Showing papers in "International Applied Mechanics in 2016"

Dynamics of Elastic Bodies, Solid Particles, and Fluid Parcels in a Compressible Viscous Fluid (Review)

Abstract: The results of linearization of the basic equations describing a compressible viscous fluid in which low-amplitude oscillations occur or solids move or that interacts with elastic bodies in which small perturbations propagate are discussed. The general solutions of the linearized equations are presented. The results of studying wave processes in hydroelastic systems using the three-dimensional linearized theory of finite deformations and theory of compressible viscous fluid are discussed. The results of studying the propagation of acoustic waves of various types in waveguides with plane and circular cylindrical interfaces between elastic and liquid media and the influence of large (finite) initial deformations, viscosity and compressibility of the fluid on acoustic waves are presented. Studies of the motion of objects in compressible ideal and viscous fluids under the action of radiation forces due to the acoustic field are reviewed. The emphasis is placed on the studies that use a method involving the solution of hydrodynamic problems for a compressible fluid with solid particles and the evaluation of the forces acting on these particles. The radiation force is determined as the constant component of the hydrodynamic force. The numerical results are presented in the form of plots, which are then analyzed

An Approximate Method for Analysis of Solitary Waves in Nonlinear Elastic Materials

Abstract: Two types of solitary elastic waves are considered: a longitudinal plane displacement wave (longitudinal displacements along the abscissa axis of a Cartesian coordinate system) and a radial cylindrical displacement wave (displacements in the radial direction of a cylindrical coordinate system). The basic innovation is the use of nonlinear wave equations similar in form to describe these waves and the use of the same approximate method to analyze these equations. The distortion of the wave profile described by Whittaker (plane wave) or Macdonald (cylindrical wave) functions is described theoretically

Exact Solutions of Boundary-Value Problems for Noncircular Cylindrical Shells

Abstract: Boundary-values problems for transversely isotropic infinitely long noncircular cylindrical shells under static loads are formulated and solved analytically. The system of basic equations is derived from a refined theory of deep shells with low shear stiffness. Expressions of the internal forces and generalized displacements for closed and open oval cylindrical shells under internal pressure and transverse force are derived. The effect of the aspect ratio and transverse-shear strains on the stress–strain state of these shells is analyzed

Three-Dimensional Problems of Thermoviscoplasticity: Focus on Ukrainian Research (Review)

Abstract: Methods and results of studying the three-dimensional viscoplastic stress–strain state of engineering structures under thermomechanical loading are presented. The following classes of thermoviscoelastic problems are considered: axisymmetric problems, nonaxisymmetric problems for bodies of revolution, three-dimensional problems for arbitrarily shaped bodies, three-dimensional problems for isotropic and anisotropic bodies of revolution

Analysis of the Effect of Local Loads on Thick-Walled Cylindrical Shells with Different Boundary Conditions

Abstract: Two approaches to the analysis of the stress–strain state of thick-walled cylindrical shells with different boundary conditions under local loads are proposed. These approaches involve the division of a thick shell into several coaxial shells. One approach uses polynomials to approximate the unknown functions in plan and over the thickness. In the other approach, the unknown functions are approximated by linear polynomials in plan, and their distribution over the thickness is found from the analytical solution of the corresponding system of differential equations. The stress–strain state of the shell in the area of local loading is analyzed for different boundary conditions. It is shown that the effect of the boundary conditions on the stress–strain state is very weak for shells of high curvature and strong for shells of low curvature

Deformation of a Flexible Orthotropic Spherical Shell of Variable Stiffness in a Magnetic Field

Abstract: An axisymmetric nonlinear problem of magnetoelasticity for an orthotropic spherical shell of variable stiffness with orthotropic conductivity is solved. The governing system of nonlinear differential equations that describes the stress–strain state of flexible orthotropic shells of variable stiffness in mechanical and magnetic fields is presented. A numerical example is given. The stress state of an orthotropic spherical shell is analyzed by varying the external current and mechanical force

Identification of the Hereditary Kernels of Isotropic Linear Viscoelastic Materials in Combined Stress state. 1. Superposition of Shear and Bulk creep

Abstract: Relations between the shear and bulk creep kernels of an isotropic linear viscoelastic material in combined stress state and the longitudinal and shear creep kernels constructed from data of creep tests under uniaxial tension and pure torsion are formulated. The constitutive equations of viscoelasticity for the combined stress state are chosen in the form of a superposition of the equation for shear strains and the equation for bulk strains. The hereditary kernels are described by Rabotnov’s fractional-exponential functions. The creep strains of thin-walled pipes under a combination of tension and torsion or tension and internal pressure are calculated

Stabilization of the Upper Equilibrium Position of a Pendulum by Spinning an Inertial Flywheel

