Safety Factor of Anisotropic Bars in the Space of Generalized Forces

© 2017, Springer Science+Business Media New York.Bars of arbitrary shape made of a homogeneous anisotropic material are considered. In the general case, in their cross section, nonzero are all internal force factors (IFF) — three forces and three moments. The values of the IFF are known from solutions of the corresponding problem. The safety factor for the load-carrying capacity of the beams is determined by comparing the known vector R∗ of IFF with the corresponding desired strength vector R in the IFF space

Estimate of strength of anisotropic bars of arbitrary cross-section in the general case of their combined stress

We consider bars of arbitrary shape made of a homogeneous anisotropic material. In the general case, all six internal force factors (three forces and three moments) are simultaneously nonzero in the transverse cross-sections of the bar. We consider the case of small displacements and strains of the bar. Using the rigid-plastic model of a strained rigid body, the associated strain law, and the traditional hypotheses of static and kinematic character for the bars, we derive parametric equations for the limit surface (the strength surface) in the space of internal forces and moments acting in the the transverse cross-section. We present several versions of the obtained equations in specific cases (for orthotropy, transversal isotropy, and isotropy) and some numerical examples. © Allerton Press, Inc., 2010

The determining of the coefficient of safety of bearing ability of anisotropic bars in the general case of their complex resistance

© Published under licence by IOP Publishing Ltd. The bars of any form made of a uniform anisotropic material are considered. Generally in the cross section of a bar all internal power factors (IPF)-three forces and three moments are other than zero. Values IPF are known from the solution of the corresponding task. The coefficient of a stock of bearing ability of a bar is defined by a way of comparison of known vector IPF ∗ with the corresponding required vector of durability in IPF space

Weyl Card Diagrams and New S-brane Solutions of Gravity

We construct a new card diagram which accurately draws Weyl spacetimes and represents their global spacetime structure, singularities, horizons and null infinity. As examples we systematically discuss properties of a variety of solutions including black holes as well as recent and new time-dependent gravity solutions which fall under the S-brane class. The new time-dependent Weyl solutions include S-dihole universes, infinite arrays and complexified multi-rod solutions. Among the interesting features of these new solutions is that they have near horizon scaling limits and describe the decay of unstable objects.Comment: 78 pages, 32 figures. v2 added referenc

Boundary layer on the surface of a neutron star

In an attempt to model the accretion onto a neutron star in low-mass X-ray binaries, we present two-dimensional hydrodynamical models of the gas flow in close vicinity of the stellar surface. First we consider a gas pressure dominated case, assuming that the star is non-rotating. For the stellar mass we take M_{\rm star}=1.4 \times 10^{-2} \msun and for the gas temperature $T=5 \times 10^6$ K. Our results are qualitatively different in the case of a realistic neutron star mass and a realistic gas temperature of $T\simeq 10^8$ K, when the radiation pressure dominates. We show that to get the stationary solution in a latter case, the star most probably has to rotate with the considerable velocity.Comment: 7 pages, 7 figure

The influence of the Lande gg-factor in the classical general relativistic description of atomic and subatomic systems

We study the electromagnetic and gravitational fields of the proton and electron in terms of the Einstenian gravity via the introduction of an arbitrary Lande $g$-factor in the Kerr-Newman solution. We show that at length scales of the order of the reduced Compton wavelength, corrections from different values of the $g$-factor are not negligible and discuss the presence of general relativistic effects in highly ionized heavy atoms. On the other hand, since at the Compton-wavelength scale the gravitational field becomes spin dominated rather than mass dominated, we also point out the necessity of including angular momentum as a source of corrections to Newtonian gravity in the quantum description of gravity at this scale.Comment: 11 pages, 2 figure

Theoretical evaluation of rheological state of sand cement composite systems with polyoxyethylene additive using topological dynamics concept

