scholarly journals Change in the amplitude of strong discontinuity wave propagating in a rod made of Murnaghan material

2021 ◽  
Vol 2131 (2) ◽  
pp. 022117
Author(s):  
M Major ◽  
I Major ◽  
B Yazyev

Abstract The paper presents calculations of the change in amplitude of strong discontinuity wave propagating in a thin rod made of hyperelastic Murnaghan material. Two functions were assumed for the calculations, describing the change of the cross-section of the rod with the constant scaling parameter?for both decreasing cross-sections of the analysed steel rods. A numerical analysis was performed based on analytical solutions. The analytical form of solution for both rods with decreasing cross-sections allowed for preparation of contour maps for the propagating wave of strong discontinuity. Furthermore, the changes in the relative amplitude of the propagating shock wave in a thin rod were determined for two rods analysed in the study, for which the differences in the values of the relative amplitude in the final cross-section were found.

2018 ◽  
Vol 219 ◽  
pp. 02002
Author(s):  
Małgorzata Gordziej-Zagórowska ◽  
Elżbieta Urbańska-Galewska

The influence of eccentricity at intersections of truss members on the load carrying capacity of the truss joint is presented in the paper. The research truss elements were designed as cold-formed open cross section. Analytical calculations, numerical analysis and experimental research were conducted to reveal how the eccentricity affects the effort of material in the joint area. The results of analysis and investigations are compared and discussed. The main achievement of the tests carried out is statement that slender plane members of the compression chords are safe compared with the results of analytical calculations.


2008 ◽  
Vol 3 (2) ◽  
pp. 081-095
Author(s):  
Małgorzata Dobrowolska ◽  
Marta Słowik

In the paper there is presented the algorithm of calculation of normal stresses in reinforced concrete three-flue chimney. The calculation has been made for full cross-section and for cross-section weakened by openings. The governing equations has been derived in an analytical form assuming linear physical laws for concrete and steel and, as for as considered cross-section weakened by openings, taking into account the additional reinforcing steel bars at the openings. In addition coefficients B and C have been determined, which are useful at dimensioning.


2014 ◽  
Vol 621 ◽  
pp. 107-112 ◽  
Author(s):  
Bogdan Szybiński ◽  
Paweł Romanowicz

Cylindrical pressure vessels with circular cross section are commonly used in the construction of various pressure apparatus; however in certain cases other cross sections are applied. The vessels with rectangular and elliptical perpendicular cross section are of the main interest and certain formulas for their calculations are stated in the respective codes [1, 2]. In these appliances flat ends of various shapes are usually used as the vessels caps. Similarly, as for the cylindrical boilers, flat end plates with stress relieve grooves are recommended. Like in the flat ends for cylindrical pipes certain variation of the groove parameters is possible but again no clear suggestion is given how to choose the optimal groove parameters providing the minimum stress concentration [3]. In this paper the numerical analysis and optimization of the admitted by code [1] groove parameters is presented for the pipe with the rectangular cross section subjected to the internal pressure.


Author(s):  
Camila A Correa

Abstract The observed anti-correlation between the central dark matter (DM) densities of the bright Milky Way (MW) dwarf spheroidal galaxies (dSphs) and their orbital pericenter distances poses a potential signature of self-interacting dark matter (SIDM). In this work we investigate this possibility by analysing the range of SIDM scattering cross section per unit mass, σ/mχ, able to explain such anti-correlation. We simulate the orbital evolution of dSphs subhaloes around the MW assuming an analytical form for the gravitational potential, adopting the proper motions from the Gaia mission and including a consistent characterization of gravitational tidal stripping. The evolution of subhalo density profiles is modelled using the gravothermal fluid formalism, where DM particle collisions induce thermal conduction that depends on σ/mχ. We find that models of dSphs, such as Carina and Fornax, reproduce the observed central DM densities with fixed σ/mχ ranging between 30 and 50 cm2g−1, whereas other dSphs prefer larger values ranging between 70 and 100 cm2g−1. These cross sections correlate with the average collision velocity of DM particles within each subhalo’s core, so that systems modelled with large cross sections have lower collision velocities. We fit the cross section-velocity correlation with a SIDM particle model, where a DM particle of mass mχ = 53.93 ± 9.81 GeV interacts under the exchange of a light mediator of mass mφ = 6.6 ± 0.43 MeV, with the self-interactions being described by a Yukawa potential. The outcome is a cross section-velocity relation that explains the diverse DM profiles of MW dSph satellites and is consistent with observational constraints on larger scales.


