Asymptotic behavior of eigenfunctions and eigenfrequencies of oscillation boundary value problems of the linear theory of elastic mixtures

The asymptotic behavior of eigenoscillation and eigen-vector-function is studied for the internal boundary value problems of oscillation of the linear theory of a mixture of two isotropic elastic media.     

On the criteria of existence of eigenfrequencies corresponding to Love waves

In this work we show the necessary and sufficient conditions for the existence of an eigenvalue of a special Sturm–Liouville operator on a semi-axis with a parameter in a coefficient. The operator corresponds to an equation of elasticity. The conditions are formulated in terms of shear wave velocities.     

On existence and stability in the theory of swelling porous elastic soils

The aim of this paper is to introduce a new functional in thestudy of swelling porous elastic soils saturated by a fluid.This new functional is a useful tool; it allows us to provethe existence of solutions in the case of a compressible fluid.We also prove the stability of solutions and the exponentialdecay in the case of an incompressible fluid. We study as wellthe continuous dependence with respect to the initial time.     

Contribution to the theory of elastic strain distribution in two-component composites

A method analogous to the known limit theorem methods of the theory of probability is proposed for establishing the law of distribution of the random elastic deformation of the structure of a composite with a nonordered arrangement of two isotropic components. It is shown that under certain conditions the strains are distributed according to a law that approximates the sum of two normal distributions.S. M. Kirov Ural Polytechnic Institute, Sverdlovsk. Translated from Mekhanika Polimerov, No.4, pp. 616–622, July–August, 1973.     

On a dynamical hierarchical model for prismatic shells in the theory of elastic mixtures

The present paper is devoted to the design of a hierarchy of two‐dimensional models for dynamical problems within the theory of multicomponent linearly elastic mixtures in the case of prismatic shells with thickness which may vanish on some part of its boundary. The hierarchical model is obtained by a semidiscretization of the three‐dimensional problem in the transverse direction. In suitable weighted Sobolev spaces we investigate the well‐posedness of the two‐dimensional problems, prove pointwise convergence of the sequence of approximate solutions restored from the solutions of the reduced problems to the exact solution of the original problem and estimate the rate of convergence. Copyright © 2005 John Wiley & Sons, Ltd.     

On the global existence and wave-breaking criteria for the two-component Camassa-Holm system

Considered herein is a two-component Camassa-Holm system modeling shallow water waves moving over a linear shear flow. A wave-breaking criterion for strong solutions is determined in the lowest Sobolev space Hs, by using the localization analysis in the transport equation theory. Moreover, an improved result of global solutions with only a nonzero initial profile of the free surface component of the system is established in this Sobolev space Hs.     

On recent existence theorems in the theory of optimization

A condition recently proposed is shown to imply the weak compactness inH ^1,1 and actually is equivalent to another condition previously proposed by the authors. Once compactness is proved, then existence theorems follow from lower closure theorems also previously proved by the authors, and extended to Pareto problems. The present analysis adds to the recent work of Goodman concerning the equivalence of seminormality conditions with concepts of convex analysis and lattice theory.Paper received February 2, 1979.     

广义静态梁方程非负解的存在性

运用Leray—Schauder拓扑理论,证明了广义静态梁方程和静态梁方程非负解的存在性,仅要求非线性项f在原点的某个邻域满足一定的符号条件,突破了以往对非线性项f的增长性限制．所获结果对工程设计具有重要的理论意义和实用价值．     

On the theory of orthotropic porous elastic rods

We employ the theory of elastic materials with voids to describe the mechanical behavior of porous rods. In this purpose, we consider the direct approach to the theory of rods, in which the thin body is modeled as a deformable curve with a triad of rigidly rotating orthonormal vectors attached to every material point. For orthotropic and homogeneous rods, we determine the constitutive coefficients in terms of the three-dimensional elasticity constants by solving several problems in the two different approaches (directed curves and three-dimensional rods). (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the existence and uniqueness of solutions in nonlinear complementarity theory

A complementarity problem is said to be globally uniquely solvable (GUS) if it has a unique solution, and this property will not change, even if any constant term is added to the mapping generating the problem.A characterization of the GUS property which generalizes a basic theorem in linear complementarity theory is given. Known sufficient conditions given by Cottle, Karamardian, and Moré for the nonlinear case are also shown to be generalized. In particular, several open questions concerning Cottle's condition are settled and a new proof is given for the sufficiency of this condition.A simple characterization for the two-dimensional case and a necessary condition for then-dimensional case are also given.The research described in this paper was carried out while N. Megiddo was visiting Tokyo Institute of Technology under a Fellowship of the Japan Society for the Promotion of Science.     

On Gibbs stability in the classical theory of fluid mixtures

We prove that Gibbs' criterion for stability is a necessary condition for the dynamic stability of a classical (non-linear) inviscid fluid mixture.

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Resumé On démontre que le critère de Gibbs pour la stabilité est une condition nécessaire pour la stabilité dynamique d'une mixture classique (non linéaire) des fluids inviscides.

     

On the Samarskii-Andreev transmission conditions in the theory of elastic beams

It is proved that the transmission conditions for elastic beams in the case of a nonideal joint are limiting in the construction of asymptotics for the transmission problem for two thin elastic bodies if the boundary between the bodies is filled by slightly extendible material.     

On corner singularities in Reissner-Mindlin's theory of elastic plates

In the framework of linear elasticity, singularities occur in domains with non-smooth boundaries. Particularly in Fracture Mechanics, the local stress field near stress concentrations is of interest. In this work, singularities at re-entrant corners or sharp notches in Reissner-Mindlin plates are studied. Therefore, an asymptotic solution of the governing system of partial differential equations is obtained by using a complex potential approach which allows for an efficient calculation of the singularity exponent λ. The effect of the notch opening angle and the boundary conditions on the singularity exponent is discussed. The results show, that it can be distinguished between singularities for symmetric and antisymmetric loading and between singularities of the bending moments and the transverse shear forces. Also, stronger singularities than the classical crack tip singularity with free crack faces are observed. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the existence of covers by injective modules relative to a torsion theory

Let R be a ring with identity. In this note we study covers of left R-modules by r-injectives left R-modules, where r is a hereditary torsion theory defined in the category of all left R-modules and all R-morphisms. When R is an artinian commutative ring, a complete answer about the existence of such covers for every R-module is given. In case that T is a centrally splitting torsion theory, we can characterize those T for which every left R-module has a T-injective cover. Also we analyze R-modules such that the injective and the T-injective cover are the same. At the end of this note we relate the concepts of colocalization and cover