© 2016 Trans Tech Publications, Switzerland.Presents the results of studies of contemporary materials in the field of rheological state. The topological mortar structure has been provided by theoretical evaluation of the rheological state of the cross-linked solutions and the experimental viscosity data of the sand cement mortar which has been modified by water-soluble additive – polyoxyethylene. The general model has been made for the structure of non-Newtonian liquideous systems including dilatant, pseudoplastic bodies with two main rheological active components in their structure – rigid and viscous phases. It is shown that in pseudoplastic systems, as the shear stress increases, the viscous phase grows because of the reduction of rigid phase content. In dilatant systems the converse situation has been observed. Furthermore, these phases are not clearly distinguishable, but to the contrary they are spatially interconnected in a complex way. The structure modeling has been made for non-Newtonian bodies using the Shklovskii-de Gennes model. The studies have found that the construction composite sand cement system is defined as the pseudoplastic body where cement and sand act as the rigid phase, water solution of polyoxyethylene – as the viscous phase. These findings can be used to prove the influence of polymer powder on the workability of dry mortar

Energy Release on the Surface of a Rapidly Rotating Neutron Star during Disk Accretion: A Thermodynamic Approach

The total energy E of a star as a function of its angular momentum J and mass M in the Newtonian theory: E = E(J, M) [in general relativity, the gravitational mass M of a star as a function of its angular momentum J and rest mass m, M = M(J, m)], is used to determine the remaining parameters (angular velocity, equatorial radius, chemical potential, etc.) in the case of rigid rotation. Expressions are derived for the energy release during accretion onto a cool (with constant entropy), rapidly rotating neutron star (NS) in the Newtonian theory and in general relativity. A separate analysis is performed for the cases where the NS equatorial radius is larger and smaller than the radius of the marginally stable orbit in the disk plane. An approximate formula is proposed for the NS equatorial radius for an arbitrary equation of state, which matches the exact one at J = 0.Comment: 12 pages, 0 figures (Astronomy Letters in press

Monodromy-data parameterization of spaces of local solutions of integrable reductions of Einstein's field equations

For the fields depending on two of the four space-time coordinates only, the spaces of local solutions of various integrable reductions of Einstein's field equations are shown to be the subspaces of the spaces of local solutions of the ``null-curvature'' equations constricted by a requirement of a universal (i.e. solution independent) structures of the canonical Jordan forms of the unknown matrix variables. These spaces of solutions of the ``null-curvature'' equations can be parametrized by a finite sets of free functional parameters -- arbitrary holomorphic (in some local domains) functions of the spectral parameter which can be interpreted as the monodromy data on the spectral plane of the fundamental solutions of associated linear systems. Direct and inverse problems of such mapping (``monodromy transform''), i.e. the problem of finding of the monodromy data for any local solution of the ``null-curvature'' equations with given canonical forms, as well as the existence and uniqueness of such solution for arbitrarily chosen monodromy data are shown to be solvable unambiguously. The linear singular integral equations solving the inverse problems and the explicit forms of the monodromy data corresponding to the spaces of solutions of the symmetry reduced Einstein's field equations are derived.Comment: LaTeX, 33 pages, 1 figure. Typos, language and reference correction

Energy Release During Disk Accretion onto a Rapidly Rotating Neutron Star

The energy release L_s on the surface of a neutron star (NS) with a weak magnetic field and the energy release L_d in the surrounding accretion disk depend on two independent parameters that determine its state (for example, mass M and cyclic rotation frequency f) and is proportional to the accretion rate. We derive simple approximation formulas illustrating the dependence of the efficiency of energy release in an extended disk and in a boundary layer near the NS surface on the frequency and sense of rotation for various NS equations of state. Such formulas are obtained for the quadrupole moment of a NS, for a gap between its surface and a marginally stable orbit, for the rotation frequency in an equatorial Keplerian orbit and in the marginally stable circular orbit, and for the rate of NS spinup via disk accretion. In the case of NS and disk counterrotation, the energy release during accretion can reach $0.67\dot{M}c^2$. The sense of NS rotation is a factor that strongly affects the observed ratio of nuclear energy release during bursts to gravitational energy release between bursts in X-ray bursters. The possible existence of binary systems with NS and disk counterrotation in the Galaxy is discussed. Based on the static criterion for stability, we present a method of constructing the dependence of gravitational mass M on Kerr rotation parameter j and on total baryon mass (rest mass) m for a rigidly rotating neutron star. We show that all global NS characteristics can be expressed in terms of the function M(j, m) and its derivatives.Comment: 42 pages, 12 figures, to appear in Astronomy Letters, 2000, v.26, p.69