This article presents the ovalization and critical ovalization of round-hole tubes (RHT) with a redundant hole (RDH) submitted to cyclic bending. In this study, 6061-T6 aluminum alloy round-hole tubes (Al-RHTs) with a fixed hole diameter of 2, 4, 6, 8 or 10 mm were drilled to acquire an RDH of the same size on the same cross section but at different positions: 45°, 90°, 135°, and 180°. It was found that the ovalization–curvature curve demonstrated ratcheting, asymmetrical, increasing, and bowtie-like trends as the number of cycles increased. The RDH position showed substantial influence on the relationship. Furthermore, larger hole diameters caused larger tube’s ovalizations. Although the Al-RHTs were tested with five different hole diameters and different RDH positions, the relationship between the critical ovalization and the controlled curvature relationships in a log–log scale displayed nonparallel straight lines for each hole diameter. Finally, a theoretical formula was proposed to simulate the above relationships. The simulation result was compared with the experimental results, and it was found that the theoretical analysis could reasonably reproduce the experimental results.
Neutralism is an absence of any interaction between members of a mixed population. i.e, The species may be living side by side but are unaware of each other and also cause no harm or nor beneficial to each other. A real life example is rabbits, deer, frogs live together in a grass land with no interaction between them. This paper is devoted to an ecological study on three species neutralism. Here all the three species S1, S2 and S3 posses limited resources and with growth rates. The model equations constitute a set of three first order non-linear simultaneous differential equations. Criteria for the asymptotic stability of all the eight critical points are established. The system would be stable if all the characteristic roots are negative.
Some bi-level linear programming problems are proposed under randomness and fuzziness. In this paper, we have introduced stochastic fuzzy bi-level linear programming problems with the right hand side parameters of the constraints in both first level\nand second level as cauchy random variables with known probability distributions. Rests of the model parameters are assumed to be triangular and trapezoidal fuzzy\nnumbers. After removing the randomness and fuzziness, the crisp equivalent deterministic bi-level programming models are established by using Mellin transformation. Then the models are solved by using K-th best approach. \nTo exemplify the utility of the proposed methodology a numerical example is demonstrated