Limit equilibrium of a closed transversally isotropic cylindrical shell with a nonthrough longitudinal crack

In the context of an analog of the Leonov-Panasyuk-Dagdeil model we consider the problem of limit equilibrium of a nonshallow transversally isotropic cylindrical shell weakened by a nonthrough surface longitudinal crack. Based on the equations that take account of the initial stresses, we reduce the problem to a system of two singular integral equations with unknown limits of integration. We carry out a numerical analysis of the dependence of the opening of the edges of the crack on the load and the geometric and physico-mechanical parameters of the shell. Translated fromMatematichni Metodi ta Fiziko-mekhanichni Polya, Vol. 39, No. 1, 1996, pp. 31–36.     

Solution of problems of the theory of elasticity for a half-space with planar boundary cracks

We propose a method of solving three-dimensional problems of the theory of elasticity for a half-space containing planar boundary cracks. The problem is reduced to a system of integro-differential equations for determining the functions that characterize the opening of the crack during deformation of the halfspace. The kernels of the equations, besides having poles, also have a fixed singularity at the points of intersection of the surface of the crack with the boundary of the half-space. The equations obtained are solved numerically for the case of cracks that are part of a circular region. Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, No. 37, 1994, pp. 58–63.     

A study of the strength of an elastoplastic orthotropic shell of arbitrary curvature with a surface crack

Using an analog of the δ _c -model, we have obtained a solution of the problem of the stress-strain state of an elastoplastic orthotropic shell, having an arbitrary curvature, with a surface crack. Here, additional constraints on the elastic parameters of the material are not imposed. Furthermore, we have studied the dependence of the length of the plastic zone and surface-crack opening on the level of load, the shell and crack geometrical parameters, and the mechanical properties of the material.     

On a method of studying the stress state of orthotropic shells and plates weakened by a hole with cracks extending to its edge

On the basis of the Timoshenko kinematic hypothesis for shells we give a formulation of the problem of studying the stress-strain state of orthotropic plates and shells weakened by a combined stress concentrator (a hole with two symmetric cracks extending to its edge). We propose a method of solving such problems on the basis of the finite-element method. To simulate the singularity of the stresses and displacements in a neighborhood of the tip of a crack we apply special finite elements with degenerate faces and nodes displaced by 1/4 the length of an edge. The stress intensity factors are found in terms of the displacements of the nodes of such elements. We give the results of computation of the concentration coefficients and the stress intensity factors for spherical and cylindrical shells loaded by internal pressure and for a cylindrical shell and a plate under the action of a distending load with various concentrators: a circular hole, an isolated crack, and a combined concentrator. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 23, 1992, pp. 48–54.     

The stress state of an anisotropic plate with two arbitrarily located elliptic holes or cracks

Using Lekhnitskii's method of complex potentials we study the stress state of an anisotropic plate with two arbitrary elliptic holes. We consider the cases when one or both of the holes become narrow slit-cracks, when the cracks extend to the edge of the hole, and when two cracks intersect or form a broken two-link crack. We give the results of numerical studies. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 24, 1993, pp. 33–43.     

The effect of the interface between media on stress concentration in the vicinity of a crack

The problem of determining the effect of the media interface in a piecewise-homogeneous body on the stress concentration in the vicinity of cracks located in one of the half-spaces is reduced to a system of two-dimensional singular equations of Newtonian potential type. We study the effect of the relations of the elastic constants of the materials of a body composed of two half-spaces on the stress intensity factors in the vicinity of a crack. We study different variants of the crack location relative to the interface. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 64–69.     

Numerical computation of the stress-strain state at the end of a crack under dynamic load

We obtain the values of the stress intensity factor at the end of a stationary crack under dynamic load using a numerical method. We compare the results with the existing experimental data. We establish that it is possible to apply the proposed method to compute stationary cracks under dynamic load. Translated fromDinamicheskie Sistemy, No. 13, 1994, pp. 61–65.     

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.     

The stressed state of elastoplastic shells with nonthrough cracks

We study the problem of the stressed state and limiting equilibrium of shells with nonthrough surface cracks. Several assumptions make it possible to reduce the three-dimensional problem to the two-dimensional problem and the latter to a system of singular integral equations whose solution is constructed using numerical methods. For cylindrical and spherical shells weakened by nonthrough cracks situated along the coordinate lines we carry out a numerical analysis of the dependence of the crack opening on the load and the geometric and physico-mechanical parameters of the shells.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 35, 1992, pp. 147–151.     

Separation of a surface crack in a spherical shell taking account of elastic deformation

We give the statement and solution of the problem of limiting equilibrium of a spherical shell weakened by a surface crack. We study the dependence of the separation of the edges of the crack on the geometric and physical parameters of the shell.     

The opening of a nonthrough longitudinal crack in a cylindrical shell taking account of elastoplastic deformation

In the context of an analog of the _k —model the problem of the stress-strain state of a shallow cylindrical shell with a nonthrough longitudinal crack is reduced to a system of singular integral equations that is solved by the small-parameter method. For a shell under an internal pressure we study the dependence of the opening of the crack on the geometric and physico-mechanical parameters of the shell.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 31, 1990, pp. 66–70.     

