Mixed-hybrid scheme of the finite element method for solving the problems on bending,free vibration,and stability of plates

To solve a problem on bending, vibration, and stability of plates, a hybrid finite element has been constructed on the basis of Zienkiewicz’s triangle. A mixed approximation is used for the plate deflection and turning angles. It is shown that with a decrease in the triangle dimensions the mixed approach ensures convergence both for the plate deflection and the bending moments, which is practically independent of the way the plate is split into triangular elements. In the problems on free vibrations and stability of plates, the mixed approach yields more exact values of the eigenfrequencies and critical loads as compared to a classical Zienkiewicz’s triangle. The results of the numerical analysis of the convergence and accuracy of the solutions to a number of test problems on bending, free vibration, and stability of a square plate are presented. __________ Translated from Problemy Prochnosti, No. 4, pp. 108–122, July–August, 2008.     

An improved model for the analysis of deformation and stability of multilayer viscoelastic shells

We propose a numerical procedure for the analysis of stability of viscoelastic multilayer shells of revolution based on an improved two-dimensional model. The calculations are performed under the assumption that the layers of the shell are made of orthotropic composite materials and their creep can be described within the framework of linear hereditary theory. We study the problem of stability of a five-layer conic shell with elastic load-carrying layers and viscoelastic fillers loaded by uniform external pressure. Translated from Problemy Prochnosti, No. 5, pp. 89–94, September–October, 1997.     

Analysis of the limiting plastic state of a thick-walled bent pipe

We propose an engineering approach to the determination of the limiting state of a bent pipe. In the first stage, the influence of some groups of external loads is analyzed separately. Then it is necessary to determine the coefficient of reduction of internal moments under the combined action of external bending moments and internal pressure. In the final stage, we use a specially developed general approach to the analysis of the limiting state at a given point of the cross-section of a bent pipe for the obtained system of internal forces, namely, for the bending moment, the tensile force acting in the circumferential direction, and longitudinal and tangential forces. We also demonstrate the possibility of application of the obtained results to the approximate analysis of cracks and three-dimensional defects appearing in a bent pipe. Scientific and Engineering Center of Materials-Science Support of the Production and Certification of Equipment of Nuclear Power Plants at the Institute for Problems of Strength of the National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 2, pp. 131 – 150, March – April, 1998.     

Stressed state of multilayer shells of revolution simulating pneumatic tires operating in contact with rigid base

We propose a procedure for the solution of the contact problem for preliminarily loaded anisotropic shells of revolution as applied to the evaluation of the stressed state of pneumatic tires. We use the principal relations of the nonclassical model of shells with regard for all types of transverse deformation. The preliminary stresses induced in the shell by axisymmetric loads of various kinds are taken into account as parametric terms in the linearization of the initial geometrically nonlinear equations of medium bending. The corresponding two-dimensional boundary-value problems are solved with the help of a combination of analytic and numerical approaches. By using a structure simulating pneumatic tires as an example, we study the influence of internal pressure on the size of the contact zone with rigid base, the characteristic of loading, and static stiffness. __________ Translated from Problemy Prochnosti, No. 3, pp. 75–86, May–June, 2007.     

Approximate method for the analysis of stability of beams under the action of a system of longitudinal and transverse forces

We propose an approximate method for the analysis of stability of uniplanar bending of beams under the action of a complex system of longitudinal and transverse forces, obtain formulas for the determination of the critical values of total longitudinal and transverse forces and the factor of stability of flange and rectangular beams that are convenient for practical applications, and present examples of the numerical analysis of actual beams. The critical values of the total forces obtained by the proposed method are compared with known results. The difference between the exact and approximate critical values does not exceed 2–7%. The experimental data enable us to recommend these approximate formulas for practical calculations of the stability of uniplanar bending of beams subjected to the combined action of complex systems of longitudinal and transverse forces. Translated from Problemy Prochnosti, No. 3, pp. 69–77, May–June, 1998.     

Bilateral bending of a plate with nonsymmetric through-thickness arc crack with allowance for the contact of its edges

The problem of bending of plates with nonsymmetric through-thickness arc crack with distributed moments at infinity with allowance for the contact of the crack edges has been examined on the basis of the classical theory of plate bending. The conditions for the existence of the solution of the problem in this formulation have been established. A numerical analysis of intensity factors of forces and moments, contact force between the crack edges has been performed, the results of which have been graphically illustrated. __________ Translated from Problemy Prochnosti, No. 5, pp. 135–141, September–October, 2006. Report on International Conference “Dynamics, Strength, and Life of Machines and Structures” (1–4 November 2006, Kiev, Ukraine).     

