the flow results in concentrations and rare-factions, so that the peak value of the flow parameter will be higher than that which an elementary computation would suggest. When stress flow in a structure is interrupted, there are stress concentrations. These are generally localized and often large, in relation to the values indicated by simple equilibrium calculations. With the advent of the industrial revolution, dynamic and repeated loading of materials had become commonplace in engine parts and fast moving vehicles of locomotion. This led to serious fatigue failures arising from stress concentrations. Also, many metal forming processes, fabrication techniques and weak-link type safety systems benefit substantially from the intelligent use or avoidance, as appropriate, of stress concentrations. As a result, in the last 80 years, the study and and evaluation of stress concentrations has been a primary objective in the study of solid mechanics. Exact mathematical analysis of stress concentrations in finite bodies presents considerable difficulty for all but a few problems of infinite fields, concentric annuli and the like, treated under the presumption of small deformation, linear elasticity. A whole series of techniques have been developed to deal with different classes of shapes and domains, causes and sources of concentration, material behaviour, phenomenological formulation, etc. These include real and complex functions, conformal mapping, transform techniques, integral equations, finite differences and relaxation, and, more recently, the finite element methods. With the advent of large high speed computers, development of finite element concepts and a good understanding of functional analysis, it is now, in principle, possible to obtain with economy satisfactory solutions to a whole range of concentration problems by intelligently combining theory and computer application. An example is the hybridization of continuum concepts with computer based finite element formulations. This new situation also makes possible a more direct approach to the problem of design which is the primary purpose of most engineering analyses. The trend would appear to be clear: the computer will shape the theory, analysis and design.

Group fission in Nilgiri langurs (Presbytis johnii)

During a field study on habituated groups of wild Nilgiri langurs (Presbytis johnii), four cases of group fission were observed which differed markedly from group changes reported in other species of the same genus. All fissions occurred in groups with more than one mature male and roughly coincided with the onset of loud call vocalization by the second mature male group member. As a result of the fission the founder group factions acquired the structure of a onemale group. The filial factions consisted of both mature males and females and occupied, at least temporarily, a part of, or an area adjacent to, the founder group. During fission, the amount of aggressive interactions between the two mature males increased. However, the majority of agonistic interactions involved ritualized threat and intimidation behavior without physical aggression. In at least three cases the two mature males involved in the fission had not joined recently but had lived in these groups for three years or more. Although the presence of all male bands and single males in the two study populations indicate that male replacement by invasive takeovers may occur, it is suggested that in Nilgiri langurs, noninvasive fissions are probably another common mechanism for the foundation and maintenance of bisexual one-male groups.