Stress state near loaded holes in anisotropic plates

Special representations of the solution are constructed and solving integral equations of the problem of the elastic equilibrium of a finite anisotropic plate weakened by an elliptical hole or rectilinear crack are derived. The absence of the unknown function for the boundary of the internal hole (crack) makes it possible to propose an effective algorithm for the problem's numeric solution. The results of calculations, which illustrate the effect of the external boundary and material anisotropy on the stress distribution near loaded holes of different sizes, are presented. Direct comparison with the finite-element method indicates that the proposed algorithm significantly lowers the amount of input data, the computer time, and the required volume of memory with comparable accuracy.Novosibirsk. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 45–51, 1990.     

Equilibrium conditions for multilayered anisotropic viscoelastic plates in a complex state of stress

Systems of linear differential-difference equations describing the complex state of stress of multilayered viscoelastic and elastic plates are obtained.Moscow Institute of Electronic Machine Building; All-Union Scientific-Research Institute of Glass-Reinforced Plastics and Glass Fiber, Moscow Region. Translated from Mekhanika Polimerov, No. 2, pp. 281–288, March–April, 1973.     

Stress concentrations around holes in anisotropic laminated plates

A general approach based on a stress function, represented by two complex potentials, in conjunction with Cauchy's integral, is applied to the analysis of perforated anisotropic symmetrically laminated plates.Results are shown for composite plates under tension with elliptic and circular openings. The stress concentration factors were found to be quite sensitive to changes in plate anisotropy and heterogeneity, direction of external tensile force and form of hole.

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Résumé Une méthode d'approche générale basée sur une fonction de tension représentée par deux potentiels complexes en combinaison avec l'intégrale de Cauchy a été appliquée à l'analyse de plaques perforées anisotropiques, laminées symétriquement.Des résultats sont présentés pour des plaques composites sous tension avec perforations elliptiques et rondes. On a constaté que les facteurs de concentration de tension sont très sensibles aux changements de l'anisotropie et de l'hétérogénéité des plaques ainsi qu'à la direction des tensions extérieures et à la forme des perforations.

     

Non-axisymmetric consolidation of poroelastic multilayered materials with anisotropic permeability and compressible constituents

This paper presents an analytical layer-element solution to non-axisymmetric consolidation of multilayered poroelastic materials with anisotropic permeability and compressible constituents. By applying Fourier expansions, Hankel transforms and Laplace transforms to the state variables involved in the governing equations of poroelasticity with respect to the circumferential, radial and time coordinates, respectively, the analytical layer-element (i.e. a symmetric stiffness matrix) is derived, which describes the relationship between the transformed generalized stresses and displacements at the surface (z = 0) and those at an arbitrary depth z, considering the corresponding boundary and continuity conditions at the layer interfaces, the global stiffness matrix of a multilayered system is assembled in the transformed domain. The actual solutions in the physical domain are acquired by applying numerical quadrature schemes for the inversion of the Laplace–Hankel transform. Finally, numerical calculation is presented to investigate the influence of layering and poroelastic material parameters on consolidation process.     

Stress state of thermosensitive thick cylinders made of anisotropic composites

The class of problems on the axially symmetric stress state of thick cylinders made of anisotropic materials is considered. The problems are solved numerically. The temperature and mechanical fields in the composite cylinders are investigated taking into account the temperature dependence of the matrix and reinforcement characteristics, as well as the variability of density and angle of reinforcement across the thickness.Institute of Mechanics, Ukrainian National Academy of Sciences, Kiev, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 35, No. 3, pp. 367–374, May–June, 1999.     

Stressed state of an anisotropic body with elliptical holes, elastic inclusions, and cracks

A method is proposed for studying the two-dimensional stressed state of a multiply connected anisotropic body with cavities and elastic and rigid inclusions, as well as planar cracks and rigid laminar inclusions. Generalized complex potentials, conformal mapping, and the method of least squares are used. The problem is reduced to solving a system of linear algebraic equations. Formulas are given for finding the stress intensity factors in the case of cracks and laminar inclusions. For an anisotropic plate with a single elliptical hole or a crack and an elastic (rigid) inclusion, some numerical results are presented from a study of the effect of the rigidity of the inclusion and the closeness of the contours to one another on the distribution of stresses and the stress intensity factor. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 175–187, 1999.     

On dispersion relations of waves in multilayered magneto-electro-elastic plates

The dispersion behavior of waves in a layered magneto-electro-elastic plate is studied. Formulations are given for open-circuit surface and short-circuit surface, respectively. Legendre orthogonal polynomial series approach is employed to solve the coupling magneto-electro-elastic controlling equations. The obtained dispersion curves for the open-circuit surface are compared with the published data to confirm the validity of the method. Through numerical examples, the convergence of the method is discussed. The differences of the two boundaries are illustrated. The influences of the piezoelectricity and piezomagnetism are illustrated and the influential factors of the piezoelectric and piezomagnetic effect are discussed. Finally, the influences of the volume fraction and stacking sequence on the piezoelectric effect and piezomagnetic effect are discussed.     

Vibrations of flexible cylindrically anisotropic annular plates

We study the problem of bending vibrations of a prestressed flexible annular plate made of a cylindrically anisotropic material. The problem is solved using the method of initial functions and the theory of multiplicative integration. Using the resulting computational formulas we analyze the critical values of the loading parameters of the plate by the dynamic criterion. One table. Bibliography: 2 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 92–97.     

Stationary stressed state of an elliptical cylinder

The theory of functions of a complex variable is used to construct an approximate solution for the stationary oscillations of an elliptical cylinder with longitudinal elliptical cavities. Some numerical results are presented for a cylinder with a single cavity. Donetsk State University. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 132–137, 1999.     

Improved linear theory of elastic anisotropic multilayered shells. Part 1

The improved linear theory of elastic anistropic multilayered shells of an arbitrary shape has been confirmed, and hence the effect of the lateral displacement and normal lateral deformations is accounted for, for each layer.