The stress-strain state of a plate with a multilayer inclusion

A modified boundary-element method is proposed to analyze the stress-strain state of a plate with a multilayer inclusion of arbitrary shape. The two-dimensional approximation of displacements on each boundary element makes it possible to determine all the stress/strain components at the interface between the inclusion and each layer. The stress state of a plate with an elliptical and a rectangular multilayer inclusion under unidirectional tension (a load uniformly distributed along the edges) is analyzed as numerical examples. The numerical examples demonstrate high accuracy and computational efficiency of the method __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 104–110, March 2007. For the centenary of the birth of G. N. Savin.     

On determining stresses in rigid inclusions. Plane problems

Plane problems of determining the stress-strain state of an isotropic elastic domain with a rigid inclusion are considered. It is shown that the stress field in the inclusion is uniquely determined. This field is uniform for a plane with an elliptic inclusion, and the stresses at infinity and in the inclusion are related by mutually single-valued formulas. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 183–186, July–August, 2009.     

Stress-strain state of an anisotropic plate with an elliptic hole and thin rigid inclusions

The stress-strain state of an anisotropic plate containing an elliptic hole and thin, absolutely rigid, curvilinear inclusions is studied. General integral representations of the solution of the problem are constructed that satisfy automatically the boundary conditions on the elliptic-hole contour and at infinity. The unknown density functions appearing in the potential representations of the solution are determined from the boundary conditions at the rigid inclusion contours. The problem is reduced to a system of singular integral equations which is solved by a numerical method. The effects of the material anisotropy, the degree of ellipticity of the elliptic hole, and the geometry of the rigid inclusions on the stress concentration in the plate are studied. The numerical results obtained are compared with existing analytical solutions. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 173–180, July–August, 2007.     

Mathematical Modeling for One New Method of Breaking Ice Cover

The spatial problem of determining the stress-strain state of an ice plate of finite thickness broken by a patented method is solved using the theory of small elastoplastic strains and a proven numerical method. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 139–146, March–April, 2006.     

Stress-strain state of an anisotropic plate with curvilinear cracks and thin rigid inclusions

A mixed problem of linear elasticity for an infinite anisotropic plate with cuts and thin undeformable inclusions located along arbitrary open smooth curves is solved with the use of complex potentials. Special representations of the solutions are constructed and a governing system of singular integral equations is obtained. A numerical algorithm for determining the stress-strain state of the plate, including the stress-intensity factors at the tips of cuts and rigid inclusions, is proposed. Calculation results are given. Novosibirsk State Technical University, Novosibirsk 630092. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 3, pp. 213–219, May–June, 2000.     

Determination of the strength characteristics of a physically nonlinear inclusion in a linearly elastic medium

An isotropic elastic plane with a physically nonlinear inclusion with unknown properties is considered. The general relations between the stress-strain state of the inclusion and the loads applied at infinity are obtained. These relations are used to develop a method of determining the viscoelastoplastic properties of an inclusion that is based on measurement of the displacement vectors of two points that lie on the boundary of the inclusion and are nonsymmetrical with respect to its center. This makes it possible to find numerical values of the constants that enter the constitutive equations of an inclusion. Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 4, pp. 178–184, July–August, 2000.     

On an inverse problem of bending of a physically nonlinear inhomogeneous plate

An elastic plate with a physically nonlinear inclusion of an arbitrary shape is considered. This plate is subjected to pure bending under the action of transverse forces and bending moments applied at the external boundary of the plate. There are no loads distributed over the surface. The problem of finding external actions that provide a necessary uniform moment state in the inclusion, i.e., prescribed constant moments and curvatures, is formulated and solved. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 104–107, September–October, 2007.     

On the stress-strain state of a transversally isotropic body with a paraboloidal inclusion

A closed solution is presented for the three-dimensional problem of the stress-strain state of an unbounded elastic body with a soldered-in transversally isotropic inclusion in the form of a paraboloid of revolution. Here, it is assumed that the body is under axisymmetric tension (compression). A solution of the corresponding problem for a paraboloidal recess is obtained as a special case. Podil’chuk [2, 3] has investigated similar problems for isotropic bodies with an inclusion assuming the form of a paraboloid of revolution or an elliptical paraboloid. Translated from Prikladnaya Mekhanika, Vol. 34, No. 11, pp. 16–22, November, 1998.     

Determination of the axisymmetric geometrically nonlinear thermoviscoelastoplastic stress-strain state of shells of revolution

A method is developed for determining the axisymmetric thermoviscoelastoplastic stress-strain state of shells subjected to bending and torsion. The problem is solved in a geometrically nonlinear formulation with allowance for transverse shear. The geometrically nonlinear deformation of an annular plate, the thermoviscoelastoplastic deformation of a cylindrical shell, and the limiting state of a corrugated shell are studied as examples. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 35, No. 12, pp. 40–48, December, 1999.     

Dynamics of a prestressed incompressible layered half-space under moving load

The paper addresses a plane problem: a concentrated force acts on a plate resting on an elastic half-space with homogeneous prestrain. The equations of motion of the plate incorporate shear and rotary inertia. The half-space is assumed to be incompressible and isotropic in the natural state. The elastic potential is given in general form and is only specified for numerical purposes. The dependence of the critical velocity of the load and the stress-strain state on the prestresses is analyzed for different ratios between the stiffnesses of the layer and half-space and different contact conditions. The calculations are carried out for a half-space with Bartenev-Khazanovich potential __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 3, pp. 36–54, March 2008.     