Abstract: A way to control a spinning flywheel that ensures the absolute asymptotic stability of the upper equilibrium position of a pendulum is proposed. The robustness of this control is proved. A method to estimate the robustness domain in the space of parameters of the mechanical system is proposed. The results obtained are exemplified by a real model

On Constraints for Displacement Gradients in Elastic Materials

Abstract: The classical, quite abstract constraint |u k,i | < 1 for elastic materials and a number of possible mathematical and physical constraints for displacement gradients are discussed Keywords: elastic material, nonlinear elasticity, constraints, displacement gradient

Analysis of the Stress–Strain State of Inhomogeneous Hollow Cylinders

Abstract: The stress-strain state of an inhomogeneous hollow cylinder with different boundary conditions at the ends is analyzed using the three-dimensional theory of elasticity. Spline collocation is used to reduce the two-dimensional boundary-value problem to a boundary-value problem for a system of ordinary differential equations of high order with respect to the radial coordinate, which is solved with the stable discrete-orthogonalization method. The results obtained using the spline-collocation, Fourier-series, and finite-element methods are compared materials, and the consideration of three-dimensional effects in thick-walled structural members necessitate studying hollow cylindrical structures in three dimensions. The stress-strain analysis of thick-walled structures based on the three-dimensional theory of elasticity involves severe difficulties associated with the complexity of the starting systems of partial differential equations and the necessity to satisfy boundary conditions on the surface of an elastic body. These difficulties are even more severe when designing cylindrical elements made of anisotropic and inhomogeneous materials, such as functionally graded materials (FGM) with variable elastic characteristics. Modern technologies make it possible to produce structures with required smoothly varying elastic moduli. The physical and mechanical properties of FGMs based on various compositions are addressed in (3, 11-13). Of great practical interest and importance for fundamental research is the analysis of the stress-strain state of various structural members made of FGMs, including finite-length cylinders. In view of the above, it is necessary to determine the dynamic characteristics of such structural members in three dimensions. Due to great computational difficulties, there are only few publications on the

Nonstationary Deformation of Longitudinally and Transversely Reinforced Cylindrical Shells on an Elastic Foundation

Abstract: The problem of the forced vibrations of a discretely reinforced cylindrical shell on an elastic foundation under distributed impulsive loading is stated. The dynamic behavior of the inhomogeneous cylindrical shell is analyzed using the Timoshenko-type theory of shells. The problem is solved with the finite-difference method. Numerical results are analyzed

Buckling Analysis of Anti-Symmetric Cross-Ply Laminated Composite Plates Under Different Boundary Conditions

Abstract: The buckling analysis of anti-symmetric cross-ply laminated composite plates under different boundary conditions is examined by using a refined higher order exponential shear deformation theory. The theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The number of independent unknowns in the present theory is four, as against five in other shear deformation theories. In this investigation, the equations of motion for simply supported thick laminated rectangular plates are derived and obtained through the use of Hamilton’s principle. The closed-form solutions of anti-symmetric cross-ply and angle-ply laminates are obtained using Navier solution. Numerical results for critical buckling loads anti-symmetric cross-ply laminated composite plates are presented. The validity of the present study is demonstrated by comparison with other higher-order solutions reported in the literature. It can be concluded that the proposed theory is accurate and simple in solving the buckling behaviors of anti-symmetric cross-ply laminated composite plates under different boundary conditions

Effect of Prestresses on the Dispersion of Waves in a System Consisting of a Viscous Liquid Layer and a Compressible Elastic Layer

Abstract: The propagation of acoustic waves in a prestrained compressible elastic layer that interacts with a compressible viscous liquid layer is considered. Use is made of the three-dimensional equations of the linearized theory of finite deformations for the elastic layer and the three-dimensional linearized Navier–Stokes equations for the liquid layer. The problem statement and problem-solving method used are based on the general solutions of the linearized equations for the elastic and liquid layers. A dispersion equation describing the propagation of harmonic waves in the hydroelastic system over a wide frequency range is derived for both thin and thick elastic layers. The effect of the prestresses and the thickness of the layers on the phase velocities and damping factors of modes is analyzed for thin and thick elastic layers. It is established that for all the modes beginning from the second one, there are certain values of fluid thicknesses and frequency at which the pretension in the elastic layer do not affect their phase velocities and damping factors. If the elastic layer is thick, each mode generated by the fluid is shown to have three such frequencies. The approach developed and the results obtained allow us to identify the limits of applicability of models based on various theories of small initial deformations and the ideal-fluid model

Stability of the Horizontal Flight of an Aircraft

Abstract: The stability of the horizontal flight of a light aircraft is studied using the singular-perturbation method. A numerical parameter is introduced into the equation of motion to correct for possible errors of modeling. A set of parameter values at which stability remains is obtained

