Showing papers in "International Applied Mechanics in 1995"
TL;DR: In this article, an axisymmetric storage tank partially field with a viscous fluid is examined, where the tank-fluid system is initially at rest and the tank then begins to rotate around its longitudinal axis, parallel to the force of gravity, at the angular velocity {omega} = 0, 0, w(t), where t is time.
Abstract: We will examine an axisymmetric storage tank partially field with a viscous fluid. Let the tank-fluid system be initially at rest. The tank then begins to rotate around its longitudinal axis, parallel to the force of gravity, at the angular velocity {omega} = 0, 0, w(t), where t is time. We use S and S{sub o} to denote the pertrubed and unpertrubed free surface of the liquid; {Sigma} is the wetted fluid-tank interface; {tau} and {tau}{sub o} are the regions occupied by the liquid in the pertrubed and unpertrubed states; {rightharpoondown}v{sub o} is the rate of translational motion of the load bearing body; {rightharpoondown}v and {rightharpoondown}u are the absolute and relative (relative to the coordinate system permanently associated with the tank) velocities of particles of the liquid. The system is acted upon by the surface {rightharpoondown}p{sup n} and body {rightharpoondown}F forces. The liquid is assumed to be incompressible, with the rheological relation.
21 citations
21 citations
TL;DR: The use of a given method to obtain a solution with a satisfactorily high degree of accuracy depends to a significant extent on the geometric and mechanical parameters characterizing certain aspects of the problem and the type of boundary conditions as discussed by the authors.
Abstract: The study of the stress-strain state of plates and shells subjected to various types of loads with different support conditions entails the formulation of boundary-value problems that generally involve systems of partial differential equations with variable coefficients. The complexity of solving these problems stems not only from the high order of the system and the variability of the coefficients, but also from the need to exactly satisfy prescribed boundary conditions. The use of a given method to obtains a solution with a satisfactorily high degree of accuracy depends to a significant extent on the geometric and mechanical parameters characterizing certain aspects of the problem and the type of boundary conditions. These factors sometimes limit the possibilities of solving problems in the important (in a practical sense) cases in which the stiffness of the shell or plate supports is also variable. In addition, problems of the shell theory entail local and edge effects, which imposes certain stiffness conditions on boundary-value problems related to the phenomenon of instability in the computation. Spline functions have recently come into wide use to solve such problems in the areas of computational mathematics, mathematical physics, and mechanics. The popularity of this approach stems from the advantagesmore » offered by spline functions compared to other methods. Among these advantages: the stability of splines in relation to local perturbations, i.e. the behavior of the spline in the neighborhood of a point has no effect on the behavior of the spline as a whole (which is not the case in a polynomial approximation); good convergence of a spline-interpolation, in contrast to a polynomial interpolation; simplicity and ease of use of algorithms that construct and calculate splines on computers. 65 refs., 5 figs., 7 tabs.« less
20 citations
TL;DR: In this paper, the stress-strain state and pliability of a shell system consisting of two coaxial cylindrical shells, one slotted and one continuous, that are separated by elastic filler is investigated in conditions of frictional contact.
Abstract: In [8], a model was proposed for investigating the frictional contact accompanying the compression of a deformable filler in an elastic cylindrical shell The elastic equilibrium of coaxial continuous cylindrical shells and a deformable filler was considered in [5], taking account of the friction at the contact surfaces In the present work, the stress-strain state and pliability of a shell system consisting of two coaxial cylindrical shells, one slotted and one continuous, that are separated by elastic filler is investigated in conditions of frictional contact The model developed here serves as the basis for calculating the slotted elastic elements of drill shock absorbers
19 citations
18 citations
TL;DR: A survey of edge effects investigated by the rigorous approach can be found in this article, where edge effects are interpreted as stressed states created in a composite as a result of zones in which the stresses exhibit a rapidly changing behavior in comparison with the slow variation of the stresses outside such zones.
