Approximate Calculation of the Inclination Angle of Beams with Variable Cross Sections

In this paper a new approximate procedure is developed for calculating the inclination angle of the end points of statically determinate beams. The method is based on the topology comparison of simple (hinge-roller combination) supported beam and a resemblant cantilever beam. Assuming that the support reactions of the beam are active forces, the virtual displacements at the points of the reaction forces are calculated. Based on these values the inclination angle is calculated. Several examples are considered and the suggested in this paper, while the procedure is applied for various types of structures and loadings. The results, obtained by the suggested numerical procedure, are compared with analytical ones, and they are in good agreement.

Approximate Calculation of the Inclination Angle of Beams with Variable Cross Sections

In this paper a new approximate procedure is developed for calculating the inclination angle of the end points of statically determinate beams. The method is based on the topology comparison of simple (hinge-roller combination) supported beam and a resemblant cantilever beam. Assuming that the support reactions of the beam are active forces, the virtual displacements at the points of the reaction forces are calculated. Based on these values the inclination angle is calculated. Several examples are considered and the suggested in this paper, while the procedure is applied for various types of structures and loadings. The results, obtained by the suggested numerical procedure, are compared with analytical ones, and they are in good agreement.

Maximal concurrent minimal cost flow problems on extended multi-cost multi-commodity networks

The graph is a great mathematical tool, which has been effectively applied to many fields such as economy, informatics, communication, transportation, etc. It can be seen that in an ordinary graph the weights of edges and vertexes are taken into account independently where the length of a path is the sum of weights of the edges and the vertexes on this path. Nevertheless, in many practical problems, weights at vertexes are not equal for all paths going through these vertexes, but are depending on coming and leaving edges. Moreover, on a network, the capacities of edges and vertexes are shared by many goods with different costs. Therefore, it is necessary to study networks with multiple weights. Models of extended multi-cost multi-commodity networks can be applied to modelize many practical problems more exactly and effectively. The presented article studies the maximal concurrent minimal cost flow problems on multi-cost and multi-commodity networks, which are modelized as optimization problems. On the base of the algorithm to find maximal concurrent flow and the algorithm to find maximal concurrent limited cost flow, an effective polynomial approximate procedure is developed to find a good solution.

Minimum orbital intersection distance: an asymptotic approach

The minimum orbital intersection distance (MOID) is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications. The most frequent case is that in which both objects have elliptical osculating orbits. When at least one of the two orbits has low eccentricity, the latter can be used as a small parameter in an asymptotic power series expansion. The resulting approximation can be exploited to speed up the computation with negligible cost in terms of accuracy. This contribution introduces two asymptotic procedures into the SDG-MOID method for the computation of the MOID developed by the Space Dynamics Group (SDG) of the Technical University of Madrid and presented in a previous article, it discusses the results of performance tests and their comparisons with previous findings. The best approximate procedure yields a reduction of 40% in computing speed, without degrading the accuracy of the determinations. This result suggests that some benefits can be obtained in applications involving massive distance computations, such as in the analysis of large databases, in Monte Carlo simulations for impact risk assessment, or in the long-time monitoring of the minimum orbital intersection distance between two objects.

Variable Preloading Force in an Archetypal Oscillator

In this paper, the influence of the time variable preloading force on the vibration of an archetypal oscillator is investigated. The oscillator is modeled as a slider-string system which is mathematically described with a second order nonlinear differential equation with time variable parameters. An approximate procedure for solving the equation is introduced. It is based on the exact solution of the pure nonlinear equation in the form of the Ateb function. The obtained result gives the vibration amplitude and phase variation of the oscillator depending on the preloading force variation. Based on this result, the procedure for regulation of the preloading force as the function of the required vibration amplitude decrease is developed. It is concluded that the preloading force may be used as a control parameter of the oscillator.

Comparison between the AFNOR Method and the Imposition of Balanced Maximum Specific Sliding in the Imposed Centre Distance Problem

Successive editions of Henriot’s treatise on gears, and an AFNOR document, present an approximate procedure for the choice of profile shift values for the pinion and wheel when a center distance value is imposed in a cylindrical gear pair. That procedure aims at achieving an approximate balancing of the maximum specific sliding values of the pinion and of the wheel. The method involves a loosely defined choice of an auxiliary parameter, but no information is available relating this choice with the level of attainment of the intended balancing of maximum specific sliding values. This assessment, if needed, requires a subsequent analysis for verification.Since no information is available evaluating the procedure, the purpose of this work is to provide a thorough rigorous analysis of the method, highlighting its qualities but also its shortcomings.

Thermal Protection of the Cylindrical Polymer Covering on the Steel Nipple of a Rubber Branch Pipe during Electric Welding

A thermal calculation of the steel nipple of a rubber branch pipe, under conditions of water cooling of the nipple, during its welding to a reciprocal part is carried out. The limit temperature in the control section – the initial boundary of the rubber covering of the nipple – that guarantees conservation of the covering is assumed to be 363 K. Heating and boiling of the cooling water are considered. A theoretical substantiation of technical solutions to protect the polymer from thermal breakdown is put forward. Comparison of calculated temperature fields shows good agreement between results obtained by the proposed approximate procedure and results obtained using the ComSol program package, which makes it possible to calculate regimes rapidly under industrial conditions.