Nonlinear inelastic uniform torsion of bars by BEM

In this paper the elastic–plastic uniform torsion analysis of simply or multiply connected cylindrical bars of arbitrary cross-section taking into account the effect of geometric nonlinearity is presented employing the boundary element method. The stress–strain relationship for the material is assumed to be elastic–plastic–strain hardening. The incremental torque–rotation relationship is computed based on the finite displacement (finite rotation) theory, that is the transverse displacement components are expressed so as to be valid for large rotations and the longitudinal normal strain includes the second-order geometric nonlinear term often described as the “Wagner strain”. The proposed formulation does not stand on the assumption of a thin-walled structure and therefore the cross-section’s torsional rigidity is evaluated exactly without using the so-called Saint-Venant’s torsional constant. The torsional rigidity of the cross-section is evaluated directly employing the primary warping function of the cross-section depending on both its shape and the progress of the plastic region. A boundary value problem with respect to the aforementioned function is formulated and solved employing a BEM approach. The influence of the second Piola–Kirchhoff normal stress component to the plastic/elastic moment ratio in uniform inelastic torsion is demonstrated. The developed procedure retains most of the advantages of a BEM solution over a pure domain discretization method, although it requires domain discretization, which is used only to evaluate integrals.     

Closure of a Longitudinal Crack in a Shallow Cylindrical Shell in Bending

We study the two-dimensional problem of contact interaction of the lips of a longitudinal crack in a cylindrical shell subjected to bending under the assumption of contact along a line. The influence of the surface curvature and crack closure on the stressed state and limiting equilibrium of the shell is analyzed. The numerical results are compared with the asymptotic solution of the problem. __________ Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 2, pp. 45–48, March–April, 2005.     

Dynamic instability of a pipe with internal mobile liquid blocks

We consider the problem of parametric vibrations of a rectilinear pipeline with internal mobile liquid blocks. As a result of its solution, we determine the influence of the size of the liquid blocks and their velocity on the character of the loss of stability of the pipe. Ukrainian Transport University, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 3, pp. 114–121, May–June, 1999.     

Analysis of the stressed state in equal-diameter T-joints of pipelines. Part 1. Action of internal pressure and bending moments in the plane of a T-joint

We analyze the stressed state of two types of T-joints in which the union makes angles of 45° and 90° with the main pipe. The character of the distribution of stresses in a T-joint illustrates the distinctive features of its operation under the action of internal pressure and bending moments applied in the plane of the T-joint. On the basis of the theory of strength for specific distortion strain energy, we determine the stress concentration factors for all considered loading modes. The numerical values of the stress concentration factors are compared with the experimental data obtained by other authors. Translated from Problemy Prochnosti, No. 6, pp. 116–123, November–December, 1998.     

A comparative investigation of an ultrasonic nozzle by optical methods

A series of experiments in a wind tunnel using optoelectronic instruments has been carried out. Flow in a 2D ultrasonic nozzle was investigated. Experimental results were obtained using three methods – the shadow method, the schlieren method and holographic interferometry, which are compared with the classical method of measuring pressure and the results of numerical calculations. Translated from Izmeritel’naya Tekhnika, No. 12, pp. 27–31, December, 2008.     

Application of volumetric method to the assessment of damage induced by action of foreign object on gas pipes

Gas pipes are submitted to three major types of damage: damages induced by impact of foreign objects, pits and craters produced by corrosion, weld defects produced during manufacturing. Damages induced by impact of foreign objects are considered as the most important problem for the gas pipes reliability and lead to dents, gouges or notches at the pipe failure. Geometrical effect of gauges or notches on brittle or elastoplastic failure of pipes submitted to internal pressure can be treated by the volumetric method. The volumetric method has been applied to a gas pipe submitted to internal pressure and exhibiting a longitudinal external and surface notch. We introduced a special procedure SINTAP, which allows one to compute the safety factor value. __________ Translated from Problemy Prochnosti, No. 4, pp. 109–117, July–August, 2006.     

