Showing papers in "International Applied Mechanics in 2008"
TL;DR: In this article, the Lagrangian technique was applied to particle dispersion in a three-dimensional lid driven cavity, which yields a substantial decrease in computing time in comparison with LES computation.
Abstract: The aim of this communication is to show the ability of POD to compute the instantaneous flow velocity when applying the Lagrangian technique to predict particle dispersion. The instantaneous flow velocity at the particle's location is obtained by solving a low-order dynamical model, deduced by a Galerkin projection of the Navier-Stokes equations onto each POD eigenfunction and it is coupled with the particle's equation of motion. This technique is applied to particle dispersion in a three-dimensional lid driven cavity. It yields a substantial decrease in computing time in comparison with LES computation and it enables treating different cases of particle dispersion
29 citations
TL;DR: In this article, a two-dimensional nonlinear magneto-elastic model of a current-carrying orthotropic shell of revolution is constructed taking into account finite orthotropic conductivity, permeability, and permittivity.
Abstract: A two-dimensional nonlinear magnetoelastic model of a current-carrying orthotropic shell of revolution is constructed taking into account finite orthotropic conductivity, permeability, and permittivity. It is assumed that the principal axes of orthotropy are aligned with the coordinate axes and that the orthotropic body is magnetically and electrically linear. The coupled nonlinear differential equations derived describe the stress-strain state of flexible current-carrying orthotropic shells of revolution that have an arbitrarily shaped meridian and orthotropic conductivity and are in nonstationary mechanical and electromagnetic fields. A method to solve this class of problems is proposed
26 citations
TL;DR: In this paper, the three-dimensional theory of elasticity is used to study the free vibrations of an anisotropic hollow cylinder with different boundary conditions at the ends, and the relevant problem is solved by a numerical-and-analytic method.
Abstract: The three-dimensional theory of elasticity is used to study the free vibrations of an anisotropic hollow cylinder with different boundary conditions at the ends. The relevant problem is solved by a numerical-and-analytic method. Spline approximation and collocation is used to reduce the partial differential equations of elasticity to a boundary-value problem for a system of ordinary differential equations of high order for the radial coordinate, which is solved using the stable discrete-orthogonalization and incremental-search methods. The calculated results for an orthotropic inhomogeneous cylinder with boundary conditions of several types are presented
25 citations
TL;DR: In this paper, a system of three nonlinear partial differential equations describing the flexural-flexural-torsional vibrations of a rotating slender cantilever beam of arbitrary cross-section is derived using Hamilton's principle.
Abstract: A system of three nonlinear partial differential equations describing the flexural-flexural-torsional vibrations of a rotating slender cantilever beam of arbitrary cross-section is derived using Hamilton’s principle. It is assumed that the center of gravity and the shear center are at different points. The interaction between flexural and torsional vibrations is accounted for in the linear and nonlinear parts of model
22 citations
TL;DR: In this article, a comparative analysis is made of the infinite-fiber and finite fiber models in the three-dimensional theory of composites, and the results analyzed have been obtained using the threedimensional linearized theory of deformable bodies.
Abstract: A comparative analysis is made of the infinite-fiber and finite-fiber models in the three-dimensional theory of stability of composites. The results analyzed have been obtained using the three-dimensional linearized theory of stability of deformable bodies. A historical sketch is given of the theory of stability for and approaches used in the mechanics of laminated and fibrous composite materials
21 citations
TL;DR: In this paper, the theory of long-term damage of homogeneous materials is generalized to particulate composite materials and an equation of damage (porosity) balance in the composite components at an arbitrary time is formulated.
Abstract: The theory of long-term damage of homogeneous materials is generalized to particulate composite materials. The damage of the composite components is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the tensile strength, according to the Huber-Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the composite components at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and corresponding curves are plotted in the case of limited microdurability
19 citations
TL;DR: In this paper, the authors developed an approach based on spline approximation and a stable numerical method of solving one-dimensional static problems for nonthin conical shells of varying thickness to examine the effect of geometrical parameters on the stress-strain state of shells.
