On deformations of transversely homogeneous foliations

A transversely homogeneous foliation is a foliation whose transverse model is a homogeneous space G/H. In this paper we consider the class of transversely homogeneous foliations on a manifold M which can be defined by a family of 1-forms on M fulfilling the Maurer–Cartan equation of the Lie group G. This class includes as particular cases Lie foliations and certain homogeneous spaces foliated by points. We develop, for the foliations belonging to this class, a deformation theory for which both the foliation and the model homogeneous space G/H are allowed to change. As the main result we show that, under some cohomological assumptions, there exist a versal space of deformations of finite dimension for the foliations of the class and when the manifold M is compact. Some concrete examples are discussed.     

Stress channelling in transversely isotropic elastic composites

Résumé Une théorie a déjà été proposée au sujet des matériaux à fibres de renforcement où l'on supposait que ces dernières étaient inextensibles et uniformément distribuées dans un composite considéré comme incompressible. Cependant, quelques unes des prédictions de cette théorie semblent être fondamentalement en désaccord avec la théorie classique de l'élasticité. Il est démontré ici que les résultats inattendus de cette théorie correspondent en fait à des cas limites de la théorie classique de l'élasticité pour des matériaux à isotropie transversale.     

Growth of leaves in transversely affine foliations

In this note we give estimates for the growth of leaves in transversely affine foliations which depend on the properties of the affine holonomy group.

     

Fluid forces on a transversely oscillating cylinder

The numerical solution of the unsteady two-dimensional Navier-Stokes equations is used to investigate the fluid forces experienced by a translating and transversely oscillating cylinder. Calculations are first performed in an oscillatory frequency range outside the synchronization when oscillatory-to-translational velocity ratio is 1.5 and at a fixed Reynolds number R = 10³. The object of this study is to examine the effect of increase of forced oscillation frequency on the fluid forces. The results of this study are in good agreement with previous experimental predictions.     

A transversely isotropic elastic model of geomaterials

Under consideration is the choice of parameters of a transversely isotropic elastic model for describing the linear deformation of geomaterials. We also discuss some analytical and numerical methods of solving the corresponding dynamic equations.     

Deformation theory for gas-impregnated transversely isotropic materials

A mathematical model is constructed for a gas-impregnated transversely isotropic material. The material is modeled by a three-phase solid at each point of which there is a solid phase, and free and sorbed gas. Gas movement proceeds in two ways: by a crack and macropores system (filtration flow), and through microcracks (diffusion flow).Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 93–97, 1989.     

Stress concentrations around openings in transversely isotropic shells

A method of investigating stress concentrations around openings in shells made of a transversely isotropic material (oriented glass-reinforced plastic [5]) is described. The use of a Timoshenko-type theory makes it possible to take into account the effect of tangential shearing stresses and the anisotropy of the elastic properties of the shell in a direction normal to the middle surface. A complex form of the resolvents of this theory, constructed in [6], is employed.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. L'vov Franko State University. Translated from Mekhanika Polimerov, No. 6, pp. 1076–1081, November–December, 1970.     

On natural frequencies of transversely isotropic circular plates

The paper discusses the impact of the material properties of transversely isotropic circular plates on its natural frequencies. Two refined theories of plates have been used to analyze the free vibration behavior of homogeneous plates. Both theories take into account normal and rotary inertias. Fundamental frequencies for plates with radial inhomogeneity have been obtained with the help of finite element package Comsol Multiphysics 5.0. It has been shown that the inhomogeneity of the plate have a profound impact on the first (lowest) frequency of the plate, while the plate orthotropy has a greater influence on the second and higher vibration mode [2] (Fig. 1, Table 1).     

On transversely flat conformal foliations with good measures

Transversely flat conformal foliations with good transverse invariant measures are Riemannian in the sense. In particular, transversely similar foliations with good measures are transversely Riemannian as transversely -foliations.

     

Basic forms for transversely integrable singular Riemannian foliations

Basic forms for a transversely integrable singular Riemannian foliation with compact leaves are in one-to-one correspondence with ``Weyl"-invariant differential forms on a generalized section of the foliation.

     

A finite deformation possible in transversely isotropic materials

Zusammenfassung Der Aufsatz beweist die Existenz einer Drei-Parameter-Familie von inhomogenen Deformationen mit konstanten Deformationsinvarianten. Diese Deformationen lassen sich in jedem anfänglich homogenen transversalisotropen, inkompressiblen elastischen Material durch Oberflächenkräfte aufrechterhalten.     

Thermoelastic deformation of a transversely isotropic compressed spheroid

An exact solution is presented for a static thermoelastic problem for a transversely isotropic compressed spheroid when an arbitrary temperature distribution is assigned on its surface. It is assumed that the surface of the spheroid is free of external forces. The general solution is expressed through four potential functions, each of which is harmonic in a certain coordinate system. The external and internal problems for the spheroid are investigated. The solution is constructed in the form of double series in products of trigonometric functions and associated Legendre functions.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 19, pp. 39–46, 1988.