2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Vu Truong Vu

The paper presents the optimization of toroidal shell cross-sections under internal pressure. The wall thickness distribution along a circular centerline is derived in an analytical form. In membrane solution, this cross-section gives a constant Mises stress all over the shell. Therefore, it leads to material saving and contained volume increase in comparison with the traditional cross-section of circular constant thickness. The optimum shapes are designed for two states of shell, one is elasticity and the other is up to destruction. The maximum material saving can reach 70% in some configurations of toroid. Results of the proposed method are as good as or better than those found in literature.


1972 ◽  
Vol 25 (3) ◽  
pp. 247
Author(s):  
JL Cook

Over restricted energy ranges, the Adler?Adler method. of parameterizing resonance cross sections is in general the exact result of inverting the channel matrix. This provides a simple analytical form for the cross section which can be used in reactor physics calculations.


2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Ali Tamayol ◽  
Majid Bahrami

Analytical solutions are presented for laminar fully developed flow in micro-/minichannels of hyperelliptical and regular polygonal cross sections in the form of compact relationships. The considered geometries cover a wide range of common simply connected shapes including circle, ellipse, rectangle, rectangle-with-round-corners, rhombus, star-shape, equilateral triangle, square, pentagon, and hexagon. A point matching technique is used to calculate closed form solutions for the velocity distributions in the above-mentioned channel cross sections. The developed relationships for the velocity distribution and pressure drop are successfully compared with existing analytical solutions and experimental data collected from various sources for a variety of geometries, including polygonal, rectangular, circular, elliptical, and rhombic cross sections. The present compact solutions provide a convenient and power tool for performing hydrodynamic analyses in a variety of fundamental and engineering applications such as in microfluidics, transport phenomena, and porous media.


2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Flávio Arrais ◽  
Nuno Lopes ◽  
Paulo Vila Real

PurposeSigma cross-section profiles are often chosen for their lightness and ability to support large spans, offering a favourable bending resistance. However, they are more susceptible to local, distortional and lateral-torsional buckling, as possible failure modes when compared to common I-sections and hollow cross-sections. However, the instability phenomena associated to these members are not completely understood in fire situation. Therefore, the purpose of this study is to analyse the behaviour of beams composed of cold-formed sigma sections at elevated temperatures.Design/methodology/approachThis study presents a numerical analysis, using advanced methods by applying the finite element software SAFIR. A numerical analysis of the behaviour of simply supported cold-formed sigma beams in the case of fire is presented considering different cross-section slenderness values, elevated temperatures, steel grades and bending moment diagrams. Comparisons are made between the obtained numerically ultimate bending capacities and the design bending resistances from Eurocode 3 Part 1–2 rules and its respective French National Annex (FN Annex).FindingsThe current design expressions revealed to be over conservative when compared with the obtained numerical results. It was possible to observe that the FN Annex is less conservative than the general prescriptions, the first having a better agreement with the numerical results.Originality/valueFollowing the previous comparisons, new fire design formulae are analysed. This new methodology, which introduces minimum changes in the existing formulae, provides at the same time safety and accuracy when compared to the numerical results, considering the occurrence of local, distortional and lateral-torsional buckling phenomena in these members at elevated temperatures.


1962 ◽  
Vol 29 (1) ◽  
pp. 40-46 ◽  
Author(s):  
M. B. Friedman ◽  
R. Shaw

The two-dimensional problem of the diffraction of a plane acoustic shock wave by a cylindrical obstacle of arbitrary cross section is considered. An integral equation for the surface values of the pressure is formulated. A major portion of the solution is shown to be contributed by terms in the integral equation which can be evaluated explicitly for a given cross section. The remaining contribution is approximated by a set of successive, nonsimultaneous algebraic equations which are easily solved for a given geometry. The case of a square box with rigid boundaries is solved in this manner for a period of one transit time. The accuracy achieved by the method is indicated by comparison with known analytical solutions for certain special geometries.


Sign in / Sign up

Export Citation Format

Share Document