Abstract: The approach developed to solve two-dimensional static problems for nonthin conical shells of varying thickness is used to examine the effect of the geometrical parameters on the stress-strain state of shells. The approach is based on spline-approximation and a stable numerical method of solving one-dimensional problems
18 citations
TL;DR: In this paper, an approach developed earlier to solve boundary value problems is used to analyze the behavior of the stress-strain state of orthotropic elliptic cylindrical shells with variation in the geometric parameters of their cross section at constant volume (weight).
Abstract: An approach developed earlier to solve boundary-value problems is used to analyze the behavior of the stress-strain state of orthotropic elliptic cylindrical shells with variation in the geometric parameters of their cross section at constant volume (weight)
17 citations
TL;DR: In this article, the stability and vibration problems for nonclosed circular cylindrical shells hinged along the longitudinal edges and reinforced with a regularly arranged discrete longitudinal ribs are solved approximately in the cases of regularly and quasiregularly arranged ribs.
Abstract: The paper gives exact solutions to the stability and vibration problems for nonclosed circular cylindrical shells hinged along the longitudinal edges and reinforced with a regularly arranged discrete longitudinal ribs. These problems are also solved approximately in the cases of regularly and quasiregularly arranged ribs
17 citations
TL;DR: In this article, the parameters of the fractional exponential creep and relaxation kernels of linear viscoelastic materials are determined by using the Mittag-Leffler function, the Laplace-Carson transform, and direct approximation of the creep function by the original equation.
Abstract: The parameters of the fractional exponential creep and relaxation kernels of linear viscoelastic materials are determined. Methods that approximate the kernel by using the Mittag-Leffler function, the Laplace-Carson transform, and direct approximation of the creep function by the original equation are analyzed. The parameters of fractional exponential kernels are determined for aramid fibers, parapolyamide fibers, glass-reinforced plastic, and polymer concrete. It is shown that the kernel parameters calculated through the direct approximation of the creep function provide the best agreement between theory and experiment. The methods are experimentally validated for constant-stress and variable-stress loading in the modes of additional loading and complete unloading
16 citations
TL;DR: In this paper, a method of characteristics is used to obtain an analytical solution describing the thickness vibrations of a piezoelectric layer polarized across the thickness and subjected to a nonstationary electric potential.
Abstract: The method of characteristics is used to obtain an analytical solution describing the thickness vibrations of a piezoelectric layer polarized across the thickness and subjected to a nonstationary electric potential. The features of how the vibrations are excited and propagate under electric loading are studied. The dynamic electromechanical state of the layer is analyzed. The electric and mechanical characteristics as functions of time are plotted
TL;DR: In this paper, an approach to solving a mixed initial-boundary-value problem with an unknown moving boundary is developed, which is reduced to an infinite system of integral equations and the equation of motion of the indenter.
Abstract: The nonstationary indentation of a rigid blunt indenter into an elastic layer is studied. An approach to solving a mixed initial-boundary-value problem with an unknown moving boundary is developed. The problem is reduced to an infinite system of integral equations and the equation of motion of the indenter. The system is solved numerically. The analytical solution of the nonmixed problem is found for the initial stage of the indentation process
TL;DR: In this paper, the authors studied the stress rupture behavior of a reinforced viscoelastic composite through which a penny-shaped mode I crack propagates under a constant load, where the crack is in the isotropy plane.