Development of a finite-element analysis methodology for the propagation of delaminations in composite structures

Analysing the collapse of skin-stiffened structures requires capturing the critical phenomenon of skin-stiffener separation, which can be considered analogous to interlaminar cracking. This paper presents the development of a numerical approach for simulating the propagation of interlaminar cracks in composite structures. A degradation methodology was introduced in MSC.Marc, which involved the modelling of a structure with shell layers connected by user-defined multiple-point constraints (MPCs). User subroutines were written that employ the virtual crack closure technique (VCCT) to determine the onset of crack growth and modify the properties of the user-defined MPCs to simulate crack propagation. Methodologies for the release of failing MPCs are presented and are discussed with reference to the VCCT assumption of self-similar crack growth. The numerical results obtained by using the release methodologies are then compared with experimental data for a double-cantilever beam specimen. Based on this comparison, recommendations for the future development of the degradation model are made, especially with reference to developing an approach for the collapse analysis of fuselage-representative structures. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 15–42, January–February, 2007.     

An approximate method of determining the stress intensity factors for two-dimensional multiply connected bodies with rectilinear cracks

We propose a new method of determining the stress intensity factors based on the representation of rectilinear cracks as elliptic holes with a zero axis and using the classical complex potentials. We calculate the stress intensity factors in terms of the limiting values of the potentials as the points tend to the ends of a crack. The efficiency of the method is shown using examples. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 24, 1993, pp. 27–33.     

The vibrations of a conical shell filled with a variable volume of fluid

We consider the vibrations of a conical shell filled with a fluid. We obtain a system of differential equations that describes the interaction of a variable volume of fluid with the shell. We solve the problem of determining the natural frequencies for a completely full shell. We obtain a formula for computing the fundamental frequency as a function of the geometric parameters of the shell. One figure. Bibliography: 4 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 22, pp. 85–88, 1991.     

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.     

A study of the influence of the orientation of a planar surface crack in the shape of a limaçon of pascal on the stress concentration in a half-space

We study the stress state in the vicinity of a planar surface crack whose boundary is described by the limaçon of pascal. The problem is solved by a conformal mapping of the region occupied by the crack onto part of a disk in the plane. This makes it possible to apply a numerical-analytic method for solving systems of double singular integral equations of the mathematical theory of cracks. We present the graphs of the dependence of the stress intensity factor on the angular coordinate for cracks that are part of a limaçon of Pascal.     

Contact interaction of the borders of edge cracks in a flexible half plane

A singular integral equation method is used to study the closure of edge cracks during bending of an isotropic half space. The cases of a single crack and of a periodic system of cracks perpendicular to the edge of the half space are considered. The effects of the free edge and the spatial period of the cracks on the distribution of the contact reaction and limiting load are investigated. The numerical results are compared with published data obtained without taking crack closure into account, as well as with results on the contact problem for bending of an infinite plate. Ivano-Frankovsk Sector, Institute of Applied Mechanical and Mathematical Problems, National Academy of Sciences of Ukraine. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 29, pp. 83–89, 1999.     

Mathematical model of an internal crack in an elastoplastic cylindrical shell

We propose a mathematical model that makes it possible to reduce the problem of the stressed state and limit equilibrium of a cylindrical anisotropic elastoplastic shell with internal crack to a system of nonlinear singular integral equations with discontinuous functions on the right-hand sides. We construct an algorithm for numerical solution of such systems together with the conditions of plasticity and boundedness of stresses near the crack. For a transversally isotropic shell, we carry out a numerical analysis of the dependence of the opening of the internal crack front on the load and geometric and mechanical parameters. Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences L'viv. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 111–116, April–June, 1998     

On the stressed state of a non-thin transversally isotropic spherical shell with a circular hole

On the basis of a generalized theory constructed using the Fourier-series expansion of the unknowns in Legendre polynomials of the thickness coordinate we give a representation of the general solution of the equilibrium equations of a transversally isotropic spherical shell for an arbitrary approximation. On this basis we study the problem of the stressed state of a shallow spherical shell with a circular cavity on whose boundary surface there are tangential stresses varying nonlinearly over the thickness. Bibliography: 3 titles. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 28, 1998, pp. 19–24.     

Fluid dynamics of an underwater electric discharge on the axis of a shell immersed in a fluid

We study the motion of a fluid during an electrical discharge on the axis of an elastic cylindrical shell immersed in the fluid. We estimate the influence of the parameters of the shell on the dynamics of a gasvapor chamber. We point out several properties of the computation of the pulsed flows in an infinite volume of fluid (the choice of the method of constructing the grid, the limitation of the computational region). We obtain the pressure distribution over space at large distances from the shell. We analyze the influence of the shell on the parameters of the flow in the interior and exterior regions. Four figures. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 120–126.