Abstract: In the present article we survey papers on edge effects investigated by the rigorous approach We interpret edge effects as stressed states created in a composite as a result of zones in which the stresses exhibit a rapidly changing behavior in comparison with the slow variation of the stresses outside such zones Here the range of the edge effect is defined as the distance from the point of its inception to the boundary of the edge zone in a given direction The transition of the stresses to the slowly varying state is determined within prescribed error limits The size and configuration of the edge zone depends on the tolerated error Clearly, the main difficulty associated with the rigorous approach is finding solutions of the elasticity problems The finite-difference approach is suggested for the approximate solution of these problems In light of the comparative time consumption of the finite-difference approach, it is best directed at certain classes of problems rather than at particular individual problems Not too many papers on the investigation of edge effects by the rigorous approach have been published to date Below, following in their footsteps, we formulate edge effect problems in composites, determine classes of problems, andmore » investigate edge effects in composite materials and structural elements using them in Cartesian (planar and three-dimensional problems) and cylindrical (axisymmetric problems) coordinate frames We note that the division of approaches to the study of edge effects into qualitative (nonrigorous) and quantitative (rigorous) reflects the authors own point of view Of course, other schemes of classification of the approaches to the investigation of the regions of rapidly varying states in composites are possible« less
18 citations
14 citations
11 citations
TL;DR: In this paper, the second part of a survey of dynamic problems of fracture mechanics is presented, where questions related to the solution of dynamic problem of the theory of elasticity for cracked bodies in which the crack edges can come into contact with one another during deformation.
Abstract: This article - the second part of a survey of dynamic problems of fracture mechanics - looks at questions related to the solution of dynamic problems of the theory of elasticity for cracked bodies in which the crack edges can come into contact with one another during deformation.
11 citations
TL;DR: The superposition method, consisting of representing the general solution in the form of a sum of solution of the corresponding singly connected regions, is widely used to construct analytic solutions of boundary value problems of elasticity theory for multiply connected regions bounded by canonical surfaces as discussed by the authors.
Abstract: The superposition method, consisting of representing the general solution in the form of a sum of solution of the corresponding singly connected regions, is widely used to construct analytic solutions of boundary value problems of elasticity theory for multiply connected regions bounded by canonical surfaces. A major aspect in applying this method is the representation of the unknown solution, while satisfying boundary conditions in different coordinate bases, based on reexpanding the partial solutions of the Lame equation, as related to some coordinate systems, in partial solutions of other coordinate systems. These re-expansion equations, called addition theorems, make it possible to reduce the original boundary value problem to an infinite system of linear algebraic equations. Addition theorems for partial Lame solutions in a spherical basis were obtained, while only partial results for coordinate systems with a common axis of revolution are known for solutions in spheroidal coordinates.
11 citations
TL;DR: In this article, an analytical model of the loading of a specimen with a fatigue crack was constructed and instruments were designed to detect a signal proportional to the change in the compliance (stiffness) of the test specimen.
Abstract: We constructed an analytical model of the loading of a specimen with a fatigue crack. We also designed instruments to detect a signal proportional to the change in the compliance (stiffness) of the test specimen. An instrument system was also developed to record the kinetics of cracks during long fatigue tests. Examination of the system in preliminary tests showed it to be highly reliable, providing stable readings of the parameters being recorded. A method was devised for experimentally studying the kinetics of fatigue fracture of specimens of alloy EP718ID and a cycle of tests was conducted. It was shown that life of the specimen after the formation of a fatigue crack depends on the level of the cyclic stresses and stress concentration.
TL;DR: In this paper, the authors used a cylindrical coordinate system to study the stress state of laminated shells of revolution made of inelastically deforming isotropic materials and elastic materials with linear orthotropy.