Abstract: The paper studies the stress rupture behavior of a reinforced viscoelastic composite through which a penny-shaped mode I crack propagates under a constant load. The composite has hexagonal symmetry and consists of elastic isotropic fibers and viscoelastic isotropic matrix. The material is modeled as a transversely isotropic homogeneous viscoelastic medium with effective characteristics. The crack is in the isotropy plane. The ring-shaped fracture process zone at the crack front is modeled by a modified Dugdale zone with time-dependent stresses. The viscoelastic properties of the matrix are characterized using a resolvent integral operator. Use is made of Volterra's principle, the method of operator continued fractions, and the theory of precritical crack growth in viscoelastic bodies. The problem is reduced to nonlinear integral equations. Numerical results are obtained for certain components of the composite, constant volume fractions, and different fracture strengths
TL;DR: In this paper, the theory of long-term damage of homogeneous materials is generalized to particulate composite materials and an equation of damage (porosity) balance in the composite components at an arbitrary time is formulated.
Abstract: The theory of long-term damage of homogeneous materials is generalized to particulate composite materials. The damage of the composite components is modeled by randomly dispersed micropores. The damage criterion for a microvolume is characterized by its stress-rupture strength. It is determined by the dependence of the time to brittle failure on the difference between the equivalent stress and its limit, which is the tensile strength, according to the Huber–Mises criterion, and assumed to be a random function of coordinates. An equation of damage (porosity) balance in the composite components at an arbitrary time is formulated. Algorithms of calculating the time dependence of microdamage and macrostresses or macrostrains are developed and relevant curves are plotted in the case of unlimited microdurability
TL;DR: In this article, a sliding mode controller for a 2DOF Planar Pneumatic Manipulator actuated by pleated pneumatic artificial muscle actuators is presented, and experimental results obtained by implementing the controller are discussed.
Abstract: This paper presents a sliding mode controller for a “Soft” 2-DOF Planar Pneumatic Manipulator actuated by pleated pneumatic artificial muscle actuators Since actuator dynamics is not negligible, an approximate model for pressure dynamics was taken into account, which made it necessary to perform full input-output feedback linearization in order to design a sliding mode controller The design of the controller is presented in detail, and experimental results obtained by implementing the controller are discussed
TL;DR: In this paper, the fracture process zone at the tip of a crack at the nonsmooth interface between isotropic elastic media is modeled by lines of discontinuity of the normal displacement at the interface.
Abstract: The paper is concerned with the fracture process zone at the tip of a crack at the nonsmooth interface between isotropic elastic media A plane symmetric problem is formulated The zone is modeled by lines of discontinuity of the normal displacement at the interface The exact solution of the elastic problem is found by the Wiener-Hopf method
TL;DR: In this article, a generalized Kantorovich-Vlasov method is used to solve stationary problems for shallow shells with rectangular planform and arbitrary boundary conditions, and the efficiency of the approach is illustrated by examples.
Abstract: A generalized Kantorovich–Vlasov method is used to solve stationary problems for shallow shells with rectangular planform and arbitrary boundary conditions. The efficiency of the approach is illustrated by examples
TL;DR: In this paper, the domain of parameter values in which an autonomous large-scale system is uniformly asymptotically stable is estimated and the comparison method with a vector Lyapunov function is chosen for analysis.
Abstract: The domain of parameter values in which an autonomous large-scale system is uniformly asymptotically stable is estimated. The comparison method with a vector Lyapunov function is chosen for analysis
TL;DR: In this article, the authors proposed a method to solve problems for interface tunnel defects in a piecewise-homogeneous elastic material that is under generalized plane strain and has no planes of elastic symmetry.
Abstract: This paper proposes a method to solve problems for interface tunnel defects in a piecewise-homogeneous elastic material that is under generalized plane strain and has no planes of elastic symmetry. The method is based on integral relations between the discontinuities and sums of the components of the displacement vector and stress tensor at the interface. Closed-form solutions are obtained for a system of interface tunnel inclusions with mixed contact conditions between the space and the inclusions. The dependences of the indices of singularity of the solutions on orthogonal coordinate transformation are established for different combinations of materials of monoclinic and orthorhombic systems. The effect of the antiplane component on the behavior of the solutions is revealed
TL;DR: In this paper, a relationship between the intensity factors for stress (SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for a purely elastic body with the same shape under a mechanical load is established.