The Effect of Hydrostatic Initial Stress on the Plane Waves in a Fiber-Reinforced Magneto-Thermoelastic Medium with Fractional Derivative Heat Transfer

Abstract: The effect of three factors—the order of fractional derivative, the hydrostatic initial stress, and parameter of magnetic field—on the plane waves in a half-space made of fiber-reinforced material described by the theory of generalized magneto-thermoelasticity is studied. The problem is solved numerically using the normal mode analysis. The results correspond to the Lord–Shulman model and the model that uses fractional derivatives and are represented in the form of graphs. The findings show pronounced effect of the three factors. The results are compared with the case where the initial stress and magnetic field are absent

Motion of an Articulated Vehicle with Two-Dimensional Sections Subject to Lateral Obstacles

Abstract: Some aspects of the geometry, kinematics, and dynamics of a three-section robotic vehicle with a front steerable wheel are studied. The constraints between the wheels and the flat ground are assumed nonholonomic. The vehicle moves in a narrow L-shaped corridor. A path for the characteristic points of the sections of the robot is designed. A dynamic model of the system is developed. The maximum possible dimensions of the robot that allow its unimpeded and non-stop motion are determined. The kinetostatic analysis of the load on a three-section vehicle moving along a planned path is modeled. The holonomic and nonholonomic constraint reactions between the wheels and the ground and in the joints between the sections are determined

Vibrations of Shells of Revolution with Branched Meridian

Abstract: A method for determining the natural frequencies of compound shells of revolution with a branched meridian is proposed. This method combines the Fourier method, the incremental search method (∆(λ)-method), and the orthogonal-sweep method. The method is tested against specific examples. The dependence of the lower frequencies of a cylinder–ring-plate system on the relative stiffness of its components is studied.

Wave Propagation in an Elastic Layer Interacting with a Viscous Liquid Layer

Abstract: The Navier–Stokes three-dimensional linearized equations for a viscous fluid and the linear equations of classical elasticity for an elastic layer are used to plot dispersion curves and to study the propagation of acoustic waves over a wide frequency range. The effect of the viscosity of the fluid and the thickness of the elastic and liquid layers on the phase velocities and the damping factors of the modes is analyzed for both thin and thick solid layers. It is shown that for the thick elastic layer, there are certain thicknesses of the liquid layer and certain frequencies at which the effect of the viscosity of the fluid on the phase velocities and damping factors of all the modes is the weakest. It is also revealed that for a number of modes, there are certain frequencies and certain frequency ranges for which the effect of the viscosity of the fluid on the phase velocities and damping factors of the modes is strong. The approach developed and the results obtained allow identifying the limits of applicability of the model of ideal compressible fluid. The numerical results are presented in the form of plots and analyzed

Influence of Cross-Sectional Ellipticity on the Deformation of a Long Cylindrical Shell

Abstract: The computational phenomenon of membrane locking in the variational-difference method is demonstrated. The delayed but stable convergence of numerical calculations of the stress–strain state to the analytical solution is shown. This problem can supplement the collection of so-called pathological tests

Nonlinear Elastic Deformation of Thin Composite Shells of Discretely Variable Thickness

Abstract: A method for analyzing the stress–strain state of nonlinear elastic orthotropic thin shells with reinforced holes and shells of discretely variable thickness is developed. The reference surface is not necessarily the midsurface. The constitutive equations are derived using Lomakin’s theory of anisotropic plasticity. The methods of successive approximations and variational differences are used. The Kirchhoff–Love hypotheses are implemented using Lagrange multipliers. The method allows analyzing the stress–strain state of shells with arbitrarily varying thickness and ribbed shells. The numerical results are presented in the form of tables and analyzed

Vibrations of Cylindrical Sandwich Shells with Elastic Core Under Local Loads

Abstract: The vibrations of a cylindrical sandwich shell with elastic core under local loads are studied. The Kirchhoff–Love hypotheses are applied to the isotropic base layers. For the thick core, the work of transverse shear and thickness reduction are taken into account, and the displacements are assumed to vary linearly with the transverse coordinate. The displacements are considered continuous at the interfaces. The Winkler hypothesis is applied to the elastic core. The analytical solutions to the problems of natural and forced vibrations are found. The variation in displacements in the shell under forces per unit length is studied

Finite-Fiber Model in the Three-Dimensional Theory of Stability of Composites (Review)

