Multicriteria optimization of a rectangular composite plate subjected to longitudinal thermal stresses and buckling in shear loading

The multicriteria optimization of the structure and geometry of a laminated anisotropic composite plate subjected to thermal and shear loading is considered. From the known properties of the monolayer and given values of variable structural parameters, the thermoelastic properties of the layered composite are determined. The optimization criteria — the critical shear load and the longitudinal thermal stresses — depend on two variable design parameters of composite properties and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subregion are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 85–92, January–February, 2007.     

Stressed state of a piezoceramic body containing a spheroidal inclusion

An exact solution is constructed to the electroelastic problem for a medium with a sealed-in spheroidal inclusion under the assumption that the medium and the inclusion are different piezoceramic, transversally isotropic bodies with coincident axes of anisotropy. The components of the associated electroelastic field of the inclusion are plotted as functions of the external load and of the geometry of the inclusion. Numerical values of the stresses and of the projection of the electric induction vector are given for the medium in the neighborhood of the inclusion. Universidade de Beira Interior, Portugal: Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev; and Ukrainian State University of Food Technologies, Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 28–42, 1999.     

Compromise optimization of a rectangular composite plate subjected to biaxial thermal loading and buckling under the action of shear

The compromise optimization of the structure and geometry of a laminated anisotropic composite plate subjected to biaxial thermal shear loading is considered. From the known properties of the monolayer and given values of a variable structural parameter, the thermoelastic properties of the layered composite are determined. The optimization criteria — the critical shear load and the longitudinal and transverse thermal stresses — depend on two variable design parameters of composite properties and temperature. In the space of optimization criteria, the domain of allowable solutions and the Pareto-optimal subregion are found. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 4, pp. 471–478, July–August, 2008.     

Axial Couette flow of a generalized Oldroyd-B fluid due to a longitudinal time-dependent shear stress

Abstract

The velocity field and the adequate shear stress corresponding to the unsteady flow of a generalized Oldroyd-B fluid in an infinite circular cylinder are determined by means of Hankel and Laplace transforms. The solutions that have been obtained, written in terms of the generalized G-functions, satisfy all imposed initial and boundary conditions. The similar solutions for generalized Maxwell fluids as well as those for ordinary fluids are obtained as limiting cases of our general solutions.     

Optimization of the thermostressed state of piecewise homogeneous glass shells of revolution during thermal processing

We propose a physico-mathematical model and state a problem of stress-optimization of regimes for heating thin piecewise homogeneous glass shells of revolution with given ranges of admissible temperature and stress values by means of an optimal choice of temperature for the surrounding medium. To solve the problem we apply the method of local variations with a specially chosen initial value of the control function and numerical analytic solution of the corresponding direct problem of thermomechanics for the shell in question.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 36, 1992, pp. 52–56.     

Stress distribution in multilayered composite material with curved structures (model of a piecewise homogeneous body)

Conclusion In the case of single-phase (antiphase) curvature in the structure of the composite under consideration, an increase of concentration of the filler entails a decrease (increase) of the values of the self-balanced normal stresses and, conversely, an increase (decrease) of the values of the self-balanced tangential stresses. With ⁽²⁾ 0.1 (where ⁽²⁾ is the concentration of the filler) a decrease of the parameter k=2H⁽²⁾/l (where 2H⁽²⁾ is the thickness of the layer of filler, l is the wavelength of the forms of curvature) entails a monotonic increase of the self-balanced tangential stress in the case of single-phase curvature. This means that with fixed wavelength of the forms of curvature (with fixed thickness of the layer of filler) a decrease in thickness of the layer of filler (an increase of the wavelength of the forms of curvature) entails a monotonic increase of the tangential stress. The correlation between the self-balanced normal stresses and the parameter k in the case of antiphase curvature with all the considered values (0.02 ⁽²⁾ 0.5) is nonmonotonic. It follows that with fixed l there exists such a thickness of the layer of filler H⁽²⁾ at which the self-balanced normal stress _nn has its maximal value. With increasing ratio of the moduli of elasticity of the material of the filler and of the matrix, and also with increasing parameter =L/l (where L is the length of the sagitta), the values of the self-balanced normal and tangential stresses in both cases under consideration increase. When the curvatures in the structure of the investigated composite materials are very small, the normal stress (in the case of antiphase curvature) and the selfbalanced tangential stress (in the case of single-phase curvature) may be a multiple of the normal stress ₁₁ ⁽¹⁾⁰ in the matrix which acts in the direction of the Ox₁ axis and is balanced by the external forces p.Presented at the 6th All-Union Conference on the Mechanics of Polymer and Composite Materials (Riga, November, 1986).Translated from Mekhanika Kompozitnykh Materialov, No. 4, pp. 592–599, July–August, 1987.     

