Axisymmetric Elastic Body Research Articles

Adhesion of an axisymmetric elastic body: Ranges of validity of monomial approximations and a transition model

The Johnson–Kendall–Roberts and the Maugis models have been used to model the adhesion of spherical elastic bodies (represented by paraboloids). Recent work has investigated adhesion of higher-order monomial shapes. These results differ significantly from those of paraboloids. Given that any practical shape will not be “exactly” either a paraboloid or a higher-order monomial, the question arises as to the ranges of validity of these models and what is the requirement, if any, for a transition model. In this investigation the ranges of validity of these models are established by considering a two-term transition model. Furthermore the need for using this transition model is shown to depend not only on the geometry of the bodies but also on material properties.

338 接続部を有する軸対称弾性体の応力波伝播

338 接続部を有する軸対称弾性体の応力波伝播

Some theorems about spectrum and finite element approach for eigenvalue problems for elastic bodies with voids

The paper concerns eigenvalue problems for elastic bodies with voids in contact with massive rigid plane punches. The linear theory of elastic materials with voids according to the Cowin–Nunziato model is used. A variational principle is constructed which has the properties of minimality, similar to the well-known variational principle for problems with pure elastic media. The discreteness of the spectrum and completeness of the eigenfunctions are proved. As a consequence of variational principles, the properties of an increase or a decrease in the natural frequencies, when the mechanical and “porous” boundary conditions and the modulus of elastic solid with voids change, are established. A finite element method is proposed for numerical solution of eigenvalue problems for elastic media with voids. Some effective block algorithms for finite element eigenvalue problems with partial coupling are described. Numerical experiments are presented for determining the first eigenfrequencies of an axisymmetric elastic body with voids.

The axisymmetric contact problem taking into account transient heat production due to sliding friction

The contact problem of the sliding of a solid heat insulator with a plane surface along the boundary of an axisymmetric elastic body is considered, taking into account heat release and the thermal distortion of the boundary of the deformable body due to friction. It is assumed that the shear stresses have no effect on the value of the contact pressures, which enables the problem to be investigated in an axisymmetric formulation. The solution is constructed in two stages: first the form of the thermally distorted surface is determined using known expressions, obtained by Carslaw and Jaeger and also by Barber, and then the contact condition is considered taking into account the elastic displacements and distortion of the form of the surface due to heating, and the integral equation of the problem for determining the unknown contact pressures is derived. The latter equation is solved numerically by approximating the unknown contact pressures by a piecewise-constant function.

A fundamental dislocation solution for an infinite plate with application to related crack problems

A fundamental solution for the three-dimensional stress field induced in an infinite plate by an infinite simal dislocation loop in the interior of the plate is presented here. The solution is derived from the associated Green's function for the same geometry, which is, in turn, found by employing an image method and Muki's formulation [Muki, R. (1960) Asymmetric problems of the theory of elasticity for a semi-infinite solid and a thick plate. In Progress in Solid Mechanics, Vol. 1, (eds I. N. Sneddon and R. Hill) Interscience Publishers, New York, pp. 399–439] for an axi-symmetric elastic body. The solution obtained falls naturally into three parts: the first part is singular, and corresponds to the solution for a full space; the second part is regular, and represents the image of the first part to account for the presence of the upper surface of the plate; the third part is also regular, and gives the correction term to maintain the lower surface of the plate free of tractions. The first two terms are expressed in closed form, whilst the third term is expressed in Hankel integral form. Convergence of the integrals is ensured by an asymptotic analysis.The fundamental dislocation solution found is then employed to analyze the growth of planar cracks in a plate, where the cracks are modelled by a continuous distribution of infinitesimal dislocation loops over the crack faces, i.e., the eigenstrain procedure.

Stress Analysis for Nano-Scale Elastic Materials : Elastic Contact Problems Considering Surface Stresses

It is known that intrinsic mechanical stress exists in a general free surface or interface, because of surface atomic structure changes relative to the bulk. We present an analysis of using the interrelationship between surface stresses, free surface and volume stress deduced in our previous paper. The surface stresses are closely related to the surface energy and surface geometry (mean curvature) of materials. In the present paper, an elastic contact problem in which an axisymmetric elastic body is pressed into an elastic half-region coated with a thin elastic film is analyzed using the three-dimensional theory of elasticity. In this analysis, the relevant dimensionless parameter, called the elastic capillary number, which is a function of surface energy, elastic modulus and the film thickness, is introduced. It is shown that the elastic modulus of the thin film apparently increases and the bulk stress also increases when the surface stresses are taken into account.

Stress Analysis for Nano-Scaled Elastic Materials. (Elastic Contact Problems Considering Surface Stresses).

It is known that intrinsic mechanical stresses exist in a general free surface or interface, because of surface atomic structure changes relative to the bulk. This paper presents an analysis using the interrelationships between surface stresses, free surface and volume stress deduced in the previous paper. The surface stresses have a close relationship with surface energy and surface geometry (mean curvature) of materials. In the present paper, an elastic contact problem which pressed an axisymmetric elastic body into an elastic half region coated with a thin elastic film is analyzed by using the three-dimensional theory of elasticity. In this analysis, the relevant dimensionless parameter, called the elastic capillary number, which is a function of surface energy, elastic modulus and the film thickness, is introduced. It is shown that the modulus for the thin film apparently increases and the bulk stress also increases by taking into account the surface stresses.

A method of identifying residual stresses in an axisymmetric elastic body by inverse analysis using the boundary element method.

Residual stresses caused by various thermal histories in a structural member occasionally affect the strength of the structure. Therefore, accurate estimation of the residual stresses is practically very important. In the present paper, inverse analysis based on the boundary element method (BEM) was formulated and applied to identifying residual stresses in an axisymmetric elastic body. Cylindrical pipes with various dimensions were taken for example, and location of the residual stress source, which was approximately replaced by appropriate body forces, was numerically searched. It was found that the evaluation parameter R1, the sum of axial directional body forces, is one of most useful indices for the location search of acting body force in the inverse analysis.

An analytical model of the stress-strain state of an axisymmetric elastic body under conditions of a two-dimensional temperature field

We have derived an analytical solution for the thermoelasticity problem involving the stress-strain state of an axisymmetric body subjected to the action of a two-dimensional temperature field.

On “finite element analysis of Axisymmetric elastic body problems”

On “finite element analysis of Axisymmetric elastic body problems”

Finite element analysis of axisymmetric elastic body problems

Linear form functions are commonly used in a long time for a toroidal volume element swept by a triangle revolved about the symmetrical axis for general axisymmetrical stress problems. It is difficult to obtain the rigidity matrix by exact integration, and instead, the method of approximate integration is used. As the locations of element close to the symmetrical axis, the accuracy of this approximation deteriorates very rapidly. The exact integration have been suggested by various authors for the calculation of rigidity matrix. However, it is shown in this paper that these exact integrations can only be used for those axisymmetric bodies with central hole. For solid axisymmetric body, it can be proved that the calculation fails due to the divergent property of rigidity matrix integration. In this paper a new form function is suggested. In this new form function, the radial displacementu vanishes as radial coordinatesr approach to zero. The calculated rigidity matrix is convergent everywhere, including these triangular toroidal element closed to the symmetrical axis. This kind of element is useful for the calculation of axisymmetric elastic solid body problems.