Effect of a gradient heating on the stress-strain state of a plate

The solution of a thermoelasticity problem is constructed and the effect of a preliminary cooling and heating by cylindrical heat sources of different intensities on the thermoelastic state of an infinite thin plate is investigated.Translated from Matematicheskie Metody i Fiziko-mekhanicheskie Polya, No. 26, pp. 35–39, 1987.     

On vibrations of an inhomogeneous anisotropic plate

An equation of motion of a flat inhomogeheous anisotropic plate is considered. Formal asymptotic solutions are constructed by applying the space-time ray method. An equation describing the flow of energy is obtained in the form of a continuity equation. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 250, 1998, pp. 73–82. Translated by A. S. Golubeva.     

Analytic investigation of the stress-strain relation for an arbitrary loading trajectory

The determination of the strain trajectory from a known arbitrary loading trajectory is described within the framework of the theory of slip. Specific calculations have been made on an electronic computer.Institute of Physics and Mathematics, Academy of Sciences of the Kirgiz SSR, Frunze. Translated from Mekhanika Polimerov, No. 6, pp. 981–986, November–December, 1971.     

Concentrated force solutions for an inhomogeneous thick elastic plate

The technique developed in refs. [1-5] is applied to the problem of a concentrated line force acting in the interior of an infinite plate. The plate is of arbitrary thickness, is isotropic, but is inhomogeneous in that the elastic moduli are any specified functions, not necessarily continuous, of the through-thickness coordinate. The mechanical properties of the plate are not necessarily symmetric about the mid-surface. The solution is based on the classical solution for a concentrated force in a thin elastic plate. This classical solution is extended to give exact closed form solutions for the displacement and stress in the thick inhomogeneous plate. For a plate that is not symmetric an in-plane force gives rise to bending as well as stretching deformations. Higher order force singularities are also considered, as is the problem of a concentrated force on the boundary of a semi-infinite symmetric plate.     

The stress-strain state of an orthotropic shell with a circular hole

We study the stress-strain state of an orthotropic shell with a circular hole. The regularities of the straiin distribution as a function of the anisotropy parameters in a spherical shell are exhibited. One table, 1 figure. Bibliography: 3 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 154–158.     

The stress-strain state of anisotropic rock

We use integrals of Cauchy type and the complex potentials of S. G. Lekhnitskii to solve the problem of the stress-strain state of a piecewise-homogeneous anisotropic rock during the working of a horizontal seam of mineral. We study the stress distribution in the deloaded zones. Three figures, 1 table. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 27, 1997, pp. 81–86.     

About the stress-strain state of growing viscoelastic systems

A problem of calculation of the stress-strain state of viscoelastic heterogeneously ageing growing systems at the various moments of time is considered. The efficient numerical technique based on the Finite Element Method (FEM) is suggested. The constitutive equation between stresses and strains in the viscoelastic growing solid is corresponded with the Maslov-Arutyunyan theory. The general system of equations of the FEM-based technique is being formed for nodal displacement increments on the basis of variation of the total energy functional by components of the vector of nodal displacement increments. The numerical technique allows to take into account linear and nonlinear creep of the material, shrinkage (if it is necessary) and the instantly-elastic modulus time-dependence. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of the stress-strain state of a ring-reinforced cylindrical section of an underground pipe

A method is presented for solving the problem of determining the stress-strain state of closed circular cylindrical shells in an elastic medium. The problem relates to the design of underground pipelines. The work of cylindrical shells is examined from the viewpoint of the theory of thin-walled three-dimensional systems, with allowance being made for the unilateral character of the interaction with the elastic medium. The stress-strain state of a cylindrical section of an underground pipe reinforced in the middle by a ring is investigated. It is shown that different factors influence the stress-strain state of the shell of the pipe.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 66–72, 1987.     

Electroelastic state of an inhomogeneous piezoceramic layer under symmetric loading

A procedure for solving three-dimensional mixed symmetric problems of electroelasticity theory for a piezoceramic layer with an inclusion, which is weakened with a through hole, is proposed. The boundary-value problem is reduced to a system of 12k (k = 1, 2, …) integrodifferential equations. Expressions for stresses characterizing the stress state of the inhomogeneous layer are found. Calculation results for characteristic stresses are presented.     

The dynamic stressed state of a rectangular composite plate rigidly fixed along its edges

Using the generalized dynamic theory of bending of plates, which takes account of the compliance of the material to transverse shear strains, we obtain an approximate solution of the problem of the dynamic stressed state of a composite plate with rigidly fixed edges subject to an impact load. We exhibit the contribution of the physico-mechanical and geometric parameters of the plate to the magnitude of the computed stresses and their time variation for different coefficients of internal dissipation of mechanical energy.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 3, 1997, pp. 129–133.     

Finite-element calculation of a plate compliant in transverse shear

A finite-element calculation of a plate with a low transverse shear stiffness is presented. As the basic kinematic parameters, the angles of transverse shear at each of four nodes of the finite element of the plate are selected. The results found for the stress-strain state of an isotropic homogeneous composite and a three-layer plates confirm that the finite-element model elaborated is also efficient in the cases of nonclassical boundary conditions for plates, including conditions for the angles of transverse shear.     

Determination of the stress-strain state of anisotropic thermosensitive cylinders

In the three-dimensional formulation we study a class of problems involving the stressed state of an axisymmetrically heated anisotropic cylinder arbitrarily inhomogeneous over the thickness taking account of the dependence of mechanical characteristics on the temperature. The solution of the boundary-value problems is carried out numerically. We study the temperature and mechanical fields in composite cylinders. Translated fromMatematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 1, 1998, pp. 73–77.     

Asymptotic behaviour of stress-strain state in the vicinity of sharp defects in an elastic body

The present paper deals with asymptotic representations of solutionsto plane and three-dimensional elasticity problems in a neighbourhoodof the tip of a sharp inclusion. In a two-dimensional case resultsare analysed for different kinds of cusp-shaped inclusions andfor a thin angular one. With regard to the equations of three-dimensionalelasticity, the stress-strain behaviour in the vicinity of cusp-shapedelastic and rigid inclusions have been studied. The dependenceof results on the geometry of a cusp (in relation to the integralDiny condition) is emphasized, and a boundary layer effect ina neighbour of a irregular point on the boundary is studied.     

Cylindrical bending of an elastic rectangular sandwich plate on a deformable foundation

Cylindrical bending of an elastic rectangular sandwich plate having a rigid filler and resting on an elastic foundation is considered. To describe the kinematics of the plate, asymmetric across its thickness, the hypotheses of broken normal are assumed. The reaction of the foundation is described by the Winkler model. A system of equilibrium equations is derived, and its exact solution is obtained in terms of displacements. A numerical analysis of the solution is presented.     

The stressed state of an elastic space with a rectangular crack

By using the method of mechanical quadratures we reduce the resolvent integral equation for the problem of an infinite elastic space with a rectangular crack to a system of linear algebraic equations. We give the results of numerical experiments in varying the stress intensity factor on one side of the crack in the case of tension in the direction perpendicular to the plane of the crack. One figure. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 24–28.