Analysis of the state of stress of cylindrically orthotropic rings subjected to concentrated loads

The state of stress of rings of different thickness with high degrees of anisotropy ²=E/E_r, ²=E_gq/G_r is analyzed on the basis of the solution of the plane problem for a cylindrically orthotropic body. The accuracy of the stress determination in accordance with approximate theories of bending of curved bars is estimated. The radial tensile stresses that develop when rings are bent by concentrated loads are calculated.Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 3, pp. 445–452, May–June, 1976.     

Elastic stress concentration near boundary defects in the case of a longitudinal shear deformation

We study the concentration of stresses due to two boundary defects located in an elastic half-space with stress-free boundary loaded at infinity with a constant shear load. The problem is reduced to solving singular integral equations for the cases in which the half-space contains defects of different types: two cracks, two inclusions, and a crack and an inclusion, whose solutions are sought by the method of mechanical quadratures. The interaction of the defects as they approach each other and the influence of their relative sizes are studied numerically. Translated fromDinamicheskie Sistemy, Vol. 11, 1992.     

Einstein metrics on even-dimensional homogeneous spaces admitting a homogeneous Riemannian metric of positive sectional curvature

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 32, No. 3, pp. 126–131, May–June, 1991.     

On the uniform stress state inside an inclusion of arbitrary shape in a three-phase composite

The stress field inside a two-dimensional arbitrary-shape elastic inclusion bonded through an interphase layer to an infinite elastic matrix subjected to uniform stresses at infinity is analytically studied using the complex variable method in elasticity. Both in-plane and anti-plane shear loading cases are considered. It is shown that the stress field within the inclusion can be uniform and hydrostatic under remote constant in-plane stresses and can be uniform under remote constant anti-plane shear stresses. Both of these uniform stress states can be achieved when the shape of the inclusion, the elastic properties of each phase, and the thickness of the interphase layer are properly designed. Possible non-elliptical shapes of inclusions with uniform hydrostatic stresses induced by in-plane loading are identified and divided into three groups. For each group, two conditions that ensure a uniform hydrostatic stress state are obtained. One condition relates the thickness of the interphase layer to elastic properties of the composite phases, while the other links the remote stresses to geometrical and material parameters of the three-phase composite. Similar conditions are analytically obtained for enabling a uniform stress state inside an arbitrary-shape inclusion in a three-phase composite loaded by remote uniform anti-plane shear stresses.     

Rigidity of locally homogeneous metrics of negative curvature on the leaves of a foliation

We consider the relationship between diffeomorphism and leafwise isometry for foliations whose leaves are locally homogeneous Riemannian manifolds of negative curvature. Partially supported by NSF Grant DMS-8301882.     

A mixed dynamic problem of the theory of elasticity for a piecewise homogeneous plane

We study the process of splitting of a compressed piecewise homogeneous medium under high-speed motion of a wedge with the formation of a crack of unknown extent ahead of the wedge. The motion of the wedge occurs along the interface between physico-mechanical properties of the piecewise homogeneous plane. We carry out numerical studies. We obtain asymptotic representations of the elastic potentials at the limiting velocities of motion of the wedge. Two figures. One table. Bibliography: 6 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 48–58.     

Singularity of the behavior of an electroelastic field in a piecewise homogeneous piezoelectric wedge

With the help of a local solution, the behavior of an electroelastic field in the vicinity of border of the contact surface of a composite piezoelectric wedge is investigated. Numerical results showing the relation between the degree of singularity of stresses and the electroelastic properties of joined materials and joint geometry are presented. In the plane of openings of homogeneous wedges, the limit curves separating the region of low stresses from the region of concentrated stresses at the border of contact surface are constructed. Some special cases are considered.     

Three-dimensional evolution of the boundary of a polluted area in a bounded piecewise homogeneous porous material

A mathematical model describing the three-dimensional evolution of a liquid-liquid interface in a piecewise homogeneous porous medium containing impermeable rock and a basin with a free liquid is constructed using the Leibenzon-Muskat model. As an example, the dispersion of pollutants from a point source is numerically simulated.     

The stress state of thick plates under homogeneous boundary conditions of mixed type on the faces

We propose a method of using homogeneous solutions in the case of mixed boundary conditions on the faces of thick plates. We obtain the exact solution of the problem of the stress state of a lamina weakened by a cylindrical cavity. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 3–8.