Diagnosis of the load-carrying capacity of pipes containing a longitudinal crack when loaded by an axial force and internal pressure

A method is developed for evaluating the load-carrying capacity and safe life of pipes with a through longitudinal crack when loaded by an axial force and internal pressure. The method is based on the use of previously developed nomograms of strain and limit load. The first nomogram is calculated on the basis of constitutive relations of the theory of plasticity, while the second is calculated in accordance with a fracture criterion for biaxial loading. The proposed method makes it possible to determine one of three parameters — critical crack length, limiting pressure, or limiting axial load — without preliminary calculations if the other two parameters are already known. As an example, nomograms are presented for a steel 15G2 pipe having a diameter of 1420 mm and wall thickness of 21.5 mm and containing a longitudinal crack. Translated from Problemy Prochnosti, No. 12, pp. 16–23, December, 1994.     

On the moment theory of elasticity. Plane deformation. Part 2

For the problem of bending of a plate under the action of a concentrated force represented as pressure distributed over a small surface, we obtain a solution by methods of the moment theory of elasticity, the principal statements of which were given in Part 1. Moscow State Institute of Food Industry, Moscow, Russia. Translated from Problemy Prochnosti, No. 4, pp. 106–115, July–August, 1998.     

Brittle-fracture criterion and durability of materials under thermomechanical action

Consideration has been give to the thermoelasticity problem for a plane containing a rectilinear crack under the conditions of constant tensile stress and a nonuniform stationary temperature field. The system’s thermodynamic potential from whose stationary condition the criterion of brittle fracture of a material has been established has been computed by solution of the problem indicated. The average durability of the material under thermomechanical action has been evaluated. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 2, pp. 394–400, March–April, 2008.     

Simulation of nonisothermal moisture transfer and stresses in wood in drying

We obtain a numerical solution for a two-dimensional problem of nonisothermal moisture transfer in the anisotropic structure of wood (lumber) in convective drying. On the basis of elasticity theory we determine internal thermal and moisture stresses. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 3, pp. 404–411, May–June, 1998.     

Bending oscillations of a rectangular orthotropic plate with massive inclusion

We study the problem of natural and forced oscillations of a hinged rectangular plate with massive elliptic inclusion. The process of bending of the plate is described by the modified equations of the Tymoshenko theory of plates. The numerical solution of the problem is obtained by the indirect method of boundary elements based on the sequential representation of distributions and the collocation method. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 6, pp. 41–46, November–December, 2008.     

Determination of the Joule–Thomson coefficient in problems of measuring the flow rate of natural gas

Existing methods of calculating the Joule–Thomson coefficient for natural gas are analyzed. A procedure for use in calculations of gas flow rate employing the variable pressure drop method is proposed which gives increased measurement accuracy by eliminating the additional error in determining the temperature of the natural gas. Translated from Izmeritel’naya Tekhnika, No. 5, pp. 46–49, May, 2009.     

Deformation behavior of rotating disks with thin high-modulus coatings

Based on equations of linear three-dimensional elasticity theory, a problem is stated for the design calculation for rotating disks with hardening coatings, allowing for boundary layers formed. A numerical integration method is proposed for the stated problem, and some particular calculations are performed. Discussion of the calculated stress fields in the disk base material and coatings provides an explanation of some effects revealed, such as a significant improvement of load-carrying capacity of disks when face-coated with high-modulus layers of about 0.1–0.6 mm in thickness and a deterioration of this parameter (in some cases) when thicker coatings are applied. The authors study the applicability range of the conventional theory of disk strength calculation which assumes a two-dimensional stressed state and no boundary layers. __________ Translated from Problemy Prochnosti, No. 3, pp. 35–50, May–June, 2007.     

Bifurcations in the trajectory problem as a cause of internal-time singularities and the onset of quantum (wave)chaos

A new theory is proposed for quantum-mechanical multichannel scattering in a collinear three-body system. This simple problem is used to show that the principle of quantum determinism is generally violated and we are dealing with microirreversible quantum mechanics. Fundamental calculations of quantum (wave) chaos are presented for the first time for the elementary reaction Li+(FH)→(LiFH)*→LiF+H. Pis’ma Zh. Tekh. Fiz. 25, 12–22 (August 26, 1999)