Abstract: In this investigation, we will use a cylindrical coordinate system to study the stress state of laminated shells of revolution made of inelastically deforming isotropic materials and elastic materials with linear orthotropy. One of the principal directions of anisotropy coincides with the axis of revolution of the body. The shells will be subjected to nonaxisymmetric loading by body {bar K} (K{sub Z}, K{sub r}, K{sub {var_phi}}) and surface {bar t}{sub n} (t{sub nz}, t{sub nr}, t{sub n{var_phi}}) forces and heating. The level of loading is such that the rheological properties of the materials of the layers are not a factor, although their thermomechanical characteristics depend on temperature. In addition, the loading and heating of the body occur in such a way that simple (or close to simple) deformation processes take place in its isotropic elements. These processes are accompanied by inelastic strains and the formation of unloading regions in which plastic strains having the sign opposite the initial strains develop. It is assumed that the layers of the body are secured to one another without interference and that conditions corresponding to ideal contact prevail at their interfaces.
TL;DR: Most theoretical investigations of the stress state of shells with stress concentrators of various types, taking account of both physical and geometric nonlinearity, have focused on axisymmetric problems as mentioned in this paper, with the exception of [1,2], where some numerical results for two-dimensional problems were obtained on the basis of the theory of flexible shells and deformational plasticity theory.
Abstract: Most theoretical investigations of the stress state of shells with stress concentrators of various types, taking account of both physical and geometric nonlinearity, have focused on axisymmetric problems [4], with the exception of [1,2], where some numerical results for two-dimensional problems were obtained on the basis of the theory of flexible shells and deformational plasticity theory.
TL;DR: In this article, a mathematical formulation of the problem of optimal (in terms of speed) control of the heating of thermosensitive canonical bodies (an infinite layer, a hollow cylinder or sphere) is obtained, with constraints on the control and the maximum tangential thermal stress, taking account of the plastic deformation of the material; an algorithm for numerical construction of the solution is developed.
Abstract: Heat treatment of materials often forms part of the production of structural components. One factor significantly increasing the productivity of such processes is minimization of the heating or cooling time of the part at the heat-treatment stage. To ensure the appropriate strength characteristics and functional properties, certain constraints on the stress-strain and thermal state must be taken into account in determining the conditions of accelerated heating (cooling) [2, 8, 11]. Accelerated heating is also an important problem in optimizing the transient operating conditions of thermal and energy equipment subjected to intense heat treatment [5, 10 , 12]. In the present work, on the basis of the inverse thermomechanics problem [3, 4], a mathematical formulation of the problem of optimal (in terms of speed) control of the heating of thermosensitive canonical bodies (an infinite layer, a hollow cylinder or sphere) is obtained, with constraints on the control and the maximum tangential thermal stress, taking account of the plastic deformation of the material; an algorithm for numerical construction of the solution is developed.
TL;DR: In this article, a method of the quasistatic inverse thermoelasticity problem for solving the problem of optimal (response-speed) control of a two-dimensional nonaxisymmetric unsteady thermal regime in a long hollow cylinder with constraints on the thermo-elastic stresses was developed.
Abstract: A method of inverse problem of thermomechanics and thermal conduction has been developed to solve the problem of optimal (response-speed) control of unsteady one-dimensional thermal regimes with constraints on the thermal stresses and control function. In this study we develop a method of the quasistatic inverse thermoelasticity problem for solving the problem of optimal (response-speed) control of a two-dimensional nonaxisymmetric unsteady thermal regime in a long hollow cylinder with constraints on the thermoelastic stresses. A numerical algorithm is given for solving the optimization problem. 8 refs., 3 figs.
TL;DR: In this article, an unbounded transversally isotropic medium containing a parabolic crack in the plane of isotropy is examined, where varying shear forces of the type are applied to the surface of the crack.
Abstract: In this paper we examine an unbounded transversally isotropic medium containing a parabolic crack in the plane of isotropy. Let varying shear forces of the type be applied to the surface of the crack. In solving the problem, we can use the expression of the general solution of the equilibrium equations in displacements in terms of the potential functions.