Abstract: Results obtained using the three-dimensional linearized theory of stability of deformable bodies (TLTSDB) and the new so-called finite-fiber model for fibrous and laminated composites are reviewed and compared with the results previously obtained using the well-known infinite-fiber model. The article consists of two parts. The first part is a short historical sketch of experimental and theoretical studies into the following two problems: (i) microbuckling of composites and (ii) failure or fracture of composites when microbuckling is the initial stage of the process. The applicability of the infinite-an d finite-fiber models to various composites is confirmed by analyzing experimental results obtained by various authors. The second part is a brief review of theoretical results obtained using the TLTSDB and the finite-fiber model for fibrous and laminated composites. The buckling problem is solved for the following cases: one and two short fibers, a periodic row of short fibers, and short fibers near a free boundary. The influence of mechanical and geometric parameters of the composite components on the critical strain and buckling of reinforcement is analyzed. The results for the finite-fiber model were obtained by solving a plane problem and considering the prospects for solving spatial problems, which is very important

Identification of the Hereditary Kernels of Isotropic Linear Viscoelastic Materials in Combined Stress State. 2. Proportional deviators

Abstract: The relationships between the hereditary and creep kernels are established. The hereditary kernels define the scalar properties of isotropic linear viscoelastic materials in a combined stress state. The creep kernels are obtained in uniaxial-tension and pure-torsion tests. The constitutive equations are chosen so as to meet the hypothesis of proportional deviators. The problems of analyzing the creep deformation and stress relaxation of thin-walled tubular specimens under combined tension and torsion are solved and tested experimentally

Analysis of Thermal-Magnetic-Elastic Stresses and Strains in a Thin Current-Carrying Cylindrical Shell

Abstract: A thermal-magnetic-elastic problem for a thin current-carrying cylindrical shell in a magnetic field is studied. The normal Cauchy form nonlinear differential equations, which include eight basic unknown functions in all, are obtained by the variable replacement method. Using the difference and quasi-linearization methods, the nonlinear differential equations are reduced to a sequence of quasi-linear differential equations, which can be solved by the discrete-orthogonalization method. The numerical solutions are obtained. The change of stresses, temperatures, and deformations in the thin current-carrying cylindrical shell with variation of the electromagnetic parameters is discussed. It is proved that the stresses, strains, and temperatures in thin shells can be controlled by changing the electromagnetic and mechanical parameters by considering a specific example

Stability and Post-Buckling Behavior of Orthotropic Cylindrical Shells With Local Deflections

Abstract: A procedure for analytical solution of the problem of the stability and post-buckling behavior of orthotropic cylindrical shells under external pressure or axial compression with allowance for transverse shears is developed. The shells are geometrically imperfect due to the presence of a local deflection. The problem is solved by analyzing the interaction of the modes that represent the critical loads of the perfect shell and using the Byskov–Hutchinson method. Equilibrium curves for both shells are plotted using the method of continuous loading

Effect of Orthotropy on the Stress State of Longitudinally Corrugated Hollow Cylinders

Abstract: The effect of orthotropy on the stress state of longitudinally corrugated orthotropic hollow cylinders is analyzed using a three-dimensional problem formulation, the analytical variable-separation and Fourier-series methods, and the numerical discrete-orthogonalization method. The results obtained are presented in the form of graphs of displacement and stress fields

Stabilization of the Motion of a Nonlinear System with Interval Initial Conditions

Abstract: The motion of a control system with many controls is studied. It is described by a nonlinear system of differential equations with interval initial conditions. To estimate the interval norm of the motion of the system, nonlinear integral inequalities are used. The estimate is used to establish the conditions stabilizing the motion of the system. A mechanical system consisting of two coupled simple pendulums controlled by forces is considered as an example

Nonstationary Vibrations of Transversely Reinforced Elliptic Cylindrical Shells on an Elastic Foundation

Abstract: The forced vibrations of transversely reinforced elliptic cylindrical shells on an elastic foundation under nonstationary loads are studied using the Timoshenko-type theory of shells and rods. A numerical algorithm for solving problems of this class is developed. A numerical example for the case of distributed impulsive loading is given

Self-Excitation of Torsional Vibrations of Long Drillstrings in a Viscous Fluid

Abstract: The problem of the self-excitation of the torsional oscillations of a drillstring rotating in a fluid in a deep borehole is stated. Three models describing the mechanical interaction between the drillstring and the viscous fluid are discussed. Governing equations with ordinary and partial derivatives are derived. A method to solve them is developed. Computer simulation shows that the self-oscillations are relaxational and the curves of the functions that describe them have sections of fast and slow motions. The results of simulation can be used to develop a technique for drilling deep oil and gas boreholes

Nonstationary Dynamics of a System Consisting of a Cylindrical Shell and a Soil Medium of Periodic Structure

Abstract: The problem of wave processes in a system consisting of a cylindrical shell and a soil medium of periodic structure under impulsive loading is solved numerically. The results obtained allow us to control the parameters of a compressional wave entering the soil and to predict the behavior of the wave processes, depending on geometrical and mechanical parameters of the shell and soil