Influence of anisotropy and boundary conditions on the thermoelastic equilibrium of nununiformly heated laminated plates

This paper deals with three-dimensional boundary-value problems of the heat transfer and thermoelasticity theory for laminated transversally isotropic rectangular plates affected by a nonuniform temperature field. An exact analytical solution is obtained for the case of both ideal and nonideal thermal and mechanical contacts of adjacent layers. Numerical calculations were performed for a two-layer rectangular plate of arbitrary thickness. The effect of material anisotropy as well as the boundary and contact conditions on the stress-strain state of a nonuniformly heated plate is revealed. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev Translated from Prikladnaya Mekhanika, Vol. 35, No. 11, pp. 96–105, November, 1999.     

Numerical solution of three-dimensional static problems of elasticity for a body with a noncanonical inclusion

A boundary-element scheme is proposed for the numerical determination of the stress-strain state of a three-dimensional composite body, which is an elastic inclusion of arbitrary shape perfectly bonded to an infinite elastic matrix. The scheme involves the reduction of the original problem to six boundary integral equations for the components of interfacial displacements and forces and the boundary-element parametrization and discretization of these equations using generalized Gaussian integrals and topological maps with regularizing Jacobians. Numerical results are obtained for a cylindrical inclusion with rounded ends in a matrix subject at infinity to constant forces acting along this fiber. The influence of the length-to-radius ratio of the fiber and the ratio of the elastic moduli of the matrix and fiber on the stresses is examined __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 27–35, April 2007.     

Discrete-continuum model of symmetric separation of a material

A problem of the beginning of motion of a finite-width cut in a linearly elastic plane under the action of symmetric external loading is formulated. The material on the way of cut propagation forms a layer (interaction layer). The stress-strain state of the material is postulated to be homogeneous across this layer. A system of integral boundary equations is obtained for determining the stress-strain state. Based on this system of equations, a discrete model of separation of the layer material is constructed under the assumption of a constant stress-strain state in an element of the interaction layer. The stress distribution in the pre-fracture zone is determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 134–140, January–February, 2009.     

Stability analysis of rectangular plates unidirectionally strengthened by ribs

The exact solution of the equations of neutral equilibrium is derived. The effect of the discrete arrangement of ribs on the behavior of the characteristics of the stress-strain state with distance from the plate edge is analyzed. The conditions of applicability of the theory of structurally orthotropic plates are formulated. The study was carried out in accordance with Project No. 614 of the Ukrainian Scientific and Technological Center. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 36, No. 4, pp. 132–136, April, 2000.     

On finite-element solution of spatial thermoviscoelastoplastic problems

A finite-element algorithm is proposed for the analysis of the thermoviscoelastoplastic stress-strain state of bodies under complex loading (thermal and mechanical). It is assumed that an arbitrary element of the body deforms along a rectilinear or slightly curved path. The three-dimensional stress-strain state of the body’s elements is determined using the iterative method of additional strains. The technique is tested by analyzing the three-dimensional viscoelastic stress-strain state of a hollow cylinder and the thermoplastic state of a disk __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 16–25, May 2006.     

Flexural vibrations of a thin circular elastic inclusion in an unbounded body under the action of a plane harmonic wave

The interaction of a plane harmonic longitudinal wave with a thin circular elastic inclusion is considered. The wave front is assumed to be parallel to the inclusion plane. Since the inclusion is thin, the matrix-inclusion interface conditions (perfect bonding) are formulated on the mid-plane of the inclusion. The bending displacements of the inclusion are determined from the bending equation for a thin plate. The problem is solved using discontinuous Lamé solutions for harmonic vibrations. Therefore, the problem can be reduced to the Fredholm equation of the second kind for a function associated with the discontinuity of normal stresses on the inclusion. The equation obtained is solved by the method of mechanical quadratures using Gaussian quadrature formulas. Approximate formulas for the stress intensity factors are derived. Results from a numerical analysis of the dependence of the SIFs on the dimensionless wave number and the stiffness of the inclusion are presented __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 5, pp. 16–21, May 2008.     

Numerical modeling of the shearing of irradiated fuel assemblies

The stress-strain state of layered bodies is studied numerically taking into account features of the loading devices used in the technological shearing processes of irradiated fuel assemblies. The effect of the localization of the hold-down clamp on the shear stress intensity and the shear stress value is studied. The dependence of the stress-strain state of the layers on the value of the gap between the blades is obtained. It is shown that the nature of the failure changes in the process of wearing of the shear blade edges. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 134–140, May–June, 2006.     

Stress-strain state of shallow shells with rectangular planform and varying thickness: Refined formulation

The stress-strain state of a shallow shell with rectangular planform and varying thickness is analyzed in a refined formulation for different boundary conditions. A numerical-and-analytic method is developed based on the spline-approximation and discrete-orthogonalization methods. The stress-strain state of shallow shells with thickness varied without change in weight is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 80–91, October 2007.     

One formulation of the problem of elastoplastic separation

The problem of the beginning of motion of a cut in a plane under symmetric external loading is considered. The material lying on the cut continuation forms a layer (interaction layer). A transition to a plastic state within the layer is assumed to be possible. The behavior of the layer is described by an ideally elastoplastic model, and the plane outside the layer is assumed to be linearly elastic. A system of boundary integral equations for determining the stress-strain state is derived. Based on this system, a discrete model of separation of the layer material is constructed under the assumption of a constant stress-strain state in the element of the interaction layer. The distribution of stresses in the pre-fracture zone is determined. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 4, pp. 187–195, July–August, 2009     

Evolution of the ice breaking process

The spatial problem of the stress-strain state of an ice sheet of finite thickness broken by a patented method is solved using the theory of small elastic strains and a proven numerical method. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 114–119, January–February, 2008.