Stability of an Elastic Layer Stack Between Two Half-Spaces Under Compressive Loads

A stability problem is solved for a multicomponent medium consisting of a layer stack and two structurally homogeneous half-spaces. The analysis is made within the framework of the piecewise-homogeneous model and the three-dimensional linearized theory of stability for small subcritical strains. The properties of isolated elements of the medium are determined within the framework of the orthotropic linearly elastic model. Specific numerical results are obtained for the case of plane strain     

Isomonodromic deformations and twisted Yangians arising in Teichmüller theory

In this paper we build a link between the Teichmüller theory of hyperbolic Riemann surfaces and isomonodromic deformations of linear systems whose monodromy group is the Fuchsian group associated to the given hyperbolic Riemann surface by the Poincaré uniformization. In the case of a one-sheeted hyperboloid with n orbifold points we show that the Poisson algebra Dn of geodesic length functions is the semiclassical limit of the twisted q-Yangian for the orthogonal Lie algebra on defined by Molev, Ragoucy and Sorba. We give a representation of the braid-group action on Dn in terms of an adjoint matrix action. We characterize two types of finite-dimensional Poissonian reductions and give an explicit expression for the generating function of their central elements. Finally, we interpret the algebra Dn as the Poisson algebra of monodromy data of a Frobenius manifold in the vicinity of a non-semi-simple point.     

Surface instability of a homogeneous half-space coupled with a finite number of laminas

In the context of the model of a piecewise-homogeneous medium in three-dimensional formulation we study the problem of the surface loss of stability in laminated semi-bounded media with a finite number of laminas. For the study we invoke a version of three-dimensional stability theory constructed for small pre-critical deformations when the pre-critical state is determined from the geometrically linear theory. To construct the resolvent characteristic equations we use the matrix representation of the basic relations. Using a computer we carry out a numerical study of the stability of a homogeneous half-space coupled to various numbers of laminas, and we conduct a comparative analysis of the results. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 8–13.     

Variational method of investigating the stability of laminar semiinfinite media

International Applied Mechanics -