Abstract: The paper addresses a thermoelectroelastic problem for a piezoelectric body with an arbitrarily shaped plane crack in a plane perpendicular to the polarization axis under a symmetric thermal load. A relationship between the intensity factors for stress (SIF) and electric displacement (EDIF) in an infinite piezoceramic body with a crack under a thermal load and the SIF for a purely elastic body with a crack of the same shape under a mechanical load is established. This makes it possible to find the SIF and EDIF for an electroelastic material from the elastic solution without the need to solve specific problems of thermoelasticity. The SIF and EDIF for a piezoceramic body with an elliptic crack and linear distribution of temperature over the crack surface are found as an example
TL;DR: In this article, the authors established a relationship between the solutions for cracks located in the isotropy plane of a transversely isotropic piezoceramic medium and opened (without friction) by rigid inclusions.
Abstract: The paper establishes a relationship between the solutions for cracks located in the isotropy plane of a transversely isotropic piezoceramic medium and opened (without friction) by rigid inclusions and the solutions for cracks in a purely elastic medium. This makes it possible to calculate the stress intensity factor (SIF) for cracks in an electroelastic medium from the SIF for an elastic isotropic material, without the need to solve the electroelastic problem. The use of the approach is exemplified by a penny-shaped crack opened by either a disk-shaped rigid inclusion of constant thickness or a rigid oblate spheroidal inclusion in an electroelastic medium
TL;DR: In this paper, the effect of the mechanical and geometrical parameters of the composite and the distance between fibers and to the free surface on the critical strains was investigated and the piecewise-homogeneous medium model and the rigorous three-dimensional linearized theory of stability of deformable bodies were used.
Abstract: The paper is concerned with loss of stability near the free flat surface of a weakly short-fiber-reinforced composite material under compression along the fibers. Emphasis is on the effect of the mechanical and geometrical parameters of the composite and the distance between fibers and to the free surface on the critical strains. The piecewise-homogeneous medium model and the rigorous three-dimensional linearized theory of stability of deformable bodies are used
TL;DR: In this paper, the forced monoharmonic bending vibrations and dissipative heating of a piezoelectric circular sandwich plate under mechanical and electrical loading were studied. And the authors showed that the natural frequency, amplitude of vibrations, mechanical stresses, and temperature of dissipative heat can be controlled by changing the area and thickness of the actuator.
Abstract: The forced monoharmonic bending vibrations and dissipative heating of a piezoelectric circular sandwich plate under monoharmonic mechanical and electrical loading are studied. The core layer is passive and viscoelastic. The face layers (actuators) are piezoelectric and oppositely polarized over the thickness. The plate is subjected to harmonic pressure and electrical potential. The viscoelastic behavior of the materials is described by complex moduli dependent on the temperature of heating. The coupled nonlinear problem is solved numerically. A numerical analysis demonstrates that the natural frequency, amplitude of vibrations, mechanical stresses, and temperature of dissipative heating can be controlled by changing the area and thickness of the actuator. It is shown that the temperature dependence of the complex moduli do not affect the electric potential applied to the actuator to compensate for the mechanical stress
TL;DR: In this paper, the active damping of nonstationary vibrations of a hinged rectangular plate with distributed piezoelectric actuators is addressed by two methods: (i) the classical method of balancing the fundamental vibration modes by applying the appropriate potential difference to the actuator and (ii) the dynamic programming method that reduces the problem to an algebraic Riccati equation.
Abstract: The paper addresses the active damping of nonstationary vibrations of a hinged rectangular plate with distributed piezoelectric actuators The problem is solved by two methods: (i) the classical method of balancing the fundamental vibration modes by applying the appropriate potential difference to the actuator and (ii) the dynamic-programming method that reduces the problem to an algebraic Riccati equation The results produced by both approaches are presented and compared
TL;DR: In this paper, the authors dealt with the coupled problem of flexural vibrations and dissipative heating of a viscoelastic ring plate with piezoceramic actuators under monoharmonic electromechanical loading.
