On one approach to studying the stress-strain state of nonlinear viscoelastic shells and plates with regard for transverse shear

Based on the theory of nonlinear viscoelasticity, we have constructed a computational scheme for determining the stress-strain state of thin taking into account transverse shells and plates with regard for transverse shear and normal stress.     

Stress state of orthotropic shells with a straight slit

A shallow orthotropic shell of arbitrary curvature with a straight slit is examined. Results are presented to describe the numerical effect of the curvature of the shell and the length and orientation of the slit on the stress and moment intensity factors in orthotropic shells made of various orthotropic materials.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 18, pp. 63–65, 1987.     

A hybrid method of studying the stress intensity factors at the tips of cracks in anisotropic plates

We propose an efficient new method of numerical analysis of the residual strength of finite plates weakened by cracks. The basis of the method is an alternating Schwartz procedure that makes it possible to achieve a successful combination of the algorithmicity and indifference to boundary conditions of the finite-element method and the application of the method of integral equations for studying singular stress fields. The numerical implementation of the scheme and the algorithm for determining the stress intensity factors at the tips of cracks is given as a software package written in FORTRAN. The efficiency of application of the computational methodology is illustrated by examples. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 34–40.     

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.     

Application of the Haar wavelet-based discretization technique to problems of orthotropic plates and shells

The Haar wavelet discretization technique for solving the elastic bending problems of orthotropic plates and shells is proposed. Free transverse vibrations of orthotropic rectangular plates with a variable thickness in one direction are considered as a model problem. In the case of constant plate thickness, the numerical results are validated by comparing them with an exact solution. The results obtained are found to be in good agreement with those available in the literature.     

Dynamic and static nonlinear analysis of cylindrically orthotropic circular plates with nonuniform edge constraints

Based on dynamic von Kármán-type equations a single-mode analysis is carried out for large-amplitude flexural forced vibration of a cylindrically orthotropic circular plate with its edge restrained nonuniformly and elastically against rotation. Numerical results are presented for static large deflection and nonlinear free and forced vibrations of isotropic and cylindrically orthotropic plates with sinusoidally restrained edges. Present values are compared with available data.

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Zusammenfassung Aus dynamischen Gleichungen vom von Kármánschen Typus für die erzwungenen Schwingungen einer zylindrisch-orthotropischen Kreisplatte mit großen Amplituden und mit variabler elastischer Einspannung längs des Randes ausgehend wird eine einzelne Schwingungsform analysiert. Numerische Resultate für große statische Auslenkungen und für nichtlineare freie und erzwungene Schwingungen isotroper und zylindrisch-orthotroper Platten mit sinusoidaler Entspannung längs des Randes werden vorgelegt. Diese Resultate werden mit Werten aus der Literatur verglichen.

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On leave from Tamkang University, Taiwan, China.

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On leave from Wuhan Institute of Building Materials, Wuhan, Hubei, China.     

The stress state of transtropic plates with ends covered by a diaphragm

We obtain homogeneous solutions of the equations of the three-dimensional theory of elasticity for transtropic plates on whose planar faces the normal stress and tangential displacements are zero. We study the problem of the stress state of a transtropic layer with a cylindrical cavity. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 3–12.     

Numerical solution of boundary value problems in the theory of thin shells and plates with a curvilinear hole

The efficiency with which coordinate systems are chosen and resolvents are constructed is illustrated for the example of linear stress concentration near a curvilinear (elliptical) hole in a circular plate and in a spherical shell. A method is proposed for bunching the grid when solving these problems numerically by a variational-difference method. The rate of convergence of solutions on uniform and nonuniform grids is studied and the results are compared with analytic values. The proposed coordinate transformations are shown to provide a substantial improvement in the rate of convergence of the numerical results on linear (nonlinear) stress concentration near curvilinear holes. Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 30, pp. 117–126, 1999.     

State of stress around a circular opening in orthotropic spherical shells with linearly varying thickness

The state of stress of a thin spherical shell of orthotropic material of linearly varying thickness weakened by a circular opening at the pole is investigated. A solution in Bessel functions is constructed for the differential equations describing the state of stress of the shell. Graphs are presented for the dependence of the stress concentration coefficients at the edge of the opening and the uniformity of the state of stress on the coefficient characterizing the variation of the thickness. It is shown that by a suitable choice of this coefficient it is possible to obtain a shell in which the stresses at the edge of the opening and on the equator are equal.     

The perturbed stress state of a closed cylindrical shell with longitudinal cracks on its inner surface

Using the Rice-Levy line spring model we find an approximate solution of the problem of elastic balance of a closed infinite circular cylindrical shell weakened by a periodic system of longitudinal interior cracks of identical length. The stress intensity factors are found at the center of a crack for various numbers of cracks with various parameters. Translated fromMatematichni Metody i Fiziko-Mekhanichni Polya, Vol. 38, 1995.     

Resolvents of the theory of orthotropic shells with low shear stiffness in force-moments and stress functions

The problem of the theory of orthotropic layered shells with low shear stiffness is reformulated in force-moments and stress functions on the basis of new strain continuity relations constructed with allowance for transverse shears.Physicomechanical Institute, Academy of Sciences of the Ukrainian SSR, L'vov. Institute of Polymer Mechanics, Academy of Sciences of the Latvian SSR, Riga. Translated from Mekhanika Polimerov, No. 5, pp. 950–952, September–October, 1970.     

The influence of the stiffness of reinforcing elements on the deformed state of shells with a hole

We propose a method of experimental estimation of the influence of the stiffness of elements that reinforce the contour of a hole on the deformed state of shells under surface pressure. We obtain the experimental data for the deflections on the contour of a lateral hole in a cylindrical shell as a function of the stiffness characteristics and the caps. We compare the results of experiments with numerical computations and give an analysis of the theoretical and experimental data obtained. Three figures. Bibliography: 5 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 67–71, 1991.     

The stress state of the finite cylinder with the circular cracks

The axysimmetrical torsion problem for a finite cylinder with an arbitrary quantity of the cylindrical layers is solved. The cylinder is weaked by the parallel circular cracks in the first internal layer. The stated boundary valued problem problem is reduced to the system of the integro-duferential equations solving with the help of the orthogonal polinomials method. The stress intensity factors (SIF) are obtained. The dependences of SIF values from the cracks' sizes, their location, and ratio of the layers' shear moduluses are concretized for the case of the two layers. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The stressed state caused by a residual strain field in plates with stress concentrators

We obtain an analytic solution of the problem of determining the stressed state caused by a given residual strain field (while taking account of three-dimensional effects) in a round plate with a concentric foreign inclusion. We study the influence of the geometric parameters of the given system, the nonlinearity of the distribution of the given residual strains over the thickness of the plate, and a possible jump in distortion at the surface of contact on the stressed state of the system. We discover an internal boundary-layer effect that is significant in the case when the given residual strain field is strongly gradient.Translated fromMatematicheskie Melody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 60–66.     

Fundamental frequency of isotropic and orthotropic rectangular plates with linearly varying thickness by discrete singular convolution method

The subject of this article is solving free vibration problems of isotropic and orthotropic rectangular plates with linearly varying thickness along one direction. For the numerical solution to evaluate the frequencies of plates, the method of discrete singular convolution (DSC) is adopted. Frequency parameters are obtained for different types of boundary conditions, taper and aspect ratios. The effect of the mode number is also analyzed. The results obtained by the present numerical method show an excellent agreement with available published results.