Abstract: The paper deals with the coupled problem of flexural vibrations and dissipative heating of a viscoelastic ring plate with piezoceramic actuators under monoharmonic electromechanical loading. The temperature dependence of the complex characteristics of passive and piezoactive materials is taken into account. The coupled nonlinear problem of thermoviscoelasticity is solved by an iterative method. At each iteration, orthogonal discretization is used to integrate the equations of elasticity and an explicit finite-difference scheme is used to solve the heat-conduction equation with a nonlinear heat source. The effect of the dissipative heating temperature, boundary conditions, and the thickness and area of the actuator on the active damping of the forced vibrations of the plate under uniform transverse harmonic pressure is examined
TL;DR: In this paper, the problem of predicting nonlinear creep strains and time to ductile rupture of prismatic rods under constant tension is addressed using models that take into account the change in the geometry of the rod during creep, the finiteness of the creep strains, and the effect of the initial and actual elastic strains.
Abstract: The paper is concerned with the problem of predicting nonlinear creep strains and time to ductile rupture of prismatic rods under constant tension. The material of the rod is assumed isotropic, homogeneous, and perfectly plastic. The problem is solved using models that take into account the change in the geometry of the rod during creep, the finiteness of the creep strains, and the effect of the initial and actual elastic strains. The conditions whereby the characteristic dimension of the rod tends to infinity and the accumulated and real strains in the viscous flow are limited are used as a failure criterion. The calculated results are compared with experimental data for a number of steels and alloys to formulate the conditions for the ductile rupture and embrittlement of metallic materials under uniaxial creep
TL;DR: In this paper, a numerical analytic approach based on the spline approximation and discrete orthogonalization is developed for the stress-strain state of a shallow orthotropic shell with rectangular planform and thickness varying in two coordinate directions.
Abstract: The stress-strain state of a shallow orthotropic shell with rectangular planform and thickness varying in two coordinate directions is studied. A refined problem formulation is used. Different boundary conditions are considered. A numerical analytic approach based on the spline approximation and discrete orthogonalization is developed. The stress-strain state of shallow orthotropic shells whose thickness is varied keeping its mass constant is studied
TL;DR: In this paper, the problem of synthesis of a control system for a wheeled robotic vehicle consisting of two links (driving and driven) is analyzed, where the robot is considered to be a controlled system of rigid bodies with nonholonomic constraints and to have two steerable wheels.
Abstract: The problem of synthesis of a control system for a wheeled robotic vehicle consisting of two links (driving and driven) is analyzed. The robot is considered to be a controlled system of rigid bodies with nonholonomic constraints and to have two steerable wheels. Additionally, it is necessary to decide where the second steerable wheel is (on the driving or driven link). In this connection, two models of a compound wheeled robotic vehicle with two steerable wheels are considered. For these models, the problem of synthesis of feedback is solved. They are compared by modeling
TL;DR: In this paper, the authors considered the motion of a heavy homogeneous cylinder as rolling without slipping along an unknown curve and found a functional in the form of the total time of rolling by solving a variational problem.
Abstract: The motion of a heavy homogeneous cylinder is considered as rolling without slipping along an unknown curve. A functional in the form of the total time of rolling is found and minimized by solving a variational problem. The algebraic equation of the quickest-descent directrix is derived in parametric form
TL;DR: In this article, the results from studies on the resonant electromechanical vibrations of piezoceramic thin-walled shells of revolution, their fragments, and segmented cylinders are analyzed, systematized and generalized.
Abstract: Scientific results from studies on the resonant electromechanical vibrations of piezoceramic thin-walled shells of revolution, their fragments, and segmented cylinders are analyzed, systematized, and generalized. Considerable attention is focused on experimental studies of resonant vibrations. It is shown that the modes in which deformation occurs inphase throughout the volume are of the highest intensity in all piezoceramic shell structures